Real Conditionals

REAL CONDITIONALS

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Real Conditionals WILLIAM G. LYCAN

CLARENDON PRESS • OXFORD

OXFORD UNIVERSITY PRESS

Great Clarendon Street, Oxford 0x2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © William G. Lycan 2001 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2001 First published in paperback 2005 All rights reserved. No part of this publication maybe reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted bylaw, or under terms agreed with the appropriate reprographics rights organizations. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Lycan, William G. Real conditionals/William G. Lycan p.cm. Includes bibliographical references and index. 1. Grammar, Comparative and general-Conditionals. 2. Semantics. I. Title P292.5 .L93 2001

415-dc21

2001021219

Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by Biddies Ltd., King's Lynn, Norfolk ISBN 0-19-924207-0 ISBN 0-19-928551-9 (Pbk.)

978-0-19-924207-8 978-0-19-928551-8 (Pbk.)

1 3 5 7 9 108 6 4 2

For Mary Lycan. Thirty-one years; Christ.

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Preface I first began thinking about conditional sentences in 1969, when I was asked to give a guest lecture on the subject in the Music Department at the University of Chicago. (Long story; e-mail me and I'll tell it to you.) But I had no ideas of my own on the topic until I came across a linguistics article, Michael Geis's '//and Unless (1973), which introduced me to some grammatical facts about conditionals that were and still are unnoticed by most philosophers. This book was directly inspired by, indeed owes its entire existence to, that article. Later in the 1970s, I had the privilege of teaching two interdepartmental graduate seminars jointly with Geis at the Ohio State University, and learnt a good deal more from him. Much later, we wrote the joint article that appears here as an appendix. I had hoped to produce a truly comprehensive book on the linguistic semantics of conditionals. The last vestiges of that hope drained away sometime during 1999; the area is just too large. Here are four important topics which I have left mostly unaddressed: (1) Deeper issues in the syntax of conditionals, particularly as conditionals interact with negation and with modifiers like 'only' and 'even'. (2) The relations between conditionals and anaphora. (I lack a satisfactory background theory of anaphora. I think I also lack prospects for one.) (3) The relation between conditionals and probability. I do say something about this in Chapter 4, including the reason why I think probability theory has played too large a role in natural-language semantics. (4) The 'conditional assertion' view of conditional sentences (Belnap, 1970), which is enjoying an upsurge as this book goes to press. I have never been attracted to that view, but Dorothy Edgington (1995) has resisted some of the standard objections that I would have thought fatal to it, and Stephen Barker (1995) has devised a subtle new version of the theory. (See also Woods, 1997, Milne, 1997; and Grandy and DeRose, 1999.) I hope to address this literature in a subsequent paper.

Acknowledgements Chapter 2 is based on 'A Syntactically Motivated Theory of Conditionals', in P. French, T. E. Uehling, and H. Wettstein (eds.), Midwest Studies in Philosophy, ix. Causation and Causal Theories (Minneapolis: University of Minnesota Press, 1984). Chapter 3 is based on 'MPP, RIP', in J. Tomberlin (ed.), Philosophical Perspectives, vii. Language and Logic (Atascadero, Calif.: Ridgeview Publishing, 1993). Chapters is reprinted almost verbatim from 'Even and Even If, Linguistics and Philosophy 14: 115-50, with kind permission from Kluwer Academic Publishers; some of Chapter 6 is drawn from that article as well. The Appendix appeared in Philosophical Topics 21 (1993), 35-56. Chapters 3 and 5 were finished while I was a Fellow of the Center for Philosophy of Science, University of Pittsburgh, 1989. The book wa completed in draft during my tenure as a Fellow of the National Humanities Center, in 1998-9. I thank both Centers, and especially the wonderful staff of the Humanities Center for their lavish support. For additional funding I am indebted to the National Endowment for the Humanities (#RA-20169-95). Warm thanks to John Barker, Jonathan Bennett, Paul Berckmans, Max Cresswell, Wayne Davis, Eva Delgado, Vic Dudman, Chris Gauker, Allan Gibbard, Bill Harper, Jim Higginbotham, Larry Horn, Lloyd Humberstone, Frank Jackson, Paul Kay, Ron Laymon, Davi Lewis, John Martin, the late Jim McCawley, Graham Priest, Greg Restall, Jerry Seligman, Walter Sinnott-Armstrong, Bob Stalnaker, the late Richard Sylvan, Rich Thomason, and Michael Tooley, for comments and conversations over the years. And especially to Stephen Barker, JC Beall, Michael McDermott, David Sanford, and an anonymous linguist referee, each of whom has generously given me extensive and helpful comments on the whole typescript, which I believe have made this book much better than it otherwise would have been. But above all, again, to Mike Geis.

Contents 1. The Syntax of Conditional Sentences

1

2. Truth Conditions: The Event Theory

16

3. Truth Conditions: Reality and Modus Ponens

48

4. In Defense of Truth Value

73

5. A Beautiful But False Theory of'Even If'

93

6. An Unbeautiful But Less Easily Refutable Theory of 'Even If

115

7. The 'Indicative'/'Subjunctive' Distinction

139

8. The Riverboat Puzzle

167

Appendix: 'Nonconditional Conditionals' (with Michael L. Geis)

184

Revisionary Postscript on Non-Conditional Conditionals

206

Bibliography

211

Index

221

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1 The Syntax of Conditional Sentences Without exception, logicians have given us to understand that 'if... then' is a syntactically unstructured binary sentence operator, and that antecedent and consequent are syntactically co-ordinate. The campaign began with D and —», but it did not stop there. Though dissatisfaction with the truth-functional representation led to the intensional —3, >, and D—>, these connectives are still syntactically unstructured binary sentence operators. And every logician awards any such operator its own distinctive base clause in the recursive truth definition for its containing language. In these ways, 'if...then' is assumed to resemble 'and' (&) and 'or' (v), however more complex its truth rule may be. Presumed equivalents of'If A, then B', such as 'B if A and 'A only if B', are treated just the same. I think this is all very wrong. I nearly said 'demonstrably wrong', but, not myself being a syntactician, I cannot do the demonstrating beyond doubt. In this chapter I shall just marshal some syntactic considerations, those most accessible to non-linguists, that count heavily against the idea that 'if.. .then' is an unstructured operator and that strongly suggest an alternative syntactic analysis. The alternative analysis will guide the rest of this book.

Conditional Sentences What counts as a conditional sentence? The paradigm is a sentence whose main connective is 'if, such as: (1) a. If Sharon leaves, I will leave. b. I will leave if Sharon does. c. If Sharon leaves, then I will leave. (2) a. That vase will break if you drop it. b. If you drop that vase, it will break.

2

The Syntax of Conditional Sentences (3) If Laura missed the meeting yesterday, there will be big trouble tomorrow. (4) If Hitler had known how good the Russian tanks were, he would never have invaded. (5) The vase would not have broken if you had dropped it on the sofa instead of right smack on the stone floor.

Understandably, philosophers have focused their attention on such 'if'-sentences, largely ignoring other conditional expressions such as 'unless', and the application to 'if of such modifiers as 'only' and 'even'. Even more understandably, the philosophers have ignored more complex adverbial constructions that are conditional in meaning and are, as we shall see, syntactically very similar to 'if: (6) a. In case Sharon leaves, I will leave. b. I will leave in the event that Sharon does. c. I will leave only in the event that Sharon does. d. I would leave only in the event that Sharon did. e. I will leave on condition that Sharon does. / I would leave only on condition that Sharon did. g. I will leave in any circumstance in which Sharon does. The two main claims of this book are that conditionals containing 'if share the semantic properties of sentences such as those in (6), and that once those similarities are brought out, a considerably wider field of data can be explained than has been by previous theories of conditionals, and some persistent errors corrected. I used the phrase 'conditional in meaning', but it is not entirely innocent. It has been applied (e.g., by Fillmore, 1987) to a variety of constructions. Some of these, and more, are illustrated in (7). (7) a. Had Hitler known the strength of the Russian tanks, he would not have invaded. b. Hitler would have invaded England but for the Luftwaffe's losing the Battle of Britain. c. Assuming it's still showing, we'll go see Saving Private Ryan. d. Leave or I'll call security. e. Are you leaving through the door or through the wall? / Insult my sister again and you'll never be invited back see what happens

The Syntax of Conditional Sentences

3

g. With your help, we can get this done by 5.00. h. For you to do that would be very generous. i. We go in there, we don't come out. [General George A. Custer's scout Boyer, a few minutes before Little Big Horn1] j. Go in there; you won't come out. k. Want to die in a searing agony of boredom? Listen to the Pachelbel Canon more than once. I doubt that any of the sentences in (7) is strictly a conditional sentence, that is, has the very same truth condition as the corresponding 'if... then' sentence. Some sentences, such as many disjunctions, are logically equivalent to conditionals even though they are not themselves conditionals.2 Even less strictly, other sentences may be conditional in their usual purport, by principles of speech-act theory or by conversational implicature perhaps, but are not even logically equivalent to conditionals. I will not try to adjudicate any of the examples in (7), but only remark that syntactically they are very diverse. The strict parallels we shall observe holding between 'if... then' conditionals and the sentences in (6) do not hold between conditionals and any of the sentences in (7). I know of no crisply reliable syntactic mark of conditionality per se.3 I will assume that the presence of 'if (or 'unless') as a clause's main operator, when the consequent has the appropriate aspect,4 suffices for that clause's being conditional. (I speak of clauses rather than sentences because obviously a sentence may contain a conditional clause without itself being a conditional sentence: 'I hate that and if you do it again I'll tell Edgar what you said about his moustache'; 1

Slightly paraphrased by Fraser (1982: 405, 453). There are several sharp syntactic differences between disjunctions and the conditionals to which they are equivalent. For example, they only dubiously admit backward pronominalization while their corresponding conditionals permit it freely: 'If you don't pay her, Melissa will sue your socks off'/ ??'Pay her or Melissa will sue your socks off. (Without further context, 'her' is hard to hear as referring to Melissa.) And as Arnold Zwicky has pointed out to me, disjunctions admit imperative left disjuncts while the corresponding conditionals' antecedents cannot be imperative: 'Be here by 7.00 a.m. or it's your job'/ *'If (you) don't be here by 7.00 a.m., it's your job'. ('If you aren't here..." would not be an imperative clause.) 'Don't start singing again or I'll gnaw my foot off'/ *'If: start singing again!, I'll gnaw my foot off.' 3 Comrie (1986) looks for syntactic marks of conditional antecedents and consequents, but finds none. Taylor (1997) concurs. 4 This qualification is needed to rule out 'if'-sentences that are really universal generalizations, such as 'If I hear someone playing the Pachelbel Canon more than once, I take the safety off my Browning.' 2

4

The Syntax of Conditional Sentences

'Tony believes that if he eats two more broccoli florets his left elbow will explode'.) And I will also count a clause as conditional if it is synonymous with—not merely logically equivalent to—one that does so contain 'if (or 'unless'). By the latter criterion, I would and will argue that the sentences in (6) are conditional sentences. In this book I shall use the symbol '>' as a superficial and theoryneutral generic representation of conditional form in English. This must not be taken to imply that I believe there is any binary conditional connective expressed by any English morpheme; I do not. But it also does not imply that there is not one; officially it leaves open the possibility, for example, that English conditionals are just material conditionals, reflections of the horseshoe. Against the Unstructured Conjunction Theory Grammatically speaking, a syntactically unstructured binary sentence operator is a conjunction, either a co-ordinating conjunction or a subordinating conjunction. 'And' and 'or' are co-ordinating conjunctions. Accordingly, they exhibit the syntactic properties that distinguish co-ordinating conjunctions from subordinating conjunctions and from operators of other types (Haiman, 1986). Co-ordinating conjunctions permit a process called Conjunction Reduction: (8a) can be shortened to (8b), and (9a) to (9b). (8) a. b. (9) a. b.

I closed the car windows and I turned up the radio. I closed the car windows and turned up the radio. I will get through Sein und Zeit or I will die trying. I will get through Sein und Zeit or die trying.

Likewise what is called Gapping: constituents of a right conjunct can be omitted if the left conjunct contains a copy of them. (10) a. I washed the windows and Debra washed the curtains. b. I washed the windows and Debra the curtains. (11) a. (8a) can be shortened to (8b), and (9a) can be shortened to (9b). b. (8a) can be shortened to (8b), and (9a) to (9b). Thirdly, an 'Across-the-Board' principle holds for co-ordinating conjunctions in regard to various properties. For example, mood: if one clause is interrogative/imperative, so must the other be.

The Syntax of Conditional Sentences

5

(12) a. Did you close the car windows and did you turn up the radio? b. *Did you close the car windows and you turned up the radio. (13) a. Will you get through Sein und Zeit or will you die trying? b. *Will you get through Sein und Zeit or you will die trying. (14) a. Go to the store and pick up some Dos Equis. b. *You are going to the store and pick up some Dos Equis. (15) a. Get through Sein und Zeit or get off the pot. b. *Get through Sein und Zeit or you will get off the pot. (Grammatical in itself but only with a different, wholly declarative meaning.5) 'If has none of these three features. Not Conjunction Reduction: (16) *I closed the car windows if turned up the radio. Not Gapping: (17) *I washed the windows if Debra the curtains. Not 'Across-the-Board'; (18) and (19) are fine. (18) If you're going to the store, are you going to pick up some Dos Equis? (19) If you're going to the store, pick up some Dos Equis.5 Finally, there is a phenomenon called Adverb Preposing that characterizes adverbial subordinate clauses but never co-ordinating conjunctions.7 An adverbial phrase that occurs as a constituent of a 5

Another property subject to 'Across the Board" is the permissibility of extracting a constituent to form a relative clause; the constituent must be extracted from each conjunct if from either: 'Sarah e-mailed Mike and Jerry called him" can be used to form 'The man whom Sarah e-mailed and Jerry called never replied to either of them", but not *'The man whom Sarah e-mailed and Jerry called him never replied..." or *'The man Sarah e-mailed Mike and whom Jerry called never replied...'. 6 There are further arguments. Co-ordinating conjunctions permit Right Node Raising, as in 'I shot the sheriff and Louise buried him'/'I shot and Louise buried the sheriff. Also, backward pronominalization and quantifier binding are possible for 'if (and for subordinating conjunctions) but not for co-ordinating conjunctions: 'If/when she arrives tomorrow, I'll ask Louise where she buried the deputy", but *'She will arrive tomorrow and I'll ask Louise where she buried the deputy". Also, there is evidence that conditional clauses are constituents of predicates, which co-ordinate clauses are not. 7 Lakoff (1972) argued that there is a specific syntactic transformation appropriately called 'Adverb Preposing'. The existence of such a transformation considered as a real

6

The Syntax of Conditional Sentences

complex verb phrase can also appear at the front of their containing clause: (20) a. Aunt Sarah got heroically drunk last Sunday. b. Last Sunday, Aunt Sarah got heroically drunk. (21) a. She took several codeine pills before she went to bed. b. Before she went to bed, she took several codeine pills. (22) a. She slept heavily until Tuesday afternoon. b. Until Tuesday afternoon, she slept heavily. Co-ordinating conjunctions never afford such equivalences. (23) *And I turned up the radio, I closed the car windows. (24) *Or I will die trying, I will get through Sein und Zeit. Granted that 'if is not grammatically a co-ordinating conjunction, it might still be a subordinating conjunction. Indeed, that is the traditional grammarians' view of 'if (Sweet, 1891, Onions, 1932). While a co-ordinating conjunction occurs in roughly the structure: S

S

Conj

S

as in S

S

Conj

S

I closed the car windows

and

I turned up the radio

a subordinating conjunction (though also a binary connective) connects a clause with an inferior constituent such as a verb phrase: syntactic process is highly disputable (Geis, 1986a, 1986b), but I do not rely on it here. I am merely calling attention to synonym pairs of the sort I shall now illustrate.

The Syntax of Conditional Sentences S

VP

NP

VP

Coni

S

as in S

NP

I

VP

VP

Coni

S

washed the windows

because

Debra washed the curtains

If we suppose that 'if is an unstructured subordinating conjunction, we avoid the foregoing four main objections to the Co-ordinating-Conjunction hypothesis. But the new supposition too runs into counterevidence. First, notice that 'if can be modified by 'only', 'even', and (in some dialects) 'except': (25) a. You will pass that course only if you wash the professor's car every Sunday. b. I will stay till midnight even if they make us put on silly hats. c. I will stay except if Bruno does. But if'if' is an unstructured subordinate conjunction, so, presumably, is its fellow conditional connective 'unless'. Yet 'unless' cannot be modified by 'only', 'even', and 'except'. We do not get (26) a. *You will fail that course only unless you wash the professor's car every Sunday. b. *I will stay till midnight even unless they make us put on silly hats. c. *I will stay except unless Bruno does. (This is also yet a further mark that distinguishes 'if from 'and' and 'or'; there are no *'I closed the car windows only and I turned up the radio', etc.)

8

The Syntax of Conditional Sentences

More importantly, 'if pronominalizes in a way that unstructured subordinating conjunctions do not. Sentence (la) ('If Sharon leaves, I will leave') is equivalent to (Ic): (1) c. If Sharon leaves, then I will leave.8 (Though Davis (1983) points out that not every sentence of the form 'If P, Q' is equivalent to the corresponding 'If P, then Q'. I shall take this up in the next chapter.) And 'then' in (Ic) is not flatus vocis or pleonastic, but is a resumptive pronoun like those in (27b) and (28 b): (27) a. When Sharon leaves, I will leave. b. When Sharon leaves, then I will leave. (28) a. Where Sharon lives, I will live. b. Where Sharon lives, there I will live. And (though they are redundant) we get (29) a. If Sharon leaves, I will leave then too. ('Then' here need not be temporal; the speaker need not mean that s/he will leave at the same time Sharon does.) b. When Sharon leaves, I will leave then too. c. Where Sharon lives, I will live there too. There is no parallel with an unstructured subordinating conjunction like 'because', 'after', 'whereas', or 'although': (30) a. *Because Sharon left, I will leave then too. b. *After Sharon left, I left then too. c. *Whereas Sharon left, I will leave then too. d. *Although Sharon left, I stayed then too. The same evidence points towards an alternative thesis: that conditional clauses are adverbial. Indeed, it positively confirms that thesis. 'When' and 'where' are sentence operators that yield adverbial clauses, and there is evidence that they remain constituents of those clauses;9 the same is true of 'if. Thus: 8

It is not only in English that a pronoun such as 'then' can begin a conditional consequent. Comrie (1986) reports that all cases known to him of overt marking in consequent clauses involve particles of pronominal origin. 9 Further pronominalization data show that otherwise temporal prepositions 'before', 'after', 'since', and 'until' are constituents of main clauses rather than of the clauses they introduce (Geis, 1985).

9

The Syntax of Conditional Sentences

S

NP

VP

Aux

Sharon

will

VP

VP

AdvP

V

Adv

leave

when

S

NP

NP

VP

N

V

you

leave

VP

Aux

Sharon

S

will

VP

VP

AdvP

V

Adv

leave

if

S

NP

VP

N

V

you

leave

10

The Syntax of Conditional Sentences

This does not yet show that 'if is not an unstructured subordinating conjunction. Indeed, the tree diagrams portray 'when' and 'if as unstructured subordinating conjunctions, though of a distinctive kind, not the same as 'because' et al. Additional argument is needed.

The Relative Clause Analysis The kind of resumptive pronominalization illustrated by (27b) and (28b) indicates two further things: that adverbial 'when'- and 'where'clauses are a type of relative clause (Geis, 1970a, 1985; Larson, 1983), and that tacit reference is made to a domain of entities or at least abstract items of a sort. To begin, notice that (27b) and (28b) are respectively paraphrased by ( 2 7 f ) and (28p): (27) t. I will leave at the time

that t which J

(28) Jf. I will live at the place

that tt which JJ

Sharon leaves. Sharon lives.

There is evidence that the relation is not merely that of informal paraphrase. First, the pronouns in (27b) and (28b) seem referential, and in particular they seem to refer back to tacitly mentioned times andplaces. They seem logically equivalent to, respectively, (27t+) and (28p+): (27) t+. When Sharon leaves, I will leave at that same time. (28) p+. Where Sharon lives, I will live in that same place. 'Times' and 'places' are considered as individual items. Second, (27t+) and (28p+) themselves seem to show that the 'when'- and 'where'-clauses make tacit reference to times and places; else what are the referents of 'that same time' and 'that same place'? Thus, 'When Sharon leaves' and 'Where Sharon lives' seem to abbreviate (or at least to be semantically equivalent to) 'At the time at which Sharon leaves' and 'At the place at which Sharon lives'. For that matter, (27a) and (28a) themselves seem equivalent to (27t+) and (28p+). So the explicit occurrence of'then'/'there' is not needed to make the argument about 'when'- and 'where'-clauses generally.

The Syntax of Conditional Sentences

11

'If behaves in a parallel fashion. We saw that (la) is equivalent to (1) c. If Sharon leaves, then I will leave. Here too, Geis (1970a, 1973, 1985) argues, the resumptive pronominalization indicates both that adverbial 'if'-clauses are relative clauses, and that tacit reference is made to a domain of abstract items—not times or places, but 'events' or circumstances. (Ic) is paraphrased by (1 e): event that Sharon (1) e . I will leave in t circumstance in which leaves. And (Ic) seems logically equivalent to (le+): (le+) If

Sharon leaves, event, circumstance.

I

will

leave

in

that

same

As before, (le+) itself seems to show that the 'if'-clause makes tacit reference to events or circumstances (or what is the referent of'that same event/circumstance'?).10 Ditto (le+t): (le+f)

a. If Sharon leaves, I will leave in that

event circumstance

too. b. Peter will leave if Sharon leaves, and I will leave in that event too. circumstance (I shall say a great deal more about the ontology of'events' in Chapter 2.) Thus, 'If Sharon leaves' seems to be semantically equivalent to 'In the event that/in which Sharon leaves'. And as before, (1) itself seems equivalent to (le+).u 10 The demonstratives in anaphoric phrases like 'in that event" and 'in that place" do not make their antecedents definite. 'I will live where Sharon lives' means first and foremost, 'I will live in any place/whatever place Sharon lives'. And as we shall see in Chapter 2, 'I will go if Sharon does and Bruno will go in that event too' means first and foremost, 'I will go in any event in which Sharon does and Bruno will go in any such event too (whichever one it turns out to be)'. 11 I know of just two syntactic/semantic differences between 'if adverbials and time and place adverbials. The first is pointed out by Rivero (1972): 'If'-clauses cleft in a way that 'when'- and 'where'-clauses do not. From 'If Juan comes, we'll leave' we get 'If it is that Juan comes, we'll leave' (though this is perhaps better in Spanish, 'Si es que Juan viene, nos iremos'). But there are no *'When it is that Juan comes...' or *'Where it is that Juan

12

The Syntax of Conditional Sentences 'Unless'

Traditional grammarians (e.g. Sweet, 1891; Onions, 1932) have called 'unless' the 'negative counterpart' of 'if, maintaining that 'unless' is semantically equivalent to 'if not'. Contemporary logic textbooks have followed them in this; I believe most logic students are told to translate sentences containing 'unless' by first rewriting 'unless' as 'if not'. But syntactically this equation is untenable. First, as we have already seen, 'unless' cannot be modified by 'only', 'even', or 'except'. This would not be so if 'unless' were syntactically equivalent to 'if not', which is so modifiable. Second, negative polarity items (expressions which can occur grammatically only if the clause or phrase in which they do so is derived from a structure that is semantically negative) cannot occur in 'unless'-clauses: (31) a. If you don't care a whit for Dudley, you shouldn't marry him. b. *You shouldn't marry Dudley unless you care a whit for him. (32) a. If you don't see any large mice, then the cat has come back. b. *The cat has come back unless you see any large mice. (33) a. If Lavinia doesn't even eat some sauerkraut, she'll get scurvy. b. *Lavinia will get scurvy unless she even eats some sauerkraut. Third, some subjunctive conditionals will not tolerate substitution of 'unless' for 'if not': (34) a. If Dudley weren't so innocent he would see what Lavinia has in store for him. b. *Dudley would see what Lavinia has in store for him unless he were so innocent. Fourth, 'either' and 'too' distinguish 'unless' from 'if not'. We generally get 'either' when the two clauses that make up a compound comes...'. The second difference, noted in Geis (1985), is that 'I will leave when you say you'll leave" and 'I will leave where you say you'll leave" are ambiguous, as between my leaving at the time/place specified by your saying and my leaving at the time/place at which you actually did the saying. 'I will leave if you say you'll leave" has only the latter reading. I know of no good explanation for either of these disparities.

The Syntax of Conditional Sentences

13

sentence are both semantically negative, as in 'Dudley isn't too bright and Lavinia isn't smart either'. But this feature does not carry over from 'if not' to 'unless': (35) a. I won't go if you won't go either. b. *I won't go unless you go either. We get 'too' when both clauses are positive, as in 'Dudley is going and Lavinia is going too', but this criterion marks 'unless'-clauses as positive rather than negative: (36) a. I will go unless you go too. b. *I will go if you don't go too. Fifth, there is evidence from the relativization of 'unless'-clauses. For example, (37) I'll leave unless Sharon leaves, in which case of course I won't leave. In (37), 'which' pronominalizes 'Sharon leaves', a positive clause. If 'unless' were equivalent to 'if not', (38) should be equivalent to (37): (38) I'll leave if Sharon does not leave, in which case of course I won't leave. But (38), far from being equivalent to (37), is anomalous; (38) sounds nearly self-contradictory, being intuitively equivalent to (39). (The data are the same when 'event' or 'circumstance' is substituted for 'case'.) (39) I'll leave if Sharon does not leave, and of course I won't leave if Sharon does not leave. Sixth, 'unless'-clauses cannot easily occur inside the scope of'and'. (40a) and (40b) are fine, but (40c) is very bad. (40) a. I will leave unless Sharon leaves and Bruno sings 'Melancholy Baby'. b. I will leave if Sharon does not leave and if Bruno does not sing 'Melancholy Baby'/If Sharon does not leave I will leave, and if Bruno does not sing 'Melancholy Baby' I will leave. c. *I will leave unless Sharon leaves and unless Bruno sings 'Melancholy Baby'.

14

The Syntax of Conditional Sentences

I am not sure whether (40c) is ungrammatical, but certainly it is anomalous, belying its alleged equivalence to (40 b). The relativization data suggest a Relative-Clause treatment of unless' that will square with the Relative-Clause theory of 'if. Notice, first, that like the relativization in (37), our other sorts of pronominalization work for 'unless' as well as for 'if. (41) a. I'll leave unless Sharon leaves, and Bruno will not leave event either except in that circumstance b. I'll leave unless Sharon leaves, and Bruno will not leave except in that same

event

ircumstance. J

As before, Geis (1973, 1985) argues that tacit reference is made to 'events' or circumstances. But what distinguishes 'unless' from 'if is an underlying distinctness clause. Geis paraphrased 'If A, B' as 'B in the event that A; he now paraphrases A unless B' as 'A in any event other than that B'. (Thus, traditional logic and grammar are correct in holding that 'unless' expresses an element of negation. But they have mislocated the negation; as we have seen, the element is not in the 'unless'-clause itself, that is, not in the scope of'unless'; rather, it is in the tacit negative quantification of 'unless' over events or circumstances.) This hypothesis explains why (37) is not contradictory as (38) seems to be. (37) says, in effect, that the speaker will leave except in the event that Sharon leaves, in which event of course he will not leave or, in the language of the paraphrase just given, that the speaker will leave in any event other than that Sharon leaves, in which event... (Contrastingly, (38) and (39) say that the speaker will leave in the event that Sharon does not leave, and the speaker will not leave in that event—hence the air of contradiction.) Geis's hypothesis also explains what is wrong with (40c). (40c) would be paraphrased as saying: 'I will leave in any event other than that Sharon leaves, and in any event other than that Bruno sings "Melancholy Baby".' Each conjunct implies the falsity of the other. Turning to modification by 'only' and 'even', Geis (1973,1985) also argued syntactically for the following equivalences. A only if B = A in no other event than that B A even if B = A in any event including that B

The Syntax of Conditional Sentences

15

I believe these too are convincing as paraphrases. Bare appeals to paraphrase not being considered weighty by linguists, Geis also supplied detailed technical argumentation, especially for the negative element underlying 'only if'.12 But rather than sloshing on through it, I shall get on with the semantic theory directly inspired by the facts here marshalled. 12

See also McCawley (1974, 1986).

2

Truth Conditions: The Event Theory In this chapter I shall propose a new semantic theory of conditionals, concentrating on the expressions 'if, 'unless', 'only if, and 'even if, and guided by the syntactic and semantic evidence assembled in Chapter 1. I intend a 'semantic theory of these expressions in the sense of a systematic assignment of truth conditions to sentences containing them. Such an assignment is to do at least three things: (a) account for such sentences' felt implications and other intuitive semantical properties, (b) explain some of the ways in which their truth values depend upon context, and (c) accord with noteworthy aspects of their surface-syntactic behavior as sketched in Chapter 1. I have argued that 'if-clauses along with 'when'- and 'where'clauses are a species of relative-clause construction. This syntactic analysis points directly to the semantics for conditionals that I shall now offer. I shall take my cue from the 'event' or 'circumstance' paraphrases cited in Chapter 1, and devote the rest of this chapter to exploring the resulting semantical advantages. We saw syntactic evidence of distinctness (negated identity) clauses in the underlying syntactic structure of the sentence-form 'P unless Q' (and I argued on those grounds that 'P unless Q' is equivalent neither to the logicians' ~ Q D P nor to any other version of'P if not Q'). And I have made much of the fact (originally noted by Geis, 1973) that there exist English paraphrases of 'if and 'unless', as well as 'only if and 'even if, that overtly allude to and/or quantify over entities or pseudoentities usually called 'events'. My semantic theory will modify those paraphrases slightly, take them seriously, and account for their equivalence to the conditionals in question. It will be shown that the theory is able to explain a number of striking and otherwise puzzling facts about these conditionals. In my dialect some of Geis's paraphrases are grammatically dubious as they stand. For example, Geis would render 'I will go even if you go' as 'I will go in any event including that you go',

Truth Conditions: The Event Theory

17

which I cannot comfortably say. The following modified paraphrases, though ornate, seem grammatically better, are more perspicuous in structure, and are still in keeping with the argumentation of Chapter 1: P if Q = P in any event in which Q. P only if Q = P in no event other than one in which Q. P even if Q = P in any event including any in which Q. P unless Q = P in any event other than one in which Q. Thus, I replace Geis's original apparent references to a unique 'Q'event by universal quantification across a domain of'events in which' Q. (My paraphrases may be understood as being equivalent to Geis's original ones, if Geis's 'the' and 'that' are interpreted non-uniquely, as in 'The philosopher who can get through Sein and Ze/Yhas a stronger head than mine'.) 'Event' here is used in a slightly uncommon way, as being roughly equivalent to 'case' or 'circumstance' or 'situation'.1 Events are not things that happen or occur, rather they obtain or materialize.2 ('Event' is my official term, but I shall use 'circumstance' interchangeably with 'event' when stylistically appropriate.) Ordinary English represents events or circumstances as possible states of affairs, but as local goings on that are much smaller than entire possible worlds or even world-futures or world-slices; we speak as if there are a number of events that will materialize, not just one. (Worlds and worldfutures may be conceived as being large aggregates or heaps of events, or, if one likes, events/circumstances may be formalized as intersections of worlds or sets of worlds.) My hypothesis is that formalizations of our modified paraphrases express the truth conditions of the conditionals under analysis. This supposition would immediately explain why the conditionals and their respective paraphrases are felt to be equivalent or to have the same truth conditions (especially if a conditional and its paraphrase are syntactically related to the same semantic representation, though I stop short of assuming that in this book). This hypothesis has a number of other explanatory advantages, as I shall go on to demonstrate. 1

In her own analysis of conditionals, Kratzer (1986) uses 'event' in much this way. Intuitively they are not unlike Perry and Barwise's 'situations'. There are formal similarities also. See Barwise (1981) and Barwise and Perry (1983). 2

18

Truth Conditions: The Event Theory

Here are preliminary formalizations of the modified paraphrases: PifQ:(e)(In(e,Q) D In(e,P)). P unless Q: (e)((f)(In(f,Q) D f + e) D In(e,P)). P only if Q: (e)((f)(In(f,Q) D f ^ e) D ~In(e,P)). P even if Q: (e)(In(e,P) & (f)(In(f,Q) D In(f,P))). In these formalizations, 'e' and 'f' range over events; 'In' is a sentential operator with an added argument place, 'In(e,Q)' being read as 'In e, Q'. The last three formulas listed are tautologously equivalent to simpler ones. (I believe these equivalences help to explain why authors of logic texts may have uncritically thought that our conditionals were simple truth-functional connectives, though I will not go into that here.) P unless Q= (e)(~In(e,P) D (3f)(In(f,Q) & f = e ) ) = (e)(~In(e,P) D In(e,Q)). Ponly if Q = (e)(In(e,P) D (3f)(In(f,Q) &f = e)) = (e)(In(e,P) D In(e,Q)). P even if Q = (e)(In(e,P) & (In(e,Q) D In(e,P)) = (e)(In(e,P)).

In Search of a Reference-Class Notice that the quantifiers occurring in my proposed logical forms must actually be restricted quantifiers, at least if I am to countenance 'events' that will not in fact materialize. If my quantifiers were to be left unrestricted, my analysans for 'P even if Q' would entail its being true in all possible circumstances that P and hence that it is logically necessary that P, an unacceptable result. Similarly, my analysans for 'P only if Q' would be equivalent to the thesis that its being true that P logically necessitates its being true that Q. But, clearly, a speaker who puts forward a conditional of the sort I am examining is not speaking of all logically possible circumstances or situations, including landings of creatures from Mars, suspension of the Law of Gravity, and the like; most such speakers would take themselves to be talking more 'realistically'. But equally, this cannot mean restricting my 'event' quantifiers to the class of actual events (call this class '@'3). For one thing, condi3

David Lewis (1973) coined '&' as a name of the actual world. For our purposes here, we may simply identify 'the actual world" with the class of actual 'events'.

Truth Conditions: The Event Theory

19

tional antecedents often express possibilities that their utterers know and/or explicitly assume are not actual. For another, utterers typically envisage alternative possibilities, alternative in the sense of being incompatible; thus, among the events in the appropriate referenceclass on an occasion of that sort will be two events that cannot both be actual.4 It remains to specify, then, how an appropriate reference-class is to be determined that contains some non-actual circumstances but not all of the logically possible ones.5 Intuitively, the reference-class appropriate to a given utterance-occasion will contain only those events that the utterer regards as 'real or non-negligible possibilities, or perhaps the union of this group with that of possibilities that are in fact real possibilities. I shall understand the notion of a 'real' possibility pretty demandingly, in terms of envisaging (more on which below). Merely nomological possibilties do not count, nor do possibilties that would not have occurred to the utterer. For a possibility to be 'real', the utterer must have it at least tacitly in mind as a live prospect. (Obviously, on my view, a speaker who asserts 'P if Q' cannot be counting the possibility that P and not Q as real.) It is hard to specify our reference-class—call it 'K—with any precision. It might be suggested that I let R be the class of all events that the utterer believes to be real possibilities in his or her situation. But this will not do. For one thing, it lets into R all sorts of irrelevant possible circumstances that, though the utterer happens to regard them as real possibilities and does not believe them to have materialized, have nothing to do with the speaker's subject-matter or deliberations—for example, the reference-class underlying my utterance of (1) I will finish this paper today unless I run out of anchovies. 4 There are more technical reasons as well. With the aid of two or three plausible reduction formulas or meaning postulates, it is easy to show that restricting our 'event' quantifiers to the actual has the effect of collapsing our conditionals back into their truthfunctional shadows and reinstating the paradoxes of material implication. I take this to be a bad thing—pace Jackson (1979, 1987), whose view I shall discuss in Ch. 4. I have as many ontological qualms about 'non-actual states of affairs' as anyone; but for now, I am having trouble enough trying to find a logical structure of any sort that will predict all that I want to predict concerning the behavior of indicative conditionals. Anyone who objects to mere possibles' being posited even for this limited purpose may think of our 'events' as small sets of propositions and the truth of a proposition 'in' an event simply as set membership. (On ontological issues of this kind, see Lycan, 1994: part I.)

20

Truth Conditions: The Event Theory

would include circumstances in which Norway has an unusually early autumn in 2010. Were this to be allowed, that sentence would automatically be falsified by the fact that none of those circumstances or situations contains either my finishing this paper today or my not finishing it today. Similarly, (2) I will finish this paper today even if they turn off the air conditioning. would entail (3) If Norway has an early autumn in 2010, then I will finish this paper today. (The proof is straightforward: (2) would entail that I finish the paper today in the event that Norway has an early autumn in 2010, which event would be a member of R.) And (2) would therefore be even more patently falsified by the fact that an event in which Norway has an early autumn in 2010 need not and very probably will not contain either my finishing this paper today or my not finishing it today.5 Someone might argue that a version of (3) is true, not false as I have assumed. It seems true in the example that I will finish the paper today whether or not Norway has the early autumn, which seems to entail that I will finish the paper today (even) if Norway has the early autumn. But the latter conditional does not mean the same as (3). (Note the mandatory absence of 'then'.) It is either what Goodman (1947) called a 'semifactual' or what Davis (1983) calls a 'weak' conditional. Semifactuals admit 'still', as in 'Even if Norway has an early autumn, I will still finish the paper today', and assert their consequents.7 I maintain that semifactual P > Q, that is, 'If P, still Q', has the same underlying form we have assigned to 'Q even if P', and does not entail the more robust 'If P, then Q'. (That last, despite the fact that the form assigned to 'Q even if P', (e)(In(e,Q) & (In(e,P) D In(e,Q)), trivially entails (e)(In(e,P) D In(e,Q)). I shall argue below 6 This is not to deny that 'Either I will finish this paper today or I will not finish it today" holds in these 'irrelevant' events. Although events or circumstances are incomplete, they are presumed closed under deduction and so contain all tautologies. I say only 'presumed' because at this point I am thinking only of possible events. Later on in this chapter I shall relax this closure and admit a variety of impossible events in order to handle conditionals with impossible antecedents. 7 Some people have said that they entail their consequents, but that claim will be shown false in Ch. 6.

Truth Conditions: The Event Theory

21

that the parameter R shifts between 'Q even if P' and 'If P, then Q', invalidating the inference.) Davis's 'weak' conditionals resemble semifactuals in that they do not entail the corresponding 'If... then' sentences. For example, (4a) does not entail (4b). (4) a. If you open the refrigerator, it will not explode. b. If you open the refrigerator, then it will not explode. (4a) would normally be used just to reassure the hearer that there is nothing about opening the refrigerator that would make it explode— compare 'Go ahead; if you ask him, he won't bite your head off'— while (4b) would suggest that opening the refrigerator would keep it from exploding, perhaps because the refrigerator has been rigged to explode unless its door is opened in time. ('If you ask him, then he won't bite your head off'.) Weak conditionals are like semifactuals also in that they readily take 'even', they do not contrapose (more on that later in this chapter), and to some degree, in context, they are felt to assert their consequents. They differ from semifactuals in that, even in context, they do not so clearly assert their consequents. (Certainly they do not entail their consequents. (5) If you open the refrigerator, it will not explode, but actually the refrigerator is going to explode anyway. (5) is odd but not a contradiction.) Davis argues that weak P > Q is entailed by the robust 'If P, then Q', and that weak P > ~Q is equivalent to weak ~ (P > Q). I am not absolutely sure how to accommodate these claims in our system, but I shall offer a suggestion below. A second objection to the suggested value of R is that the utterer may be wrong about which logical possibilities are 'real' relative to the occasion, or be unjustified in holding her/his modal beliefs, or both. One consequence of this is that the utterer may fail to include the real outcome (the relevant event that does in fact go on to materialize) among the envisaged possibilities, thus excluding it from R. For example, suppose department chair Professor Arid says, (6) I will promote Sieg to full professor unless his productivity drops significantly during the next year.

22

Truth Conditions: The Event Theory

but then decides not to promote Sieg when he finds out that Sieg has lent Use a copy of Lewis's Counter/actuals, despite there being no drop at all in Sieg's productivity. (Suppose also that there is nothing the least bit unusual about Sieg's lending Use a copy of Counterfactuals, nor any other reason why Arid should not have regarded this event as a real or non-negligible possibility; he has simply and perhaps irrationally failed to envisage it.) On the present suggestion for delineating our reference-class, Arid's sentence will still count as true on the occasion imagined; but it seems clear that the sentence ought to be counted as false, both socially speaking (Arid did not keep his word) and because its felt antecedent is true but its felt consequent false.8 My tasks, then, are two. I must do something to ensure the relevance of each of the members of R. And I must modify the original 'real possibility' condition in such a way as to abstract away from the possible irrational oversights of particular speakers; we do not want a conditional's truth value to depend on the actual epistemic state of the utterer. We might achieve the first task by restricting the quantifiers underlying 'P if Q' etc. to events e such that either it is true in e that P or it is true in e that ~P or it is true in e that Q or it is true in e that ~Q. The rationale for this particular characterization of relevance (call it the Moderate Relevance Restriction) would be that express articulation of the antecedent and consequent states of affairs defines a conditional's subject-matter by (vaguely) specifying two overlapping neighborhoods of hypothetical fact, the antecedent state of affairs with its closely related facts and the consequent state of affairs with its closely related facts; no hypothetical facts extraneous to those two neighborhoods would be considered relevant. Alternatively, I might restrict the class of relevant events still further, to just events e such that either it is true in e that P or it is true in e that ~P. (Call this the Strict Relevance Restriction.) This would leave open the possibility that some conditionals could be considered 'wild', in that their consequents expressed states of affairs that were not relevant to their respective antecedent 8 It may be objected that Arid's utterance was true and that its defect was rather that it was misleading to any normal hearer (such as Sieg in the imagined situation), in that the hearer would have a right to expect that Arid's reference-class did include the unexotic possibility that Sieg would lend Use his copy of Counterfactuals. I will not discuss this objection here, since I take it to be just a special case of the general philosophical problem o whether it is intention, convention, or some unsuspected factor that predominates in fixing the denotatum of a demonstrative token.

Truth Conditions: The Event Theory

23

states of affairs. But it would also have the effect of making it easier for a conditional to be true, because it would shrink the domain of the governing universal quantifier. I think that probably both types of conditional (those interpreted according to the Moderate Restriction and those interpreted according to the Strict Restriction) occur in English. One reason the exact formulation of a relevance restriction is important is that, as we shall see, it is that condition and related requirements that play a selection-functional role in my theory9 and that generates some of the semantically important truth-value distributions. I shall treat the reference-class as a hidden parameter that will vary with context in a way yet to be fully described. Accordingly, I speak of my conditional as 'parametrically strict', thus distinguishing it from Stalnaker's (1968) and Lewis's (1973) Variably strict' conditionals.10 (In Chapter 3 I shall expound Stalnaker's and Lewis's theories and compare them more explicitly with my own.) Our second task is more difficult. Several questions arise. First, should we stipulate that all actual relevant outcomes are members of R, whether or not those outcomes are envisaged by the speaker? It does seem that the speaker is making a serious claim about reality. And yet it is not absolutely clear how responsible the speaker is for unforeseeable contingencies. Suppose Marcia says, 'I will call you on Monday if I get home before 10.00', and she does get home at 9.30, but (unforeseeably) the Venusians have landed at 9.00 and destroyed all telephones. Was Marcia's utterance true or false on that occasion? There is a disinclination to call it false, because I do not want to conclude that Marcia broke her word, and it would be perfectly reasonable for Marcia to say afterward, 'Well, obviously I didn't mean, even in the event that all phones are destroyed.' On the other hand, it seems more repugnant to call the sentence true, because Marcia certainly asserted that she would call if she got home in time, and the fact that I do not (morally or socially) blame Marcia for having failed to anticipate the Venusian invasion should not blind us to the fact that she did not in fact call. We might want to say that the sentence tokened was false, despite Marcia's good 9 See Stalnaker (1968) and Lewis (1973: sec. 2.7), for discussion of selection functions

and their duties. 10 Lycan (1984c). Similar hidden-parameter ideas have been suggested independently by Nozick (1981: 17 n.) and Kratzer (1981, 1986). In the latter essay, Kratzer suggests, as I had in Lycan (1984c), that the parameter is controlled by epistemic considerations. I shall expound Stalnaker's and Lewis's theories in Ch. 3.

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Truth Conditions: The Event Theory

intentions and despite Marcia's perhaps having meant something by it that was true. One way of seeing what is at stake here is to note that, with the inclusion or non-inclusion of all actual relevant events in R, stands or falls the validity of Modus Ponens. If some actual but unenvisaged event escapes R, then even though it is true that P (even though there is some event 8 @ in which P) and every P event 8 @ is also a Q event, it may not be actually true that Q (there may be no actual Q event 8 R). This may reinforce our inclination to hold a speaker semantically (though not morally) responsible for the falsification of her/his consequent due to justifiably unenvisaged developments. Also, it is natural to be squeamish about a theory of conditionals that allows a conditional to be true even though its antecedent is true and its consequent is false. In fact, a number of crucial issues in the logic of conditionals converge just here. I postpone them till the next chapter. It remains to comment, very briefly, on the final related task that would complete our delineation of R. that of abstracting away from the irrationalities of individual speakers. We have a number of options. Should we require that every event that the speaker's beliefs justify her/him in foreseeing be included in R? Or should we follow legal custom and require the inclusion of any event that 'a reasonable person' would have envisaged? I shall forego pursuing these options for now. But the delineation of the referenceclass is a matter that must be settled fairly crisply before any truly serious adjudication of our theory can be achieved (just as, I would claim, an antecedent delineation of David Lewis's relativized notion of'similarity of worlds' is a prerequisite to truly serious adjudication of his11); until that matter is settled, we will not know exactly what cases would count as satisfying our analysantia, which will make it difficult to test the analysis for counterexamples.

Some Further Benefits of the Theory I have motivated the Event theory using syntactic considerations and my modified relative-clause paraphrases. In particular, the theory has also been seen to explain several syntactic facts: for example, that 'if'11

See Lewis (1973: sec. 4.2) and especially (1979); more on this in Ch. 3.

Truth Conditions: The Event Theory

25

conditionals pronominalize using 'then', and that conditional antecedents ground such anaphora as 'in that event too'. Accordingly, the Event theory treats 'if.. .then' not as a syntactic primitive but rather as disparately part of a complex sentential structure, 'if being a species of relative pronoun and 'then' being a pronoun bound by a quantifier. One must not be misled either by the fact that a conditional's superficial antecedent and consequent are still represented by the Event theory as sentential argument places, or by the similarity of our resulting semantics to other purely semantical treatments such as Stalnaker's and Lewis's in that it incorporates a device that plays a selection-functional role in order to block the standard set of intuitively invalid inferences (see below). The Event theory is not vulnerable to the sorts of objections I advanced in Chapter 1 against the prevailing unstructured-sentential-operator picture. Nor, on the Event theory, does 'if.. .then' require its own special clause in the truth definition for English. The truth value of an ordinary indicative conditional can be computed from the semantic values of its components using just our standard recursive clauses for quantifiers and the horseshoe (provided one is willing to countenance the domain of 'non-actual events' for which the theory's quantifiers are defined). 'If... then' need no longer be regarded as one or more isolated semantical primitives having little connection to other locutions.12 Now I shall catalogue some of its semantic benefits—some fairly routine, others quite striking. The Paradoxes of Material Implication The theory frees indicative conditionals13 from the paradoxes of material implication, and in an illuminating way, without (implausibly) treating them as being strict conditionals of any sort 12 This virtue is shared by the proposal of Kratzer (1986). She too denies that the conditional is a binary sentence operator at all, but for a syntactic reason different from mine. She is concerned to extend Lewis's (1975) suggestion that 'conditional antecedents' are really restrictions on hidden modal quantifiers. Dudman (1984a, 1986) has also rejected the binary-operator syntax and the idea that conditionals have 'antecedents' and 'consequents' as constituents; his idea is a forerunner of Kratzer's, in that he portrays an 'if'-clause as a 'complication' of a modal 'verdict' packed inside the predicate of what is overall a subject-predicate sentence, but his syntactic/semantic framework is non-standard and hard to relate directly to Kratzer's truth-conditional format or to mine. 13 Following Dudman (1984a, 1984fo) and Bennett (1988), I am unhappy with the terms 'indicative' and 'subjunctive' as they have been used in the mainstream literature on

26

Truth Conditions: The Event Theory

and without importing exotic semantical machinery. It is easy to see that the theory avoids validating the three most objectionable inferences involving the truth-functional 'if... then': (I) A / . ' . B > A. Example: Richard will go on a five-mile run tomorrow/.'. If Richard is killed by a terrorist bomb this afternoon, then Richard will go on a five-mile run tomorrow. (II) ~ A / . ' . A > B . Example: Mimi is not going to turn off the air conditioner / .'. If Mimi turns off the air conditioner, then the planet Saturn will explode and shower Europe with radioactive digital watches. (Ill) ~ ( A > B)/.-.A&~B. Famous example: It's not true that if a benevolent God exists, then there is random gratuitous evil in the world / . ' . A benevolent God exists, and there is no random gratuitous evil in the world.14 Those argument-schemata would be represented respectively as:

(I*) Q (e ER )(In(e,P) D In(e,Q))

(II*)

~P

(e ER )(In(e,P) D In(e,Q)) (III*)

~(e ER ) (In(e,P) D In(e,Q)) P&~Q

(I) is invalid because some non-actual event e may contain P but not Q even though no actual event does. (II) is invalid because some nonactual event e £R may contain P but not Q, even though an actual event contains Q. (Ill) is invalid because the event in which both P conditionals; but I shall stick with them until we meet the 'indicative'/'subjunctive' distinction head-on in Ch. 6. 14 Thus the indicative-as-material or Horseshoe theory presents us with a proof of God's existence and a theodicy, all in one breath. (I heard this joke from the late Alan Ross Anderson; a version of it appears in Stevenson (1970); I do not know whether Stevenson got it from Anderson or vice versa.) See also Stalnaker's example: 'Surely I may deny that if the butler didn't do it, the gardener did without affirming the butler's guilt' (1981: 193).

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27

and ~Q, whose existence is guaranteed by (III)'s premise, may not be an actual event. (Sometimes it is argued on behalf of a material interpretation of indicative conditionals that such conditionals are logically equivalent to disjunctions, which disjunctions are truth-functional.15 But in general A > B is not entailed by ~A v B. Suppose it is not in fact going to snow in Chapel Hill next winter. Then truth-functionally, either it is not going to snow in Chapel Hill next winter or President Clinton will be kidnapped in 2003 by very large echidnalike creatures from the planet Mongo. It hardly follows that if it snows in Chapel Hill next winter, then Clinton will be kidnapped in 2003 by very large echidna-like creatures from the planet Mongo. I believe that conditionals are perceived as being equivalent to disjunctions because English sports a strong non-truth-functional disjunction as well as a stronger-than-material conditional, but I shall not pursue that here.) I have said that the Event theory blocks the paradoxical inferences in an illuminating way. To illustrate, consider (III)'s premise. Read crudely, what it says is that there is some event or circumstance that is a real and relevant possibility (but is not necessarily going to materialize in fact) and in which P but ~Q. This is a natural reading of 'It's false that Q if P', and it seems intuitively to capture what is intended by a speaker who denies 'Q if P'. Finally, this reading makes it clear why (III)'s premise fails to imply anything about its being true or false that P or that Q in the real world.15 The Stalnaker Invalidities Slightly supplemented, the Event theory will also explain the now standard invalidities exhibited by Stalnaker (1968), AntecedentStrengthening and Transitivity. On either the Strict or the Moderate 15

As by Jackson (1979, 1987). For further critique of this argument, see Edgington (1986). Hanson (1991) reminds us that if we reject the material interpretation (and retain Reductio), we must restrict the logical rule of Conditional Proof, else we get the obvious derivation of A > C from ~(A & ~ C); Thomason (1970) does this in formalizing Stalnaker's (1968) non-material conditional. In support of the material interpretatio, Hanson defends unrestricted Conditional Proof for indicatives, but unconvincingly in m view. 16 McDermott (1996) offers an interesting set of conditionals that would counterexample my analysis if his judgments of their truth-values are correct. I will say a bit more about them in Ch. 7.

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Relevance Restriction, R will contain at least one event in which the conditional antecedent itself is true—unless no such event is envisaged as a 'real' possibility. But intuitively, if a conditional is actually tokened, its uttering forces speaker and hearer to envisage a state of affairs in which its antecedent holds, however outlandish that event may be. Indeed, one might say that is the point of a conditional antecedent, to put a possibility on the table. 'If P, then Q' is almost paraphrased by 'Assuming P, Q', 'Suppose P; then Q', and 'What if P? Then Q'. So it seems that a conditional forces the 'envisaging' of its antecedent event and in the context deems it to be a 'real' possibility, however unlikely. Thus we may lay down the Antecedent Requirement: R must contain at least one event in which the conditional antecedent itself is true. Antecedent-Strengthening (A > B/ .'. (A & C) > B) fails because its conclusion's antecedent forces us (via the Antecedent Requirement) to envisage a possibility that had not been envisaged, because not counted as a 'real' possibility, until after the premise had been tokened: (7) If my good friend Smedley finishes his book, I'll be happy. .'. If my good friend Smedley finishes his book and concludes it with a vicious and totally unfair personal attack on me, I'll be happy. Since it would never occur to me that Smedley might conclude his book with a vicious attack on me, the premise's value of R does not include any such event; but the conclusion's value of R must include at least one, indeed all such events. This is why our parameter R plays a selection-functional role: it has the power to alter the range of possible states of affairs that must be counted. (Of course, if the parameter is held fixed, the conditional will sustain Antecedent-Strengthening. But this does not mean that any instance of A > B / .'. (A & C) > B found in nature will be a valid argument, since there is no guarantee that the parameter does stay fixed in the course of arguing from premise to conclusion. Indeed, for arguments such as (7), the Antecedent Requirement prevents the parameter from staying fixed.17) 17 Obviously it would be too strong to hold that an argument is invalid whenever there is a possibility of parameter shift; practically any argument containing more than one quantifier would meet that condition. The reason Antecedent-Strengthening fails is that the parameter shift can be forced, by systematic pragmatic factors.

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29

Transitivity fails also. Not surprisingly: any counterexample to Antecedent-Strengthening yields a corresponding counterexample to Transitivity; use the form (A & C) > A, A > B / .'. (A & C) > B. On the event analysis, 'P if Q' is relative, in that it is elliptical for 'P if Q in all the relevant events envisaged'. As before, the value of R associated with 'P if Q' will include at least all those events in which P and in which ~P and which are 'real' possibilities in the situation of utterance, while the value associated with 'Q if R' may exclude some events in which P or in which ~P. It is a bit harder to find clear counterexamples, for indicative conditionals, that do not turn on the invalidity of AntecedentStrengthening. Something like the following may do: (8) If Clinton takes it easier, his friends will be glad. If Clinton resigns the presidency, he will take it easier. .'. If Clinton resigns the presidency, his friends will be glad. Perhaps better: (9) If Gore is nominated for President, I will skip the front page of my newspaper. If all the other Democratic candidates are squashed by a falling meteorite, Gore will be nominated for President. .'. If all the other Democratic candidates are squashed by a falling meteorite, I will skip the front page of my newspaper. This last is plainly invalid, and the event analysis provides an obvious explanation: the antecedent of the second premise forces the hearer to envisage an event in which all the other Democratic candidates are squashed by a meteorite. But the value of R associated with the first premise did not contain any such event because it is not one that a speaker would normally envisage, and it is with this assumption that the speaker has asserted the first premise. Since the conclusion continues to force the hearer (and speaker) to envisage the event(s) in question, the argument is invalidated by straightforward parameter shift.18 18 This phenomenon is quite similar to that which invalidates the corresponding counterfactual argument on a 'similarity' analysis of counterfactuals such as Stalnaker's (1968) or Lewis's (1973). In each case it is the improbability of the second premise's antecedent that makes the counterexample work.

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But there is a problem: order of tokening matters less than has just been suggested.1 Antecedent-Strengthening is felt to be invalid even when the conclusion is tokened first, as in, 'If Smedley finishes his book and concludes it with a vicious and totally unfair personal attack on me, I'll be happy; that's because if he finishes his book, I'll be happy'. But my account as formulated so far predicts otherwise. Likewise the Clinton and Gore examples, though perhaps less obviously. (But note that reversing the premises in (8) and in (9) has the predicted effect; the original first premises now seem false and the arguments seem to turn valid.) I believe this shows that there is something slightly artificial or stylized about 'envisaging' as I am trying to characterize it (we will see this confirmed in Chapter 3). 'Envisaging' is not purely a de facto cognitive or other psychological state; it is in small part a stance or a posture. When one hears the conclusion of an Antecedent-Strengthening counterexample uttered first, of course, one is both caused psychologically and required by my theory to envisage the unlikely conjunct. And so, we naturally think, the hearer is still envisaging that far-fetched possibility when s/he hears the premise half a second later; the premise ought now to sound false and the argument seem valid. But I think that hearers can and do wnenvisage possibilities when they know, or think they know, that those possibilities do not obtain. A conditional antecedent calls us to assume something for the sake of argument and, to that extent, to treat that thing as a 'real' possibility for the duration of the assuming itself. But knowledge to the contrary can reassert itself very quickly, in time to make us reaffirm the truth of the premise. Again, do not take 'reassert itself very quickly' as a de facto psychological phenomenon. It is partly a dialectical and conversational one. Psychologically, one does still recognize the far-fetched possibility as a possibility, but since one knows or thinks one knows that it does not obtain, one reverts, after listening to the far-fetched assumption, to refusing to countenance it as 'real'. At least, this is what happens to the extent that one still hears the argument as invalid. As a further example of invalidation by parameter shift, here is why 'Q even if P' does not entail 'If P, then Q', even though (e)(In(e,Q) & (In(e,P) D In(e,Q))) seems trivially to entail (e)(In(e,P) D In(e,Q)). As always, each of the quantifiers is restricted. According to the first 19

The problem was called to my attention by Michael McDermott.

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clause of our representation of 'Q even if P', every member of the relevant R is an event in which Q; so R contains only Q events, and the formula's second clause says only that every so qualified (that is, Q-including) P event is a Q event. But when we evaluate 'If P, then Q' on its own, of course, we may envisage more P events than just Q-including ones, and if so the result is falsity. Incidentally, it is important to see the exact dialectical relation between my event semantics and the Relative Clause analysis sketched in Chapter 1. For the event semantics is going to have the best semantic features of the Stalnaker-Lewis similarity analysis,20 and so it might be thought unoriginal, unexciting, or at any rate no big semantical news. To think that would be a mistake, for each of two reasons. The main reason is motivation: my quantification over 'events' is motivated, not by possible-world semantics or by any other philosophical identification of modal notions with quantification over intensional objects, but purely and independently by the Relative Clause analysis, specifically the parallel between 'if and 'when' and 'where'. Other semanticists have simply assumed that possible-worlds semantics is the appropriate truth-conditional format and then asked how best to approach conditionals in terms of possible worlds. Contrastingly, Geis has found our own possibilia in nature, as pronominal referents. This is very happy robustness. Secondly, for that matter, in Chapters 3 and 7 my semantic analysis will be shown to better the Stalnaker-Lewis similiarity theory on points, in regard to an array of particular cases. Contraposition, Semi/actuals, and 'Weak' Conditionals Stalnaker and Lewis dump Contraposition along with AntecedentStrengthening and Transitivity; but I think Contraposition is a little trickier. Here is Stalnaker's original counterexample (1968: 107): (10) If the US halts the bombing, then North Vietnam will not agree to negotiate. .'. If North Vietnam agrees to negotiate, then the US will not have halted the bombing. (Quite a period flavor.) Stalnaker's speaker is assuming that the North Vietnamese are determined to press for a complete and unconditional 20

Again: Stalnaker (1968); Lewis (1973).

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withdrawal of US troops, so that a bombing halt would not suffice to bring them to the negotiating table, but also that a bombing halt plus a great deal more would be required to bring the North Vietnamese to the table. But I do not find this as clear a counterexample as are the standard ones against Antecedent-Strengthening and Transitivity. Perhaps (11) is better: (11) If Gore is not happy, he will be permitted to go on residing in the United States. .'. If Gore is not permitted to go on residing in the United States, he will be happy. (ll)'s conclusion is (presumably) false, (ll)'s premise strikes me as true, though admittedly the premise is an odd sentence and I have to hear it as containing a tacit 'even' or 'still'. Still better, from Adams (1975: 15): (12) If it rains tomorrow there will not be a terrific cloudburst. .'. If there is a terrific cloudburst tomorrow it will not rain. The conclusion is hideously false and the premise is less odd. (13) If the cat got out, it's not the case that the cat got out and the back door was not left unlatched. .'. If the cat got out and the back door was not left unlatched, the cat did not get out. (Similar to an unpublished example of Ernest Sosa's. The speaker is assuming that the only way for the cat to have gotten out is for someone to have left the back door unlatched.) Appropriately or not, my own theory as developed so far gives equivocal judgment on (10)-(13). The reason is that, just as we have not decided as between the Moderate and the Strict Relevance Restrictions, we have not considered whether to add a Consequent Requirement to our Antecedent Requirement. If uttering a conditional antecedent enforces envisaging the corresponding circumstance, should the same be said of uttering a conditional consequent? My argument for the Antecedent Requirement, that it is the very function of a conditional antecedent to hold up a possibility for examination, is not available for consequents. On the other hand, one might contend that explicit mention of a state of affairs,

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even in the comparatively unshowy consequent position, suffices for its envisaging, especially when the conditional is uttered as true and its antecedent has been envisaged. If the Consequent Requirement is imposed, then since (10)-(13)'s premises' consequents would have to be envisaged, (10)-(13) would differ from (7)—(9) in that their conclusions' antecedents would not force the envisaging of a new event not already introduced by their premises. Nor is there any other reason why the parameter R would shift between premise and conclusion; so my theory seems to predict that (10)-(13) would be valid. However, that reasoning is inconclusive. Even if the premises' consequents ('North Vietnam will not agree to negotiate', 'Gore will be permitted to go on residing in the United States', 'there will not be a terrific cloudburst', 'it's not the case that the cat got out and the back door was not left unlatched') are envisaged, it does not follow that the conclusions' antecedents are ('North Vietnam will agree to negotiate', 'Gore will not be permitted to go on residing in the United States', 'there will be a terrific cloudburst', 'the cat got out and the back door was not left unlatched'), prior to the conclusions' tokenings, for they express different propositions even though closely related by presence or absence of negation. And if the Consequent Requirement is not imposed, of course, we would not be required to count the premises' consequents as envisaged, and (10)-(13) would be invalidated in the same way as were (7)-(9).21 Now, it maybe thought tendentious to hold that one can envisage a negative circumstance without envisaging the opposing circumstance that it negates, or vice versa. And specifically, it seems strange to suggest that North Vietnam's agreeing to negotiate, Gore's not being permitted to go on residing in the United States, etc., are not envisaged by the respective utterers of the premises of (10)—(13) when they 21 Prescinding from the Consequent Requirement would help with a problem put to me recently by Daniel Nolan. Consider a famous example of E. W. Adams's (1970): 'If Oswald did not shoot Kennedy, someone else did." Clearly true. But suppose that prior to anyone's uttering that sentence, someone had uttered 'If Oswald did not shoot Kennedy, then either someone else did or there's been an elaborate charade'. Then, on my view, Adams's original sentence should seem false, since a possibility has been envisaged according to which Kennedy was not shot. But without the Consequent Requirement, we would not be forced to envisage that possibility. (If the Requirement is kept, we would need to fall back on the move I made in response to the problem about order of tokening: if I know perfectly well that Kennedy was shot, then even once Nolan's sentence has forced me to envisage an event in which he was not, I unenvisage it in considering Adams's.)

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are so closely related to those premises' explicit subject-matter. But at least in some cases, there is an argument for taking such a position. Consider (11) 's premise, 'If Gore is not happy, he will be permitted to go on residing in the United States.' If we take that sentence to be true, it is not because Gore's non-happiness would somehow lead to his being permitted to go on living in the United States, or make that circumstance more likely than it otherwise would have been. Rather, so far as we take it to be true, we do so because we already firmly believe that Gore will be permitted to go on living in the United States regardless of his happiness or unhappiness; it is either a semifactual or one of Davis's 'weak' conditionals. In short, when a sincere speaker utters it, the speaker does so because s/he does not (just at that point) envisage Gore's not being permitted to go on living in the United States. (Indeed, the latter possibility would never occur to most Americans.) And this obtains despite the explicit occurrence in the consequent of 'he will be permitted to go on residing in the United States'. My semantics predicts all this, since it paraphrases the premise as, Any relevant and envisaged event in which Gore is not happy is one in which Gore is permitted to go on living in the United States.' The latter is true, not because (so to speak) envisaging an event in which Gore is not happy makes us conclude that in that event Gore will be permitted to go on living in the United States, but because we were not envisaging any event in which Gore would not be so permitted, in the first place. We could have made the stronger assertion, 'Gore will be permitted to go on living in the United States in any event, including events in which he is not happy.' That assertion is our paraphrase of'Even if Gore is not happy, he will (still) be permitted to go on residing in the United States'; and, sure enough, I believe, one who takes (1 l)'s premise to be true would readily accept the insertion of 'even'. It is generally true of semifactuals and weak conditionals that a speaker who asserts one would also be willing to insert 'even'. And notice that all of the premises of (10)-(13) are either semifactuals or weak conditionals. I know of no purported counterexample to Contraposition that does not have such a conditional as a premise. What to conclude? If we try to give a uniform account and if we accept (10)-(13) as counterexamples and agree with Stalnaker and Lewis that Contraposition is invalid for indicatives, we shall either have to take a debatable stand against the Consequent Requirement or

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insist that consequent circumstances can be envisaged even though their negations are not. But more likely we should not give a uniform account; after all, the weaker types' truth conditions differ from those of robust conditionals. If I am right in thinking that the premises in genuine counterexamples to Contraposition are all semifactuals or weak conditionals, none of them robust conditionals, then (with Davis) we should support Contraposition for robust conditionals and deny it only for the weaker types. The Consequent Requirement obviously does not hold for semifactuals and weak conditionals. Our discussion of (11) suggests a way of representing weak conditionals parametrically. A conditional is weak when R contains no events in which its consequent is false. An utterer of weak 'If you open the refrigerator, it will not explode' would not envisage an Explode event at all, much less not an Open-and-Explode event, while an utterer of the robust 'If you open the refrigerator, then it will not explode' does envisage Explode events, even though none of them is an Open event. A weak conditional is judged false when its antecedent forces speaker and hearer to envisage events in which its consequent is false. This hypothesis explains why weak conditionals do not contrapose: if the foregoing weak conditional is contraposed, its antecedent becomes 'the refrigerator explodes', and the Antecedent Requirement then forces the speaker newly to envisage an Explode event, which widens R, leaving in some Open events. The hypothesis also explains why weak P > ~Q is felt to be equivalent to weak ~ (P > Q); if no Explode event is envisaged, then obviously it will not be the case that every envisaged Open event is an Explode event. Finally, the hypothesis explains in part why weak conditionals do not lexicalize using 'then'. Aweak conditional is made true by the fact that the falsity of its consequent is not envisaged; its antecedent does no positive work, but sits by merely not interfering with the consequent's truth. That, I believe, is why the conditional does not admit 'then': to pronominalize its antecedent event would be to call attention to that event in an inappropriately emphatic way. (But if my hypothesis is correct, why is (5) 'If you open the refrigerator, it will not explode, but actually the refrigerator is going to explode anyway' not a contradiction? Its first conjunct is supposedly true because no Explode events are envisaged at all. But if the speaker envisages no Explode events, then to assert the second

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conjunct, which says precisely that the refrigerator is going to explode, is anomalous. True, but I think the sentence is merely anomalous rather than contradictory. There is no semantic contradiction. In fact, even the robust 'If you open the refrigerator, then it will not explode, but actually the refrigerator is going to explode anyway' is not a contradiction, though it may entail that you will not open the refrigerator. Rather, the speaker asserts something s/he does not envisage, which is a pragmatic anomaly.22) Subjunctive semifactuals also afford reasonably clear counterexamples to Contraposition. Lewis's (1973: 35) is: (14) If Boris had gone to the party, Olga would still have gone. .'. If Olga had not gone, Boris would still not have gone. (The facts are that Olga did attend, but Boris 'stayed away solely in order to avoid Olga'.) Premise true, conclusion false. An adequate theory of conditionals needs to distinguish between robust, semifactual, and weak conditionals. As Davis has pointed out, Stalnaker's (1968) theory does not do so. (Davis argues that we can take Stalnaker's theory, which rejects Contraposition, as a theory of weak conditionals, and construct from it a theory of robust conditionals by simply adding contrapositives as conjuncts, but this leaves semifactuals to be accounted for.)23 So the Event theory is currently ahead on this issue. 22 We may take the position that once the speaker has asserted that the refrigerator is going to explode, s/he is forced to envisage an Explode event, and on my hypothesis she should then retract the first conjunct. I think that consequence is correct. The speaker would have to rephrase the first conjunct: 'I meant only that opening the door wouldn't make the refrigerator explode." 23 If David Lewis has discussed weaks or semifactuals as such, I have missed it. (Stephen Barker, who has also emphasized the importance of semifactuals to me, has in unpublished work criticized Lewis extensively on this ground.) But how does my own theory distinguish semifactuals from weaks? The relation between the two is very close. A semifactual 'If P, still Q' has the same underlying representation as does the corresponding 'even' conditional: (e eR )(In(e,Q) & (In(e,P) D In(e,Q))). A weak conditional has an intimately related one, (eeR) (In(e,P) D In(e,Q)) where Rcontains no ~Q events. By the Antecedent Requirement on the latter, R must contain some P events and hence some Q events but, as just noted, no ~Q events; that makes the weak equivalent in context to the semifactual. Yet the semifactual is more emphatic and is more strongly felt to assert its consequent. I conjecture that this is the function of'still'. That is, 'still' adds the semantically explicit conjunct '(In(e,Q) &', which in a weak conditional is guaranteed only pragmatically. 'If conditionals lexicalized without 'then' and without 'still' will always be ambiguous between robust and weak readings. 'Then' and 'still' each serve to disambiguate, in opposite directions.

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Modifiers of 'If' On the event analysis, 'even' in 'even if means 'even', and 'only' in 'only if means 'only'. This feature is almost non-existent among philosophers' theories of conditionals. I suppose this is because logic students are taught that 'if...then' is a sentential connective and that 'only if is a sentential connective too; this gets us into the habit of translating 'only if automatically by the horseshoe, and subsequently by some more arcane conditional connective when we become sufficiently troubled by the paradoxes of material implication. But no philosopher stops to ask why that word 'only' occurs there. Why not 'blup if or 'bagel if or, more to the point, some single morpheme such as 'schmif'? 'Only' in 'only if feels like the ordinary word 'only', as in 'Only Susan left early'. And 'only' reflects a quantificational construction. The point is reinforced by the fact that 'only if can be paraphrased by 'only in the event that' and by 'in only one event: that', which sound more explicitly quantificational because of their equivalence with 'in no event other than one in which'. The event analysis explains these facts; any analysis of indicative or of subjunctive conditionals that (seriously) renders conditional connectives as syntactically primitive officially declares them inexplicable.24 Similar points can (and will in Chapter 5) be made regarding 'even'. The Direction of Conditionship For that matter, the event analysis explains the presence of 'if in 'only if. Notice that if one paraphrases one's target conditionals, 24 Richmond Thomason and others have argued to me that in its normal uses, 'only' generates an entailment (or a 'presupposition') of existence as well as uniqueness. Thus, 'Only Susan left early' implies not only that no one other than Susan left early, but that Susan did leave early. Thomason's claim has been controversial at least since the Middle Ages. Aquinas defended it (1945 edn.: 311-12), but it was attacked by William of Sherwood (1968 edn., as documented by Horn, 1989). In our own time, Atlas (1993) defends it, but Horn (1992) and McCawley (1993) argue vigorously against it and that the implication is merely pragmatic. I tend to side with the Thomists. And I believe (contrary to the letter of the semantic representation I have assigned to 'P only if Q') that in colloquial English 'P only if Q' carries a similar implication, whether entailment or pragmatic; 'I will pass you only if you get an A on the final' implies that I will pass you if you get an A on the final. ('I will pass you only in the event that you get an A on the final' clearly implies that I will pass you in that event but in no other.) What about the logician's contrasting monoconditional use of 'only if? I surmise that at some point 'only if acquired a technical use in mathematics, a syntactically fused sense that permits the otherwise redundant 'if and only if (compare 'Susan and only Susan') and that this technical use has filtered into ordinary academic English from mathematics and logic, perhaps via various sciences. If the Thomists are right, then in this technical idiom, 'only' does not have its entire normal meaning.

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appropriately enough, in terms of conditions, 'If P, then Q' and 'P only if Q' differ sharply in direction of conditionship:25 (15) a. If you start throwing lamps, I'll leave. given b. 111 leave, n the condition J tha you start throwing lamps. (16) a. You (will) start throwing lamps only if I leave. b. You (will) start throwing lamps only given , that TI leave. n the condition J As the received doctrine(s) of conditionals would have it, (15a) and (16a) are not only logically equivalent but effectively synonymous, in that they are translated by one and the same logical primitive. Yet the condition in (15a) is the condition that you start throwing lamps, while the condition in (16a) is the condition that I leave. (This explains why undergraduates in logic courses usually resist the translation of'only if by the horseshoe or arrow, complaining that it is 'the wrong way around'.) The Event theory accommodates and explains this fact; 'you start throwing lamps' appears as the antecedent of a conditional in the event analysans of (15a), but'Heave' appears as the antecedent of a conditional in the analysans of (16a). Parametric Differences between Apparent Equivalents Any logician would take (17) If I leave, then Joe will leave. (18) Joe will leave if I leave. (19) I will leave only if Joe leaves. to be equivalent. Are they? Even the event analysis might seem to entail that they are, and yet they differ at least in connotation. Statement (17) hypothesizes the speaker's leaving and remarks on or suggests something that will be triggered by that event. (18) focuses on the question of Joe's leaving and can be heard either as being part of a list of conditions under which Joe will leave, or as emphasizing a 25

This was first pointed out to me by V. H. Dudman; see also McCawley (1981). Sanford (1989: ch. 11) urges a qualification.

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consequence of the already stipulated hypothesis that the speaker leaves. Statement (19) reports a necessary condition for the speaker's leaving. Perhaps these differences in purport are simply differences in focus and/or in emphasis and/or in conventional implicature and/or in resolution of vagueness. But there is some temptation to insist that there is a difference in the proposition expressed as well. The Event theory can account for this, despite its assigning (17), (18), and (19) each a formula logically equvalent to (20) (C E R) (In(e, I leave) D In(e, Joe leaves)) as a semantic representation. To see this, note that 'R is a parameter or free variable and may be assigned a different value on each occasion of its use. Therefore, it is at least possible that different ranges of possible 'events' are being envisaged by the utterers of (17), (18), and (19), and thus that distinct propositions are expressed even though the logical forms (in the narrow sense) of (17), (18), and (19) are the same. For example, (17) suggests that my leaving would be a reason for or cause of Joe's leaving, whereas (18) suggests the reverse; thus, the value of R on an occasion of the utterance of (17) would very likely not include any event(s) in which Joe had already left some time before the speaker left, while the value of R associated with an utterance of (19) would include these but would exclude events in which Joe is still in the room when I leave but leaves some time thereafter. It should be noted that the difference between 'If P, then Q' and 'P only if Q' holds for subjunctives as well. Compare (21) and (22): (21) If Joe were to leave, then he would get a headache. (22) Joe would leave only if he were to get a headache. An analysis of subjunctive conditionals such as Lewis's offers no way of distinguishing these, but it seems plain that they can differ in truth value.25 This leads me to suspect the presence of quantification over 26 Actually it is open to Lewis to distinguish the truth values by stipulating that different similarity relations are mobilized by the two surface constructions i f . . . then and only if. But (a) this would be ad hoc unless the distinction between the similarity relations could be independently motivated, and (6) no light would be shed in any case on the presence of 'only', the direction-of-conditionhood datum, etc. Michael McDermott has pointed out that Lewis could also distinguish 'P only if Q' from 'If P, Q' by translating it as ~ Q > ~ P. Since Lewis rejects Contraposition, this would remove the equivalence. But the difference between (21) and (22) seems greater than just the questionable invalidity of Contrapositio; (6) above still holds.

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possible outcomes in the semantic structures underlying counterfactuals and other subjunctives as well—much more on which, shortly. It is interesting to ask whether any change in AntecedentStrengthening or Transitivity is occasioned by the replacement of one of our 'if... then.. .'s with an 'only if. The event analysis may be taken to suggest that no such change should occur, since on it 'P if Q' and 'Q only if P' are assigned equivalent logical forms. But to conclude this would be to overlook the difference in direction of conditionship, as well as the parameter shift required by our account of relevance. Here is the 'only if version of argument (7). (23) Smedley will finish his book only if I'll be happy. .'. Smedley will finish his book and conclude it with a vicious attack on me only if I'll be happy. Peculiar, and not as obviously invalid as (7). One might naturally think that if A is a necessary condition for B, then surely A is necessary for B & C. But a complication here is the possibility that 'only if in English is really biconditional (see n. 24). Here is the 'only if counterpart of argument (9), our counterexample to Transitivity. (24) Gore will be nominated for President only if I skip the front page of my newspaper. [!!] All the other Democratic candidates will be squashed by a falling meteorite only if Gore is nominated for President. .'. All the other Democratic candidates will be squashed by a falling meteorite only if I skip the front page of my newspaper. This too, is not obviously invalid, but complicated by the possibility that 'only if is biconditional. What about a mixed example? Consider (17) ('If I leave, then Joe will leave') and (25) Joe will leave only if the booze runs out. Transitivity would entitle us to infer (26) I will leave only if the booze runs out,

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which is counterintuitive. Actually I tend to hear (17) and (25) themselves as contradicting each other: Joe will leave only if the booze runs out, but he will also leave if I do? This points importantly toward the nature of 'only' in 'only if, as Geis originally saw. Yet any competent classical logician would infer (26) from (17) and (25) without seeing any irregularity at all. The Event theory also neatly explains our somewhat paradoxical feelings about this. The reason that (17) and (25), uttered in the same context, seem to contradict each other is that we presume that roughly the same set of circumstances is envisaged by the speaker in making each utterance. The speaker must be envisaging at least one event in which I leave, and presumably at least one in which I leave but in which the booze does not run out. Statement (17) entails that Joe leaves in the latter event, but (according to the event analysis) (25) entails that he does not; hence the air of incompatibility. (Notice too that a sentence like 'Joe will leave only if the booze runs out and only if Bruno sings "When the Moon Comes Over the Mountain"' is selfcontradictory or at best anomalous. This fact alone would demolish the logicians' idea that 'only if is a conditional connective. To counter the logicians' and philosophers' tendency to hear 'only if as expressing just a necessary condition, remember what 'only' means.) And even if we were to juggle parameters in such a way as to repair this, we would still leave open the possibility of parameter shift that would account for the failure of surface transitivity. Similar points may be made about 'P unless Q'. Interestingly, 'unless' itself does not commute.27 (27) and (28) are not synonymous: (27) They will play the Pachelbel Canon unless I attend. (28) I will attend unless they play the Pachelbel Canon. On the Event theory, (27) means that they will play the canon in any event 8 R other than ones in which I attend; (28) means that I will attend in any event 8 R other than ones in which they play the canon. R must take different values here, or the two sentences would be synonymous. And so R does: (27) specifies the only thing that will keep them from playing the canon, while (28) specifies the only thing that will keep me from attending. The utterer of (27) envisages a whole bunch of Canon events plus some non-Canon events that are 27

This was pointed out, and the example given me, by David Sanford.

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also Attend events, while the utterer of (28) envisages a wider range of Attend events plus some non-Attend events in which they play the Canon.

Simplification of Disjunctive Antecedents Nute (1975) defended a form of inference (SDA for short) that had been ruled invalid by Stalnaker and Lewis: (Av B) > C / .'. (A > C) & (B > C).28 Some apparently valid instances are: (29) If you eat either the broccoli or the Brussels sprouts, you'll get sick. .'. If you eat the broccoli you'll get sick, and if you eat the Brussels sprouts you'll get sick. (30) If either Mom or Dad comes to my show, I'll be happy. .'. If Mom comes to my show I'll be happy and if Dad comes to my show I'll be happy. (31) If we have good weather this summer or the sun grows cold before September, we'll have a bumper crop. .'. If we have good weather this summer, we'll have a bumper crop, and if the sun grows cold before September, we'll have a bumper crop.2 (Intuitively valid because the falsity of the conclusion's second conjunct makes us reject the premise.) (Of course, SDA is valid for the material conditional.) Yet we should be suspicious. For one thing, SDA is a case of Antecedent-Strengthening; at least, the conclusion's conjuncts' antecedents are each logically stronger than that of the premise. That hardly proves the invalidity of SDA, since SDA is a markedly special case of Antecedent-Strengthening. But various theorists have produced counterexamples to SDA, and Nute himself (1980a) has abandoned SDA, though he insists that some of its instances are validated by powerful pragmatic principles. Here are a few counterexamples. 28 Strictly, Nute defends the principle only for subjunctive conditionals, but the same issue arises for indicatives. See also Creary and Hill (1975) and Fine (1975). 29 Paraphrased from Nute (1975: 776).

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(32) If Spain fights on one side or the other [the Allies or the Axis in the Second World War], she will fight with the Axis. .'.If Spain fights along with the Allies, she will fight with the Axis, and if she fights along with the Axis, she will fight with the Axis. (The conclusion is garishly false thanks to its first conjunct; paraphrased from McKay and van Inwagen (1977).) (33) If Gladhand runs for Congress [= the House or the Senate] , he will run for the Senate. .'. If Gladhand runs for the House he will run for the Senate, and if he runs for the Senate he will run for the Senate. (False first conjunct again.30) (34) If Hitler attacks Czechoslovakia or Britain, he will not attack Britain. .'. If Hitler attacks Czechoslovakia, he will not attack Britain, and if Hitler attacks Britain, he will not attack Britain. (Paraphrased from Nute, 1980a: 164.) The problem, then, is to say what distinguishes the apparently valid instances of SDA from the apparently invalid instances. One strategy is to reject SDA tout courtbut to appeal to 'translation lore' (Loewer, 1976; McKay and van Inwagen, 1977) to explain the apparent validities. The idea is that the respective premises of (29)—(31) should in the first place be translated, not as (A v B) > C, but as (A > C) & (B > C) itself; it is pointed out that 'or' in English sometimes does mean 'and'.31 A drawback here is that absent an independently defended general semantic criterion for the conjunctive use of 'or', the move is somewhat ad hoc.32 And the criterion would have to rule in the premises of (29)—(31) while ruling out the syntactically very similar premises of (32)—(34). A second strategy would be to dismiss the apparently valid instances of SDA as being merely conversational implicatures. I know of no one who has attempted this (though Loewer appeals to Gricean 30

Paraphrased from Nute (1978: 324), attributed to Michael Dunn. 'Either the Well-Ordering Theorem or Zorris Lemma leads to the Axiom of Choice"; 'I can fly or take the train" (McKay and van Inwagen, 1977; the second example is attributed to David Lewis). 32 Loewer does make a start at justifying his translation move itself (1976: 534-7). 31

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machinery in pursuit of his translation-lore approach). Nor does it seem promising, because it is hard to hear the implications in (29)— (31) as cancellable in the manner of conversational implicatures. ('If you eat either the broccoli or the Brussels sprouts, you'll get sick; but don't get me wrong—I'm not implying that if you eat the broccoli you'll get sick.') A third strategy would be to insist that SDA is valid but contend that (32)—(33) involve a deviant type of conditional. This is suggested by Nute (1978: 324, 'But such cases also appear to involve a conditional with a radically different logical structure than the kind of conditional we have been discussing in the earlier parts of this paper'). However, the mere suggestion is unhelpful; it would have to be made good. There is no obvious way in which the premises of (32)—(33) in themselves differ logically from those of (29)-(31).33 I believe it would be best if strategy were not needed—that is, if one's conditional semantics itself predicted the distinction we are after, and if possible, by simply ruling the apparently valid instances of SDA as valid and the apparently invalid instances as invalid. And, I am delighted to say, the Event theory does just that. Since the SDA inference results in a conditional whose antecedent is logically stronger than that of the premise, we would at first expect my theory not to endorse SDA at all. There is little mystery about the invalidity of (32)—(33): the premises of (32)—(34) would be uttered precisely because their relevant antecedent disjuncts are not envisaged. For example, although Spain may or may not fight at all, her fighting on the Allied side is not a real possibility; the speaker does not envisage that disjunct. The premise is true because every envisaged Fight event is an Axis event. The conclusion's first conjunct is false because, now that the Antecedent Requirement newly forces the speaker to envisage an Allied event, there are Allied events that are not Axis events (indeed, of course, no Allied event is an Axis event). Similar reasoning holds for (33) and (34).34 33 Nute points out that the premise of (33) seems to imply 'If Gladhand runs for Congress, he will not run for the House". But I do not see why that is supposed to show that the premise is a different kind of conditional; it merely reflects our background knowledge that people who are running for the Senate do not (perhaps cannot) simultaneously run for the House. 34 For the same reason, of course, (32)—(34) afford counterexamples to Transitivity as well. Nute (1978: 320) considers a further apparent counterexample to SDA, attributed to Charles Kielkopf, that does not yield to the present treatment, (cont. on p.45)

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(If it seems peculiar—not to say suspicious, illegitimate, outrageous, etc.—to suppose that one can envisage a disjunction without envisaging one of its disjuncts, recall our discussion of negation in the context of Contraposition and semifactuals. We saw that a circumstance can be envisaged even though a close logical relative is not; it is quite common to envisage an event in which P but not any in which ~ P. Here too, we may be forced by the Antecedent Requirement to envisage a disjunction even though one of its disjuncts is still not a real possibility for us and so remains unenvisaged.) It remains to explain why the apparently valid instances of SDA are valid. But that is no trouble at all. What distinguishes those instances from the invalid ones is that each of the relevant antecedent disjuncts is envisaged as a real possibility at the time the premise is uttered. So each conjunct of the conclusion follows by vel-Introduction inside 'events' plus standard quantificational logic. For example, (29) is translated as (e E R)(In(e, You eat the broccoli v you eat the Brussels sprouts) D In(e, You get sick)) • '• (eeR)(In(e, You eat the broccoli) D In(e, You get sick)) & (e E R)(In(e, You eat the Brussels sprouts) D In(e, You get sick)) Take any event a 8 R in which you eat the broccoli. (There are such events, because the eating of broccoli is envisaged.) By vel-Introduction, in a you either eat the broccoli or eat the Brussels sprouts. ('Events' are closed under deduction even though they are not maxi(cont. from p.44) If we can clinch the title by beating team A or by beating team B, then we have two ways in which we can clinch the title. .'. If we can clinch the title by beating team A, then we have two ways in which we can clinch the title, and if we can clinch the title by beating team B, then we have two ways in which we can clinch the title. (Both conjuncts may be false.) But here I think it is clear that 'or' is conjunctive to begin with. That is because of the modal 'can' and the reification of'ways', i.e., possibilities. The premise is plausible only because its antecedent conjunctively enumerates the two ways. Consider a parallel argument minus the modalities: If Gore is elected or Bush is elected, then we will have two Presidents. .'. If Gore is elected, then we will have two Presidents, and if Bush is elected, then we will have two Presidents. There is no temptation to accept the premise.

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mally consistent, that is, not entire possible worlds.) So, by the premise, in a you get sick; a having been an arbitrarily chosen Broccoli event 8 R, it follows that every Broccoli event is a Sick event. Since the eating of Brussels sprouts is envisaged too, parallel reasoning establishes the conclusion's second conjunct. Thus, the Event theory has solved the SDA problem in what I take to be the optimal way. What is more, no other going semantic theory of conditionals has done so.35 Impossible Antecedents Natural-language conditionals can and sometimes do have impossible antecedents. A theory of conditionals should be able to accommodate them. But no mainstream semantic theory, truth-conditional or probabilistic, has accommodated them. In particular, possibleworlds accounts such as Stalnaker's or Lewis's would have to be augmented with impossible worlds (which Lewis himself (1986) would not tolerate). What says the Event theory? Two cases should be distinguished: those in which the antecedent is impossible but unbeknownst to speaker and hearer, and those in which the antecedent is known to be impossible. But in either case, the Event theory's epistemic origins should be of assistance, since one can envisage the impossible. Also, 'events' in my sense can themselves be impossible; they need not be possible states of affairs.3 In the first case, if the impossibility is unrecognized, and especially if no reasonable person has the cognitive means to recognize it, it can be envisaged as surely as can a possible event. This envisaging may be entirely rational. Or it may be irrational; but the envisaging, whether genuinely psychological or stylized in the way suggested earlier in this chapter, takes place none the less. And it still makes perfect sense to quantify over impossible envisaged events—even, in this first case, to call them 'real possibilities', for they can be epistemically real 35

In particular, neither Stalnaker's nor Lewis's systems allow valid instances of SDA (except that, as I shall execrate in Ch. 4, Lewis treats indicative conditionals as truthfunctional). Nute (1980) comes close to solving the SDA problem, by adopting a selection-functional semantics and pragmatically manipulating the selection function depending on comparative probabilities. His solution is in the spirit of mine—or if he likes, mine is in the spirit of his. 36 My ersatzing modal metaphysics (n. 4 above) is designed in part to provide for this. See Lycan and Shapiro (1986) and Lycan (1994: 38^41). Also, Lycan (1996) argues that it can be entirely rational to believe each of two mutually contradictory propositions. Thanks to JC Beall for reminding me to say something about impossible antecedents.

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possibilities. Obviously we cannot allow that they are closed under classical deduction, or all conditionals with impossible antecedents would come out trivially true, but a paraconsistent logic will serve instead.37 Thus, if there is a barber in the village of Alcala who shaves all and only those men who do not shave themselves, then he owns a razor and he earns money using it. (Note that neither of those consequent conjuncts follows logically from the antecedent except by classical contradiction explosion.) Every envisaged Barber event is a Razor event and a Money event. But it is false that if there is such a barber, he shaves every man in town, and of course that if there is such a barber, then David Lewis will be discovered to be the hereditary king of France. Also, of course, if there is such a barber he shaves himself, and if there is such a barber he does not shave himself, but our unawakened speaker and hearer will not have got that far. In the second case, that of an antecedent known to be impossible, the speaker is presumably either engaging in extreme fantasy or (more likely) assuming the antecedent for reasoning, probably for the very purpose of demonstrating its impossibility by Reductio. If so, then that speaker is not, in the genuine cognitive sense, considering the antecedent a real possibility or even an unreal one, but is 'envisaging' it only in the stylized sense introduced above. None the less, the envisaging itself is quite real, and it plays a key role in the substantive reasoning that follows. That the Event theory provides for impossible antecedents is, I believe, a considerable mark in its favor. 37 e.g. Priest (1988, 1995); Priest etal (1989). Though it itself is not a natural-language semantics, some of its techniques may be helpful for linguistic purposes.

3

Truth Conditions: Reality and Modus Ponens It is fair to say that the past thirty-five years of exciting research in the semantics and pragmatics of conditionals began with Adams (1965), Stalnaker (1968), and Lewis (1973). Those three works set the philosophical agenda that still occupies us, an agenda that has provided a highly unified vision and afforded some gratifying progress on a notoriously difficult cluster of problems despite the philosophers' inattention to syntax.

The Ramsey Test Perhaps embarrassing my claim of unification, the corpus consisting of those three essays offers not one but two paradigms for the semantic evaluation of conditionals. Adams offered an epistemic assertibility semantics for indicative conditionals, according to which a conditional A > C is assertible for a speaker S in direct proportion to the conditional probability Pr(C/A) relative to S's belief set. This is a probability-theoretic adaptation of F. P. Ramsey's (1931) now wellknown procedure. To evaluate A > C, add A hypothetically to your current belief set, make such revisions in your new total belief set as would be rationally required to preserve coherence while retaining A, and see whether C would be a member of the revised set. If it would, the conditional may be asserted; if not, not. (According to standard Bayesian probability theory, the value assigned to C by the subjective probability function representing the new belief set would be equal to the conditional probability Pr(C/A) according to the original belief set.) Following standard usage (see particularly the essays collected in Harper et al, 1981), I shall speak generically of the 'Ramsey Test' for the evaluation of conditionals. For Adams, indicative conditionals have only epistemic assertibility values determined by the Ramsey Test, and no truth values (he says nothing of subjunctive conditionals

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save that they differ from indicatives). This no-truth-value claim for indicatives—call it NTV—has caught on; I shall try to refute it in Chapter 4. Just after the publication of Adams's article, happily and inevitably, the theory of conditionals met possible-worlds semantics. Stalnaker essayed to recast the Ramsey Test in terms of alternative possible worlds and a selection function defined on them. To evaluate A > C, Stalnaker advised, hop over to the most similar world to ours at which A holds and see whether C holds there also. (This corresponds to Ramsey's adding A hypothetically to one's current belief set, making minimal revisions to preserve coherence, and seeing whether C is now a member.) Stalnaker introduces a function /that maps a world and an antecedent proposition onto a 'nearest' world (intuitively the antecedent-world that differs as little as possible from the home world). Thus A > C is true at world w just in case C is true at f(A,w). The resulting semantics brilliantly predicted the inferential failures, noted in Chapter 2, that characterize everyday English conditionals as opposed to either material or strict conditionals—most importantly, failure of Antecedent-Strengthening and Transitivity. Though similarly inspired by the Ramsey Test, Stalnaker did not join Adams in rejecting truth values for indicatives; rather, his semantics predicts conditionals' truth values rather elegantly, given our intuitive ideas of overall similarity of worlds. (Only later (1975) did Stalnaker address the 'indicative'/'subjunctive' distinction.) Lewis objected to several features of Stalnaker's semantics,1 notably to the assumption of a uniquely 'nearest' world and to the consequent licensing of Conditional Excluded Middle. To shed these, he introduced a notion of comparative similarity; for Lewis, A > C is true at a world w just in case some world at which A & C is true is closer or more similar to w than is any world at which A & ~C holds. Like Stalnaker, Lewis appealed to an intuitive, pre-analytical notion of overall similarity of worlds, much like overall similarity of cities or of planets. Thus one can see a smooth and natural line of conceptual development from Ramsey's procedure through Adams and Stalnaker to Lewis's comparative similarity theory. None the less, it should be clear that Lewis's view is quite different from Ramsey's and has very 1 This should not be taken to imply that Lewis's theory was merely a reaction to Stalnaker's. Lewis had been independently developing a similarity theory of conditionals by 1967.

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different implications for the semantics of conditionals. Viewed cold, without the sort of historical preface I have just provided, the Stalnaker-Lewis approach would not bring the Ramsey Test instantly to mind. Consider the passage of Stalnaker's in which he (somewhat laconically) makes the shift from Ramsey's epistemological method to a purely metaphysical truth condition: Now that we have found an answer to the question, 'How do we decide whether or not we believe a conditional statement?' the problem is to make the transition from belief conditions to truth conditions; that is, to find a set of truth conditions for statements having conditional form which explains why we use the method we do use to evaluate them. The concept of a possible world is just what we need to make this transition, since a possible world is the ontological analogue of a stock of hypothetical beliefs. The following set of truth conditions, using this notion, is a first approximation to the account I shall propose: Consider a possible world in which A is true, and which otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world, (p. 102) Two pages later Stalnaker confirms that this definition 'implies ... that there are no differences between the actual world and the selected world except those that are required, implicitly or explicitly, by the antecedent [A]', and that it 'suggest[s] ...that the selection is based on an ordering of possible worlds with respect to their resemblance to the base world'. The resulting metaphysical interpretation of Stalnaker's selectionfunction/deliberately distorts the Ramsey Test that initially motivated it, even if—contrahistorically—we are taking both as proposals of truth conditions. I shall exhibit a number of ways in which the two differ. (For now I leave open the question of which is better, though my own view is that a mixture is needed.) 1. The Ramsey Test requires us to stipulate our counterfactual antecedent and then make minimal revision of our beliefs. Stalnaker and Lewis require us to stipulate the counterfactual antecedent and then make minimal departure from reality. But those are two different revisions or departures, since we may be sure our beliefs do not entirely match reality. 2. Lewis took over Stalnaker's notion of metaphysical similarity, rejecting only the idea that for each world and counterfactual antecedent, there is a single most similar antecedent world. Now, in

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reviews and discussion notes, various early commentators urged counterexamples against Lewis's analysis, based on an intuitive notion of similarity. Examples: Suppose that due to the peculiar effects of a rare and eccentric compound of kryptonite, Superman is rendered incapable of lifting any object weighing more than 100 pounds and less than 100.1 pounds. He can, however, still lit all objects he could previously lift which weigh 100 pounds or less, or more than 100.5 pounds. Since his exposure, Superman has not had occasion to lift anything weighing over 100.1 pounds, but he has attempted to lift several objects weighing between 100 and 100.1 pounds. After lifting an object weighing exactly 100 pounds, Superman tells Lois Lane, [(!)] 'If that had been any heavier, I wouldn't have been able to lift it.' (Originally from George Schumm, cited as a personal communication in Nute, 1980fo: 70. Not quoted entirely verbatim, since I have cleaned up several small infelicities.) Both Stalnaker's and Lewis's analyses predict that Superman's conditional (1) is true, since worlds which differ minimally from the Superman-world are ones in which the last object weighs only infinitesimally more than 100 pounds. But (1) is false, since if the object were even a quarter pound or more heavier Superman would have no trouble with it. The counterfactual [(2)] 'If Nixon had pressed the button there would have been a nuclear holocaust' is true or can be imagined to be so. Now suppose that there never will be a nuclear holocaust. Then that counterfactual is, on Lewis' analysis, very likely false. For given any world in which antecedent and consequent are both true it will be easy to imagine a closer world in which the antecedent is true but the consequent false. For we need only imagine a change that prevents the holocaust but that does not require such a great divergence from reality. (Fine, 1975: 452) As I said, such arguments invoke an intuitive sense of overall metaphysical similarity, and most people I know share the intuitive judgments. But Lewis responded to such counterexamples by noting that similarity is said in many ways; counterfactuals mobilize their own distinctive similarity relation which may or may not coincide exactly with the everyday one. Unfortunately, Lewis has provided no independent characterization of this special notion of similarity; so, until and unless he does, his analysis is immunized against counterexample and so is untestable. This line of defense got aufgehoben into an articulate methodology in Lewis (1979), in which he sets out to investigate the extension of the (= his) similarity relation by

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examining some odd cases. He continues to call it 'similarity'. In my opinion he would be better advised to call it just 'closeness' or something equally abstract, since the notion is now almost purely formal.2 The upshot is that either the metaphysical-similarity analysis succumbs to counterexample or one has to make the 'similarity' relation ad hoc and unpredictable. The latter disjunct is hardly a fatal criticism—possibly not even a criticism at all, in view of the power of Lewis's counterfactual logic purely as a logic. My point in mentioning it is just to show a second way in which the metaphysical-similarity analysis differs from the Ramsey Test. The principal difference is that if we return to thinking of the selection of antecedent-worlds to be searched as an epistemic procedure, we can then bring to bear on it the epistemology that we already have. We know how to answer questions of what readjustments we ought to make in our total belief system in response to a troublesome epistemic impact; therefore, if we return to understanding the evaluation of counterfactuals in Ramsey's way, we would once again have an independent check on the correctness of our analysis' predictions, and so our theory would be testable again. Testability is fallibility, of course, and so a Ramsey-Test analysis might also be counterexampled. In fact, for fun, let us try the Ramsey Test on each of the foregoing two counterexample cases. In the Superman case, we start with the assumptions that (among other things) (K) Superman was affected in that peculiar way by the kryptonite, and (L) Superman did lift the last object. Suppose we add the new belief that (H) the last object was heavier (than 100 pounds). Which should Superman reject, epistemologically speaking, (K) or (L)? In his situation, uttering his counterfactual just after lifting the object, he would have to reject (K), not (L). Thus his counterfactual (1) comes out false; what is true from his point of view is rather (3) If that had been heavier, the kryptonite would not have affected me (in the way they said). Very bad; it seems the Ramsey-Test analysis is counterexampled too. On the other hand, the Ramsey Test is sensitive to the evaluator's epistemic circumstances. Suppose we are ourselves the evil enemies of 2

Lewis does try to spell out his own notion; the details are scrutinized and counterexamples offered by Kvart (1986).

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Superman who administered the kryptonite, and the time is just before Superman tackles the last object. We hypothetically add (H) to our belief systems. We know the kryptonite is online, and for that reason we would not suspend (K). Now, 'If that object were heavier than it is...'—what? Strictly speaking, one does not know; the answer depends on how much heavier. Consequently, sentence (1) has no truth value, though (1) a. If that object were a very tiny bit heavier than it is, Superman would not be able to lift it is true and (1) b. If that object were very much heavier than it is, Superman would not be able to lift it is false. Perhaps we should also assert (1) c. If that object were heavier than it is, Superman would probably be able to lift it, on the grounds that if the object were heavier than it is it would probably be more than .1 pounds heavier. Turning to Fine's holocaust case: Currently we believe that (N) there has not been and will never be a nuclear holocaust, and that (B) Nixon's red button is in good working order. We now stipulate that (P) Nixon did push the button. Clearly, that would be a reason to reject (B) rather than to reject (N). Here again, from our present epistemic point of view, things come out wrong; the Ramsey Test licenses (4) If Nixon had pushed the button, it would have been broken instead of Fine's opposing conditional (2). But the judgment depends on one's point of view. Suppose we are the technicians who have just installed the red button and we know (B) is true. Then from (B) and (P) we would infer the denial of (N), and assent to (2). 3. As we have just seen, the Ramsey Test infects conditionals with a relativity to epistemic situation; a conditional's truth value depends on the epistemic circumstances (though not directly on the psychological state) of its evaluator. This can be a valuable feature for the case of some conditionals. But it distinguishes that RamseyTest conditional from the Stalnaker-Lewis conditional, for, although

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the latter may exhibit some interest-or purpose-relativity owing to such relativity inherent in the notion of similarity, the latter is a different relativity from the Ramsey-Tester's thoroughgoing relativity to current evidence base. (Never forget the relativity of relativity.) 4. Finally, there are simple counterexamples to the identification of the metaphysical-similarity test with the Ramsey Test. Our last Superman example yields one. Consider the statement (5) If that object were any heavier than it is, it would be more than .1 pounds heavier. On the Ramsey Test (5) might well come out true, for we may suppose the Acme Object Company only machines their products in fairly gross multiples of weight, say at whole-pound intervals. Thus, if we add, 'This object is heavier than [ 100 pounds]' to our stock of beliefs, we would have to infer that the object weighs at least 101 pounds, and so assent to (5). But suppose the fact also is that it would be trivial for the Acme Company to reset their equipment to machine more finely. Then the similarity theorist can easily find a world metaphysically more similar to ours than is any 101-pound world, say a reset 100.1pound world, and so Stalnaker or Lewis would deny (5). Here is another counterexample, though slightly degenerate: I am attending a caucus of radical leftists, because a friend has begged me to come. My sympathies are less with the leftists than with the conservative establishment, but I do not mind attending just to see what the meeting is like. The fleeting thought crosses my mind that the meeting might have been infiltrated by the CIA. I immediately reject that suspicion as wild, but I say to myself, (6) If there were a CIA agent here, I'd be in trouble, since I justifiably reckon that my name would be put on a list of dangerous radicals. On the Ramsey criterion, my statement is true or at least assertible given my epistemic situation. But in fact there is a CIA agent present, and in fact unbeknownst to me I am not in any trouble for, surprisingly, the CIA is aware of my conservative sympathies. On Stalnaker-Lewis semantics, (6) is false, for it has a true antecedent and a false consequent. (Perhaps the simple Ramsey Test might be modified to allow such conditionals to be false despite their reasonableness. My own view can be seen as such a modification.)

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Yet a third counterexample can be adapted from Kratzer (1989: 625):3 Last year, a zebra escaped from the Hamburg zoo. The escape was made possible by a forgetful keeper who forgot to close the door of a compound containing zebras, giraffes, and gazelles. A zebra felt like escaping and took off. The other animals preferred to stay in captivity. Suppose now counterfactually that some other animal had escaped instead. Would it be another zebra? Not necessarily. I think it might have been a giraffe or a gazelle. Kratzer argues that this case refutes the similarity analysis, since a world in which a different zebra escapes is clearly more similar to our world than is one in which a giraffe or a gazelle escapes, other things being equal, but we do not accept (7) If a different animal had escaped instead, it would have been a zebra.4 The Ramsey Test again contrastingly gives the correct result: adding 'It was a different (individual) animal that escaped' to our existing stock of beliefs does not preserve the implication that a zebra escaped for, by hypothesis, we have no reason to think that zebras are more likely to escape than are giraffes or gazelles. Consider a slight variation. What if a second animal had escaped, in addition to the actual zebra? A world in which two zebras escape is intuitively more similar to the actual world than is one in which one zebra and one giraffe or gazelle escape. But again, (8) If a second animal had escaped as well, it would have been a zebra is not true, given our assumptions, and unlike the similarity analysis, the Ramsey Test predicts that adding 'A second animal escaped' does not result in an adjusted belief set containing A second zebra escaped', for the same reason as before. 3 A similar example is offered in Kvart (1986), as is an extended discussion of Fine's sort of case. 4 Kratzer's sentence 'The other animals preferred to stay in captivity" might be taken to suggest that the other species, giraffes and gazelles, are (as classes) more timid or docile, which might generate some sympathy for the test counterfactual she rejects; but her purpose makes it clear that 'other animals' means other individual animals. Anyone who thinks otherwise should simply omit the sentence from consideration. We shall also take the species escape-propensities of zebras, giraffes, and gazelles to be epistemically equal. On this understanding, Kratzer's case certainly does counterexample the similarity analysis.

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There are many more counterexamples where those came from. But having exhibited the sharp differences between the Ramsey Test and the metaphysical-similarity criterion, let us pause to see how my own account applies to such cases. Superman Superman's sentence (1) was 'If that had been any heavier, I wouldn't have been able to lift it', which on my view is true if every event 8 R in which the relevant object is heavier is one in which Superman fails to lift it. Thus my theory correctly predicts the falsity of (1), the whole trouble being that, given the very narrow window of inopportunity (Superman is disabled only within the 100-100.1 pound range), it is all too easy to envisage object-heavier events in which Superman lifts the object, namely events in which the object is heavier than 100.1 pounds but still within Superman's ordinary power to lift it. Nixon According to my theory, (2) ('If Nixon had pressed the button there would have been a nuclear holocaust') is true if every Buttonpressing event 8 R is a Holocaust event. And since a sincere utterer of that sentence is not envisaging a defect in the button, every Button-pressing event 8 R is a Holocaust event; the sentence comes out true as desired. (If an utterer did have some reason to think the button might be defective, (2) would not be true as uttered in that context.)

CIA My truth condition for (6) ('If there were a CIA agent here, I'd be in trouble') is that every CIA-agent event 8 R is a Trouble event. The situation here is like that of Marcia and the Venusians in Chapter 2: there is an event the speaker is entirely reasonable not to envisage, but which is, however improbably, actual. If we insist that all actual relevant events be included in R, envisaged or not (call this the Reality Requirement), then of course (6) comes out false, the fact being that there is a CIA agent present; the Reality Requirement forces us to include every CIA-agent event in R, but our protagonist is not in trouble in all or even in any of those events.

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Suspending the Reality Requirement, as I shall be urging we do, leaves (6) questionable, I think. (6) maybe false, since the speaker can envisage or should have envisaged a CIA agent hip enough to know of his conservative politics. On the other hand, if we tax the speaker with the latter possibility, he might respond, 'I meant, of course, an ordinary CIA agent who thinks s/he's watching an undifferentiated crowd of commies.' I believe (6) itself is indeterminate as between these two evaluations of R. Zebra (7) ('If a different animal had escaped instead, it would have been another zebra') comes out clearly false on my view, precisely because on our background assumptions it is just as easy to envisage a giraffe or gazelle escaping as it is another zebra. Likewise for (8) ('If a second animal had escaped...'). So far, then, my view is ahead of the similarity theory and ahead of the simple Ramsey Test on points.5 Let us now turn to the question of Modus Ponens.

The Reality Requirement and Modus Ponens Notice that Modus Ponens is prima facie embarrassed by the caucus example. If the Ramsey Test (taken as a criterion of truth, not just of assertibility) is applied to the example and accordingly my conditional (6) comes out true, Modus Ponens is thereby counterexampled; for 'There is a CIA agent here' is also true, but, by hypothesis, I am not in trouble. This is of course no embarrassment to Ramsey-Testers such as Adams himself who use the test only to determine assertibility, not truth value. Indeed, an assertibility analogue of Modus Ponens is unscathed by the example, since 'There is a CIA agent here' is unassertible even though actually true. Bear in mind that, rejecting NTV, 5 As this book went to press, I noticed McGee (2000), in which Vann McGee construct an ingenious counterexample to the Ramsey Test itself (not just to the Ramsey Test considered tendentiously as an account of truth conditions). It raises the very interestin issue of basing conditional beliefs on authoritative testimony. It may well be a counterexample to the Event theory. (McGee contends that it also counterexamples Stalnaker's similarity theory, but I do not find his argument convincing.) I shall have to take up the example, and the more general issue of testimony, in subsequent work.

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I join Stalnaker and Lewis in seeking the truth conditions, not the assertibility conditions, of my target sentences. So (very) much the worse, many philosophers will feel, for the Ramsey Test considered as determining truth value. It is now entirely obvious that the test must be modified in the direction of reality, at least to the extent of preventing true conditionals with true antecedents from having false consequents. Most philosophers will feel that the preservation of Modus Ponens is probably worth the slight ad hoc quality of stipulating that our reference class R shall contain all the actual relevant events whether they are 'envisaged' or not. The trade-off was noted (by Brian Chellas as I recall) during the discussion of an early version of Lycan (1984c) at the monumental 1978 University of Western Ontario Workshop on Conditionals and Pragmatics. The suggestion that a special adjustment was needed in a theory of conditionals in order to make Modus Ponens come out valid caused considerable merriment at the time. Adjustment or not, the idea of questioning Modus Ponens would until recently have seemed totally out of hand to virtually any philosopher—much on a par with speculating that there are true contradictions.5 Yet some considerably stronger doubt can be cast on Modus Ponens, without simply cleaving to the naive Ramsey Test—as soon as one realizes that indicative conditionals, like subjunctives, admit Sobel sequences (Sobel, 1970).7 To take the indicative analogue of Lewis's (1973) famous example: (9) a. If Albert comes to the party, it will be great. b. If Albert and Betty come to the party, it will be awful. c. If Albert and Betty and Carl come to the party, it will be great

All the members of such a sequence may be true. Now, consider the first two members of the foregoing sequence, and suppose that in fact Albert and Betty both do come to the party. The application of Modus 6 That last phrase is reprinted from Lycan (1984c). In light of the recent rise of dialetheism—precisely the view that there are true contradictions—and its impressive defense by Priest (1988, 1995) and others, perhaps a different example should be substituted, say that the events of Alice in Wonderland really happened and the Second World War did not. 7 Harman (1979) also rejects Modus Ponens, but only as a rule of logic as opposed to a matter of implication more broadly construed, on the grounds that 'if... then" is not a strictly logical connective. Happily, he argues for the latter claim by denying that 'if... then" is grammatically a sentence connective.

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Ponens to each of the two sentences in turn along with that fact yields a contradiction; but the two sentences are jointly compossible with the supposed fact, and so (unless Conjunction Reduction fails) Modus Ponens must be invalid. Our own theory could avoid this result only if we did impose the Reality Requirement, thus falsifying (9a) owing to the actual though quite unexpected attendance of Betty. One might think that Sobel sequences of subjunctives would have likewise refuted Modus Ponens for Lewis's system had Lewis not resourcefully stipulated that A > C is false when A & B > C and A & B are true. But Lewis's 'stipulation' was hardly ad hoc, for it falls right out of the basic metaphysical-similarity model for the interpretation of subjunctives. This illustrates yet a fifth difference between the metaphysical-similarity model and the Ramsey Test. It is fairly obvious why Sobel sequences do not embarrass Modus Ponens in evaluation by metaphysical similarity. Suppose A & B is true. Then it is false that some A & C world is closer to @ than is any A & ~C world. For by anyone's standards, any world is most similar to itself, and that goes for @; since by hypothesis @ is an A & B world and hence a ~C world, the A world more similar to @ is a ~C world rathe than a C world. So A > C is false, and Modus Ponens is legitimately saved. But now consider the simple Ramsey Test. When we affirm A > C, we do so because adding A to our present belief-store does not incline us to add B as well, and epistemically minimal coherence-adjustment preserves C. When we affirm A & B > C, we do so because adding A & B to our belief-store and performing coherence-adjustment does not preserve C. But, as I said in the previous section, reality has nothing to do with it. In particular, there is no counterpart to the Lewisian principle that the real world must be most similar to itself: the actual truth of A & B does nothing to show that the epistemically nearest A world is an A & B world and hence a ~C world. And the latter claim is false, for the epistemically nearest Aworld is not an A & B world. Thus the faithful (naive) Ramsey-Test interpretation of 'closeness' does impugn Modus Ponens, which is our fifth difference between it and the metaphysical-similarity interpretation. (And the point provides still further motivation for the Ramsey-Tester to contend, however implausibly, that Ramsey-Test conditionals, indicative or subjunctive as the case may be, have no truth value. Thus an argument against NTV is to that extent an argument against Modus Ponens. I shall be offering such arguments in the next chapter.)

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Truth Conditions What about my own mixed view? I translate A > C as (e E R )(In(e,A)Dln(e,C))

while A & B >~C comes out as (eER)(In(e,A&B)Dln(e,~C)) If the Reality Requirement is not imposed, both can be true, since in asserting the first I do not envisage a circumstance in which Betty comes, while (by the Antecedent Requirement) I cannot assert the second without envisaging such an event. So much the worse for Modus Ponens. I pause to rebut three obvious and closely related objections. First, it might be said ad hominem that even in the terms of my own account of conditionals, one could not assert both the first two propositions in the same breath, because the envisaging of Betty's attendance required by the second would make one reassess the first and take it back. I do not think the latter claim is correct. For as we shall see in Chapter 5, many English sentences belie the idea that a reference-class cannot be expanded within a single utterance context. Indeed, even within a single complex sentence the implicit reference-class parameter can take one value at one occurrence and a distinct, more inclusive value at a later occurrence, and without any doxastic change having taken place within the speaker: (10) I'll eat anything on pizza, even squid or bull's testicles, but not bull's testicles laced with ground glass. It would be misguided to demand that, after the speaker had finished uttering that sentence's concluding clause, the speaker take back its first clause as erroneous.8 Thus, no reason has been shown why the members of a Sobel sequence cannot be asserted in the same breath, if they do differ only by expansion of reference-class. Second, it may be complained that regardless of my particular theory, the first member of our sequence just is false, if the second 8

An attested example, overheard in line at the Subway sandwich shop: 'Subway Club with everything and also hot peppers, please." (The shop has a list of default ingredients, which the server will give you unless you refuse them, but also some other ingredients which you will be given only upon request.) It would be not only pedantic but inaccurate to insist that this sentence is redundant, especially since if the speaker had stopped after 'with everything", he would not have received hot peppers.

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member is true and Albert and Betty both do come to the party. (The claim would be that Stalnaker and Lewis are intuitively right, not just technically able to save Modus Ponens because they want to.) But one might make just the same move in defense of AntecedentStrengthening, and say that, once one sees the obviously false conclusion that follows, especially if its falsity is underscored by the realworld truth of its conjunctive antecedent, one will naturally take back the premise because the premise does not survive consideration of the new conjunct. And that move does not work. Antecedent-Strengthening is still invalid; we do not judge ordinary conditionals in this way, holding truth hostage to an infinitely open future. (On first hearing, some people object to such alleged counterinstances that, once one considers the quite properly derived conclusion, one sees that the premise is actually false after all—in initially assenting to it, one had mistakenly neglected the real possibility mentioned in the conclusion's expanded antecedent. That is a position one can take, certainly. But it has an ugly consequence: since any contingent conditional can have its antecedent strengthened in such a way as to produce an obvious falsehood, no contingent conditional is ever true. 'If you take this rifle and shoot that man right through the heart, he will die/.'. If you take this rifle and shoot that man right in the heart, but a team of nanobots who have travelled here from the future are standing by to repair all his tissue damage in a hundredth of a second, he will die.') Further, the second objection holds that whether (9a) is true, as uttered in a context where Betty's attendance is not envisaged, depends entirely on whether Betty will in fact come, however unlikely and unforeseeable that might be. That immediately generalizes to the view that any contingent conditional, no matter how highly assertible on the evidence possessed by any reasonable person, can be falsified by an actualized possibility, no matter how bizarre and remote that possibility might be. Such is the Reality Requirement, of course; and also, as a staunch truth-conditional semanticist, I endorse the separation of truth conditions from assertibility conditions. But simply to insist that the most highly assertible conditionals are falsified by the most bizarre and unlikely events is simply to insist that the Reality Requirement stands and that Modus Ponens must be valid—and thus to beg the question. At best it is a stand-off. Of course it is hardly remarkable that highly probable propositions might still turn out to be false. Rather, the point is that most people at

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least feel the pull of epistemic theories of indicatives.9 What would be tendentious is for someone to insist on radically non-epistemic truth conditions for indicatives. (Often people suggest that the 'indicative'/ 'subjunctive' distinction lines up well with the epistemic/metaphysical distinction.) And I see little difference between insisting on radically non-epistemic truth conditions and just announcing that if a conditional in fact has a true antecedent and a false consequent, whatever the speaker's epistemic circumstances, it is false—which would beg the question. Still further, as we shall see in the next section, adjoining Sobel sequence members can be concatenated into intuitively true conjunctions. The third objection, still in a similar vein, is that a sincere utterer of the first member of our sequence is assuming, however tacitly, that Betty will not come. That is probably true (though we would do well to observe the distinction between assuming-not and merely not assuming). But the point would be damaging to my case only if it showed that Stalnaker and Lewis are right, and the first two members of our sequence as given cannot after all both be true in the case where Albert and Betty both do come. What is true, the objector may say, is only that (11) If Albert comes to the party and Betty does not, it will be great is compatible jointly with the other two propositions. But this objection assumes that for the original first sentence to be true in the case at hand, it must be elliptical for (11), which is a very daring claim, much stronger than merely the observation that an utterer of the first sentence in some sense tacitly assumes that Betty will not come. First, actual semantic ellipsis is rare and computationally expensive (the former because the latter, I suppose). Second, once we go into the business of seeing ellipsis in the antecedent whenever a conditional is threatened by Antecedent-Strengthening, we find there is no end to it. Since every contingent conditional has some potential defeater or other, we would again have to say that every apparently contingent conditional is really elliptical for a necessary one; there are no contingently true conditionals. I take that to be unacceptable.10 9

Thanks to Walter Sinnott-Armstrong (1999) for requiring this clarification. David Sanford has pointed out to me that the ellipsis need not be so specific, making reference to Betty in particular. It might be as simple as, 'If Albert comes to the party and 10

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Now again, if the Reality Requirement is imposed, the restriction class R must contain all relevant actual circumstances. In a Sobel case, at least one such circumstance is one in which A & B holds. That circumstance would have to be included in R when we were evaluating even the first of our two conditionals, and would falsify that conditional. End of Modus Ponens problem. In my experience, people's intuitions divide over indicative Sobel sequences. Sometimes people side with the similarity theory and insist that earlier members of a sequence be rejected when later ones are accepted. Other people agree with my own feeling that each member of the sequence is still true taken on its own. The irenic thing would be to claim a pragmatic ambiguity, granting that the Reality Requirement is an option; we might concede that Modus Ponens is valid for indicatives on their Realistic understandings, while insisting that it is invalid for indicatives on their Ramseyan Libertine understandings. Yet I believe the latter predominate and the former are at best hard to hear. Moreover, and more to the point, the Sobel argument can be strengthened, as we shall now see. Consider a sentence that was put to me (years ago) by Allan Gibbard in conversation:11 (12) I'll be polite even if you insult me, but I won't be polite if you insult my wife. (12) is perfectly consistent, and creates an immediate objection to Modus Ponens. Suppose I token (12) and you do proceed to insult both me and my wife, whereupon I am very impolite. Then, although (12) was presumably true, its first surface conjunct Til be polite (even) if you insult me' has a true antecedent and a false consequent, and Modus Ponens leads to contradiction. Somehow, (12)'s second conjunct cancels or suspends the Reality Requirement we would ordinarily impose on the first. Notice too that the problem is not generated by the presence of 'even'; it persists when 'even' is deleted from (12); call the result (12—): Til be polite if you insult me, but I won't be polite if you insult my wife.' nothing interferes,...' But I still have the same two basic objections. It is hard to swallow that the verb 'interfere' appears anywhere in the underlying structure of (9a); and 'nothing interferes" would have to be taken so strongly as to make (9a) a necessary truth (else it could be defeated in turn). 11

A similar example is given by Frank Jackson (1979: 579).

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(12—) poses a problem for my Event theory also (as was Gibbard's original intention in exhibiting (12) to me). My official analysans for (12-) is (C E R) (In(e, you insult me) D In(e, I am polite)) &(£ E R) (In(f, you insult my wife) D In(f, ~(I am polite))). 12 This formula entails that there is no event 8 R in which you insult both me and my wife. Thus, assuming the Reality Requirement, it is incompatible with your actually being so comprehensively insulting; but intuitively (12—) can have been true even if you do unexpectedly turn out to do that, so long as your insulting my wife was considered a remoter possibility than your merely insulting me.13 Lycan (1984c) made the following obvious move in response to (12): to claim that.. .'R'. .. changes its value from the first conjunct to the secon conjunct, the idea being that an utterer of [(12)], while tokening the first conjunct, did not envisage his hearer's insulting his wife, but suddenly cam to envisage it and therefore uttered the second conjunct. Though perhaps a bit forced, this is not implausible;... the intuitive content of [(12)] could then be expressed as I do not as things are envisage any real and relevant possibility that I will not be polite, not even one in which you insult me, but if I now make myself envisage one in which you insult my wife, I do not see myself being polite in any such event. That is not too bad as a gloss... (p. 447; except that the original had 'envision' instead of'envisage') This parameter-shift hypothesis may or may not seem persuasive as a move against (12). But, happily for the attack on Modus Ponens, the same move does not work for (12—). 14 For so long as the Reality Requirement continues in force, my official analysans still contradicts the fact of your being doubly insulting. As I have said, (12—)'s second 12 This formula omits a clause I posited in Lycan (1984c), designed to capture the force of even." We shall return to 'even' and 'even if in Chapter 5. 13 JC Beall (in correspondence) has raised the question of whether 'but' in (12—) commutes. My theory predicts that strictly it does not. For the reference class R underlying the first conjunct includes no Wife events but widens in the second conjunct to include some. In the commutation of (12—)—'I won't be polite if you insult my wife, but I'll be polite if you insult me'—the first conjunct's reference class includes Wife events but no Me events, then widens to include some Me events. Distinct reference classes, so, strictly, different proposition expressed. Happily, I think the prediction comes true: I do not hear (12—) and its commutation as synonymous (though an opponent could argue that that is solely because of the usual asymmetric contrastive function of'but'). 14 The difference was pointed out to me by Chris Gauker.

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clause somehow removes the Reality Requirement from the first clause, and so much the worse for Modus Ponens. The foregoing treatment may seem unconvincing if one takes a very literal view of 'envisaging'. It is psychologically unlikely that anyone could utter the Gibbard sentence (12) without actually having considered the possibility that the hearer might insult his wife; the speaker does not literally first come to think of that possibility in mid-sentence. But I have not intended my reference-class parameter to be understood in so crude and concrete a way. 'Envisaging' is to some extent a stylized matter of conversational pose; I tried to indicate this by the wording of my English gloss on (12). That raises the question of exactly what 'envisaging' is, then. But as I mentioned in connection with Sobel sequences, there are plenty of examples even of single sentences within which quantifier restriction classes are widened, without any actual doxastic change occurring episodically in the speaker. It is easy to see that (12—) is cognate with Antecedent-Strengthening and with Sobel sequences; if we take two adjacent members of a Sobel sequence and conjoin them, we get a sentence like (12—). For that reason, one might say, Gibbard's example adds little to the case I had already made against Modus Ponens. But (12—) does have its own dialectical point. Since it is a single sentence that could reasonably and unequivocally be tokened on a single occasion, there is no temptation to protest (as people sometimes do in response to failure of Antecedent-Strengthening or to standard Sobel sequences) that we cannot legitimately lump together premises and conclusions that would actually be accepted only by different people in different epistemic situations. For 'envisagings' do often switch within one and the same context, in the way I have illustrated earlier. Thus one should accept (12—) as a counterexample even if one's intuitions about Sobel sequences are equivocal; and when one does, it helps to firm up one's Ramseyan intuitions about Sobel sequences. Notice that the undermining of Modus Ponens by Sobel sequences and by sentences like (12) is already foretold by the well-known failure of Antecedent-Strengthening. For that failure is what gives rise to Sobel sequences in the first place. Only the wiping out of earlier contrary sequence members by metaphysical-similarity analysis saves Antecedent-Strengthening from itself being a counterexample to Modus Ponens. As we have seen, Antecedent-Strengthening does constitute a counterexample either on the Ramsey Test or on our analysis sans Reality Requirement.

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In fact, it is odd that logicians were, comparatively, so compliant in abandoning Antecedent-Strengthening and the rest, but at the same time entirely unaware of the exactly similar objection to Modus Ponens. It is of course possible to construct a logic that invalidates Antecedent-Strengthening while preserving Modus Ponens—Stalnaker and Lewis, after all, did so—but it is hard to see why anyone would want to, save for being tacitly scandalized by the very idea of rejecting Modus Ponens. Once one sees how and why the contextual shift of background assumptions leaves room for an AntecedentStrengthened conclusion to be false, it seems arbitrary to insist that the same does not happen to Modus Ponens. Moreover, I maintain, any argument in defense of Modus Ponens against my Sobelian counterexamples has an exactly parallel argument in defense of Antecedent-Strengthening. If one upholds the validity of Modus Ponens by explaining the counterexamples away, one will have to uphold Antecedent-Strengthening in the same way, and reject Stalnaker's and Lewis's conditional logics as well, reverting to the logic of the nomological conditional or something very like it. I turn to a different type of objection to Modus Ponens. In a now wellknown article, Vann McGee (1985) has offered a distinctive type of alleged counterexample to Modus Ponens, featuring major premises whose consequents are themselves conditionals. A typical instance is (regarding the 1980 Presidential campaign between Ronald Reagan and Jimmy Carter, with Republican John Anderson a distant third): If a Republican wins the election, then if it's not Reagan who wins, it will be Anderson. A Republican will win. .'. If it's not Reagan who wins, it will be Anderson. (McGee, 1985: 462) Premises true, conclusion false (since the truth was rather that if Reagan had not won, Carter would have). McGee couches his own discussion mainly in terms of assertibility rather than of truth, and if indeed what is in question is an assertibility-analogue of Modus Ponens rather than Modus Ponens itself, his examples are highly disputable.15 But if we hew to the line of truth 15

e.g. Sinnott-Armstrong etal (1986); Lowe (1987); Over (1987).

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conditions, the examples are powerful. Maddening as they are on first consideration, they seem to refute not only Modus Ponens but (of course) every analysis of conditionals that unconditionally licenses Modus Ponens—which is to say, Stalnaker's, Lewis's and every other mainstream theory to date. I believe McGee's cases are genuine counterexamples to Modus Ponens and to the theories that license it. I think the two premises of his Republican argument are just plain true and the conclusion just plain false.15 Moreover—initially to my own surprise—my own theory not only predicts but explains McGee's data. In my most straightforward terms, the Republican argument is formalized as (C E R) (In(e, a Republican wins) D In(e, (£ E R) (In(f, ~(Reagan wins)) D In(f, Anderson wins))) (3eE@) (In(e, a Republican wins)) [i.e. A Republican will win] • '•(fen) ( m (f> ~ (Reagan wins)) D In(f, Anderson wins)) When I first glanced at McGee's examples, I assumed that like my own they involved questioning the Reality Requirement. But the foregoing translation shows that they do not; for we may allow the Requirement to be imposed, indeed insist that all actual circumstances be included on the conclusion's reference-class, and the conclusion is if anything even more obviously false than otherwise. McGee's examples work on a different principle entirely. (Here we have a jubilant case of confirming a 'novel prediction'; my theory was not designed to explain facts like McGee's, for those facts had never remotely occurred to me when I devised the theory in the 1970s. To my shame, I had not even considered questions of iteration.) We must begin by asking whether the parameter R shifts its reference from its first occurrence to its second within the major premise; to avoid begging that question, let us hereafter represent the second occurrence instead by '.R*,' leaving open the question of whether R* = R. There is excellent reason to think that the parameter does shift. The premise's main antecedent should have the effect of closing off the subclass of initially envisaged Democratic victories. That is, although the conditional as a whole envisages both Republican and Democratic victories as 'real and relevant possibilities', the nested consequent 16 It is of course plain that the Republican argument is no counterexample when the conditionals are read materially, for the conclusion is true on that reading; I assume with McGee that the conditionals are stronger than horseshoes.

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conditional is explicitly premised on a Republican victory, and we are no longer to envisage otherwise when we evaluate it in its embedded state. Let us see what happens to the argument. If R* does thus exclude Democratic victories, then every non-Reagan circumstance is indeed an Anderson circumstance, and the first premise as a whole is plainly true. The second premise of course remains simple fact. But the conclusion is false, and for just the right reason: since a Carter victory is still a blatantly real and relevant possibility, one could hardly say that every non-Reagan event is an Anderson event. And if the conclusion is considered on its own, Anderson's victory not being intrinsically a real possibility, the opposite is true: every non-Reagan circumstance is a Carter circumstance, which neatly assures the truth of 'If Reagan does not win then Carter will'. The argument fails because the premise's consequent is evaluated under a restricting assumption that does not apply to the same formula when it stands alone as the argument's conclusion. And both the restricting assumption and its removal are independently and well motivated by our intuitive ideas about 'real and relevant possibilities'. I turn without delay to meet an obvious objection: R* ^ R, I have argued. Therefore someone may complain (exactly as some hearers have complained against counterexamples to Antecedent-Strengthening, Transitivity, and the like) that since the background assumptions held fixed are varied between premise and conclusion, the Republican argument commits a fallacy of equivocation by tacit parameter shift, and so is not a counterexample to Modus Ponens, because it is no longer an instance of Modus Ponens. Indeed, our present analysis brings the parameter shift into glaring relief: the premise's consequent conditional has R* as its parameter but the conclusion still has R, and the two are distinct. In the latter, technical sense the point is correct. (Cf. my remarks on my own counterexample to Transitivity in the previous chapter, which just as strictly speaking is not after all an instance of Transitivity. And as always, the very same point can be made against counterexamples to Antecedent-Strengthening.) But that very strict sense of 'instance' is neither specified nor intended in logic textbooks that present Modus Ponens as a valid form of inference. What students and professional philosophers have always been told is that, barring equivocation or overt indexicals, arguments of the sentential surface form A > B, A / .'. B are valid arguments, period. And that is what is

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refuted by McGee's examples. One can continue to insist that Modus Ponens is valid for the strict sense of 'instance', but at the price of keeping us from telling easily and uncontroversially when a set of ordinary English sentences is an 'instance' of an argument form. So I shall continue to use 'instance' in the ordinary loose and popular sense. Now, suppose that contrary to our earlier argument the parameter does not shift—R* = R, and the set of envisaged relevant possibilities remains constant even for the consequent conditional. Even so, although a Carter victory stays envisaged throughout, any R-event in which a Republican wins has presumably got to be such that, in it, any event in which Reagan does not win is one in which Anderson does. So the first premise seems true even on its dubious non-shifting interpretation and the counterexample goes through as before. Perhaps our presumption is wrong, and even in a Republican Revent, the class R continues to contain Democrat circumstances; the idea would be that even in the in-fact-Republican circumstance, a Carter victory would still count as a real possibility. (And we are, after all, trying to stipulate that R remains fixed throughout the argument.) That would yield a sense in which the first premise is false, and false for much the same reason that the conclusion is false. Perhaps one can hear that sense, given suitable emphasis: '(Even) if (in fact) a Republican is going to win the election, then the following is a true thing to say: If it's not Reagan who wins, it will be Anderson.' I doubt linguistically that McGee's premise can express that last paraphrase; I doubt on account of my views on the control of R that the non-shifting interpretation of the premise is possible; and I think the latter impossibility explains the former. But even if I am wrong, the more natural reading of the premise and the more intuitive shifting interpretation each dominate heavily, conspiring to vindicate and explain McGee's data. This I take to be a triumph for my semantics at the expense of Stalnaker and Lewis, the greater for its being entirely unanticipated.

Gallimore's Problem Our approach has been to fix the value of our parameter '.R' by a mixture of epistemic with real-world factual considerations. Our standard gloss on '(C E R)' is 'For any event that is a real and relevant

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possibility,...', and I have suggested tying the notion of a 'real and relevant possibility' to that of what would be foreseen or envisaged in the context by a 'reasonable person' or the like. Richard Gallimore has (in conversation) raised an objection to this, and his point illustrates yet a sixth difference between the metaphysical-similarity model and the Ramsey Test, though perhaps it actually boils down to the same variety as our CIA example above. Consider two propositions that are for us mutually irrelevant: for example, 'I will finish this chapter today' and 'Norway will have an unusually early autumn in 2010'. Normally we would not assent to their conditional (13) If I finish this chapter today, Norway will have an unusually early autumn in 2010, but would count it as false or truth-valueless. However, suppose that unbeknownst to us and even to the world's most competent physicists, there are arcane laws of nature L such that the conjunction of L with my finishing this chapter today entails Norway's having the early autumn; that is, (13)'s antecedent happens to lead by law to (13)'s consequent, even though no one would rationally suppose that. Stalnaker or Lewis would count the conditional (13) as straightforwardly true, since a world in which I finish the chapter but Norway fails to have the early autumn would have to differ from our world in its laws of nature (a large difference). So for the similarity theorist (13) is true even though no one knows that, no one could even guess it, and everyone denies it. Denial of (13) is just a case of perfectly well justified but false belief. But now consider the simple Ramsey Test. We would affirm (13) only if adding 'I will finish...' to our present belief-store and performing epistemically minimal coherence-adjustment requires the further addition of 'Norway will have...' (I assume 'Norway will have ...' was not already among our beliefs; otherwise (13) would be a semifactual.) But here as usual, reality has nothing to do with it, and in particular the mere existence of the arcane laws L does nothing to make (13) either true or assertible. If we understand our notion of a 'real and relevant possibility' purely in terms of what a reasonable person would foresee, our treatment of (13) would go the same way for the same reason; by hypothesis, no reasonable person would foresee the existence of L. So, there will be envisaged circumstances in which Norway does have the

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early autumn and envisaged circumstances in which it does not, and (13) comes out false. Now, two questions arise. (Ql) Is there really a sense in which (13) is true? (Q2) Is there really a sense in which (13) is false? Both questions are disputed, especially since the NTV faction says nay to both. It seems undeniable that there is at least a sense in which (13) is true, since (13) 's antecedent leads by strict law to its consequent. (This is one in the eye for NTV, I should say. To continue to maintain the truth-valuelessness of indicative conditionals, NTV would have to deny that indicative conditionals follow from the corresponding nomologically strict conditionals, which would be very strange.) By the same token, the truth of (13) in any sense precludes one's being a thoroughgoing Ramsey-Tester even if contra NTV one understands the test as delivering truth values for conditionals. And as regards my own view, we must impose the Reality Requirement in order to guarantee a sense in which (13) is true. Indeed, we must do more than that, for we must ensure that the arcane laws L get applied to all the Finish events, which they will not unless they are themselves made officially relevant possibilities. We can do that by stipulating that when the Reality Requirement is in effect, the laws of nature are also included in R. Thus it seems we do not have the option of junking the Reality Requirement entirely; we have to grant that it is sometimes imposed, and in this strengthened form. To (Q2), then—can (13) be false despite L? That is a tough one, an its toughness embarrasses largely epistemic accounts like mine. It is perhaps tempting to concede that, given L, there is not any sense in which (13) is false, even though (13) is eminently deniable, especially since, as I said, (13) could not otherwise be held to follow from the corresponding nomological. But I maintain that there is a sense in which (13) is false. This should become clearer once we see what principle stands behind the reflex idea that indicative conditionals are entailed by the corresponding nomologicals. Of course we get a sense in which (13) is false as soon as we drop the Reality Requirement. But, interestingly, we do not have to go that far: (13) does not simply stand or fall with the Reality Requirement. The Requirement alone does not enforce the truth of (13); we needed the additional stipulation that the laws of nature are relevant. The Requirement does ensure that at @ it is not only true but nomologically necessary that Finish D Norway. But on my semantics (13) is true iff every Finish circumstance that is a 'real and relevant' possibility is also

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a Norway circumstance. And some of those Finish circumstances are non-actual, so the Reality Requirement by itself (without the added stipulation) leaves it open that, in at least one of them, Norway fails to have an early autumn. The problem is only that such a circumstance is nomologically impossible. Now, why should nomological impossibility exclude a circumstance from being a 'real and relevant' case? Remember that reality has already been taken care of, so far as Gallimore's Problem is concerned; we have been forced to envisage all the relevant events that actually obtain. But nothing forces us to envisage everything that is nomologically necessary in addition, especially in light of the epistemic spirit of my theory given the (by hypothesis) epistemically remote nature of the laws L. (Here is yet another divergence of our theory from the metaphysical-similarity paradigm.) There is at least one Finish event that is a real and relevant possibility but which is not also a Norway event, even though it is in fact nomologically impossible—quite consistently with the Reality Requirement. And so in that sense, (13) is false after all despite the continued imposition of the Reality Requirement. Of course, if one stoutly denies that there is any sense in which (13) is false, one will not have been persuaded by the preceding paragraph. All that has strictly been shown is that my theory can provide such a sense, which was half of the alleged problem to begin with. But I think it helps at least a bit that the largely epistemic sense provided persists even when my usual nod to reality, the Reality Requirement, is in force. Further issues regarding the Reality Requirement will be taken up in connection with 'even if conditionals in Chapter 5. But for now this concludes my case against Modus Ponens. I have not pursued a scorched-earth policy, for I have granted the possibility that on certain subordinate interpretations, Modus Ponens is a valid form of inference. And obviously I grant that textbook examples of Modus Ponens are themselves valid arguments. I deny only that they are valid simply in virtue of having the form A > B, A/.'. B.17 Modus Ponens is not per se a valid form of inference. But after all, following the demise of Antecedent-Strengthening and Transitivity, Modus Ponens was bound to be the next domino. 17 McGee points out the utter presumptuousness of our usual method in elementary logic—that of looking at two or three very simple instances of an inference-schema, seeing that those two or three instances are valid arguments, and directly inferring the general validity of the schema—without even considering e.g. compound antecedents and consequents. When you think about it, that presumption is very dangerous.

4

In Defense of Truth Value NTVowes much of its popularity, as well as its birth, to E. W. Adams— somewhat ironically, since his paper kicked off the contemporary literature on the truth conditions of conditionals.1 Dormant for some years, NTV was revived by Gibbard (1981) and further fomented by Appiah (1985), Edgington (1986), and Bennett (1988). As I have said, I reject NTV. In this chapter I shall offer some arguments against it, and then rebut the arguments for it, so that I may move on to my further truth-conditional investigations with a clear conscience. One qualification:2 I have characterized 'NTV as the thesis that indicative conditionals have no truth values. Against that, it may be that all indicative conditionals have truth values, but it may also be that some indicatives have truth values and some do not. Suppose, for example, that Emotivism is true and moral judgments lack truth value. Then a conditional with a moral judgment for a consequent ('If he has lied to his mother, that is morally wrong') would presumably lack truth value also, even if NTV is generally false. We should understand NTV firmly as the claim that no indicative conditional has a truth value. But even here there are subtleties, because still in the spirit of NTV, someone might grant that non-contingent conditionals, perhaps just those that are logical truths or their negations, have truth values even though contingent conditionals do not. I shall take this up below, in the form of an objection. Contra NTV The arguments against NTV are as follows. 1. Philosophical Peculiarity Of course some philosophers question the truth-conditional view of meaning (some question even the health of the very notion of truth). 1 2

Appiah (1985) notes that the view was anticipated by Finch (1957-8). Here I am indebted to David Sanford.

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But if one accepts the truth-conditional view generally, as I do, the suggestion that, alone among English declarative sentences, indicative conditionals by their nature lack truth values is peculiar to say the least. Why would just one type of sentence, though 'assertible' under specifiable conditions, be barred from truth and falsity, especially when sentences of that type admittedly have probabilities, interact in truth-seeking discourse with uncontroversially truth-valued sentences, are agreed on or disagreed over, figure in valid argument, etc.? Moreover it is very odd to talk, as Adams and Gibbard do, of a sentence's 'probability' when that term does not mean probability of being true. Further, NTV denies indicative conditionals a home in possible-worlds semantics or in any other version of a prepositional theory of meaning, since as Gibbard himself puts it, NTV holds that indicatives (alone among English sentences as I said) do not express propositions at all. Even if one rejects all propositional and truthconditional theories and inclines toward pure assertibility semantics for all of natural language, one will be hard put to explain why the assertibility-not-truth view should be so much more obviously right for indicative conditionals than for any other sentence. And consider again the matter of indicatives that are logically or otherwise necessarily true, or (not to beg the question) that would normally be regarded even by someone otherwise inclined toward NTV as being non-contingent and maximally assertible (assertible no matter what). I think NTV ought to make an exception here; if one is generally a truth-conditional semanticist and one's usual logic is based on the idea of truth preservation, then a sentence derivable from no premises or ruled true by one's semantics alone should be counted as true. But this would increase the philosophical peculiarity of the now thus restricted NTV: why would just the class of contingent indicatives be so strongly set apart from other English sentences, including even necessary indicatives? 2. Linguistic Bizarreness The claim that ordinary conditional sentences lack truth values is grossly implausible on linguistic grounds. If we maintain that a conditional like (1 a) lacks truth value even though the corresponding temporal sentence (\b) has one, we shall have to attribute that vast semantic difference solely to the lexical difference between 'if and 'when'.

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(1) a. I will leave if you leave. b. I will leave when you leave. NTV advocates are going to have to explain how it is that those two words could have virtually the same syntax but differ so drastically in their semantic treatment. Moreover and more to the point, Chapters 1 and 2 have argued that 'if and 'when' exhibit dramatic semantic similarities as well, especially in regard to modification, pronominalization, and relativization (the second and third of these both requiring semantical coreference). It would be amazing if (la) and (Ib) were semantically as similar as they have been shown to be, and yet (la) did not even have a truth condition at all.3 And consider the locution 'if and when', as in 'If and when she submits a paper, we'll read it within a month'; does NTV award that sentence a truth value, or not? Further, NTV would have to be extended to 'unless' sentences (cf. 'unless and until') and to all variants of the 'in the event that' construction (Til leave in the event that she does', 'In that case I'll leave too', etc.), as well as 'on the condition that' and the like. The crass unlinguisticness of NTV becomes all the more evident when one applies it to the numerous languages that employ the same word for our 'if and 'when.'4 NTV would have it that a temporal/ conditional sentence of such a language has a truth condition when understood temporally, but entirely lacks one when understood conditionally. Yet speakers of such languages usually do not trouble to notice the distinction, treating 'when' as simply a factive variant of 'if;' the distinction is virtually pragmatic, resolved automatically by context without anyone's noticing. Suppose you tried to tell a linguist who is a native speaker of such a language that actually the ambiguity is very dramatic, not just semantic but hyper-or metasemantic in that one of the two readings has an entirely different kind of meaning from the other's. The linguist would think you were crazy.

3 Again, I am assuming that linguistic semantics is truth-conditional overall. The present point obviously would not impress someone who favored an assertibility semantics acros the board. My complaint is against the idea that indicative conditionals are a surd in truthconditional semantics. 4 Traugott (1985) reports that those languages include Hittite, Swahili and Tagalog. Comrie (1986) adds Mandarin; he further maintains that even German wenn has a tempora as well as a conditional sense, though surely wann is more common.

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3. Conditional Speech Acts Conditionals can be used to perform speech acts among whose felicity conditions are sincerity and truth. Promising and vowing are the obvious examples: (2) M A R S H A : And what if I leave? Can I count on you? J O H N : I swear it: In that case, I'll leave with you. A truth-valueless, indeed truth-conditionless, sentence, is not a good one with which to undertake profound obligations. Suppose Marsha leaves, but John breaks his promise and stays. How can the notion of breaking a promise be explained except in terms of the truth value of the promise's complement? (The NTV defender is not without resources here. S/he could appeal to the idea of a conditional promise and maintain that, for a conditional promise, to break it is only not to make its consequent false when its antecedent is true. But some such extra apparatus is required, and it is a bit ad hoc.) These first three considerations of prima facie plausibility are hardly decisive. They could be overridden by a convincing direct argument for NTV. But a convincing direct argument would be needed. 4. The Many Parallels between Indicatives and Subjunctives On the assumption (granted by Gibbard and uncontested by Adams) that subjunctive conditionals have truth conditions of the usual sort, NTV entails that indicative conditionals and subjunctives differ from each other in as fundamental a semantical way as any types of sentence could possibly differ from each other. (Gibbard seems to acknowledge this: He maintains that the superficial similarities between indicatives and subjunctives 'hide... a profound semantic difference' and are 'little more than a coincidence' (1981: 211). If Gibbard did not exist, I would have to invent him.) But that consequence of NTV makes nonsense of the glaring parallels and analogies between indicatives and subjunctives.5 Indicatives and subjunctives are expressed by the same lexemes, not only in English but in most other languages. Indicatives and subjunctives have the same syntax but for their distinctive tense and aspect differences, including their modification by 'only' and 'even'. More importantly, they have 5

This point is emphasized to effect by Stalnaker (1984: 111-12).

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virtually the same logic. And they admit almost all the same paraphrases. All this is surprising, to say the least, if the two kinds of sentences differ semantically as far as any kinds of sentences might possibly differ. The matter is aggravated if we are persuaded by Dudman's (1983, 1984a) argument that future indicatives and the corresponding future subjunctives are semantically identical (more on this in Chapter 7). The NTV defender would have to narrow her/his thesis, and maintain just that non-future indicatives lack truth value. Thus, s/he would have to hold that 'If you dropped that vase [at time i\, your father found out' lacks truth value, even though 'If you drop that vase, your father will find out' said prior to tis true (or false). It is hard to believe that those two sentences bear 'a profound semantic difference' from each other and that their similarities are 'little more than a coincidence'. 5. Embedding Phenomena Indicative conditionals embed in longer sentences, both longer conditionals and complex sentences of other sorts—including, Kremer (1987) points out, propositional-attitude constructions other than belief contexts.5 That fact creates two problems for NTV: (i) when a conditional occurs embedded in that way, it is not asserted, and so we will need rules for projecting assertibility values through sentential compounding that do not presuppose that indicative conditionals ever are actually asserted; (ii) a three-valued logic would be needed to accommodate embedded constructions. NTV would have to confront such sentences as (3) Marsha believes that John will leave if she does, and Sharon dislikes John so much that if she concurs, she will try to persuade Marsha to leave. 6. Redundant Equivalences Many indicative conditionals are logically equivalent to briefer nonconditional sentences. Consider 6 The significance of Kremer's point is that, although the NTV defender can plausibly construe the belief that if A, B as a subjective probability in the sense of a cognitive disposition, rather than as belief in a true or false proposition, the same treatment will not work for hoping that if A, B, wondering whether if A, B, being embarrassed that if A, B, etc.

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In Defense of Truth Value (4) a. John murdered Sandra if anyone did. b. No one other than John murdered Sandra. (5) a. If Reagan is a Russian spy, no one knows he is. (Appiah, 1985: 164) b. No one knows that Reagan is a Russian spy.

I do not see how Adams can accommodate such equivalences, unless in some defensible three-valued logic a truth-valueless sentence can be strictly, logically equivalent to a truth (and such a logic is surely not what Adams has in mind). Further, many conditionals are equivalent to the corresponding disjunctions. Are the disjunctions truth-valueless, or must three-valued logic be mobilized again? A similar point can be based on universal generalizations: (6) Every good boy deserves fudge. An indicative universal generalization obviously has a truth value. So does a generalization that is formulated using pronouns that express bound variables: (7) Take anything you like: if it's German, it's precise. (8) If you're a music department, you're a snake pit. But if ordinary indicative conditionals had only assertibility values and no truth values, then it is hard to see how truth values could be imparted to open indicative conditionals by the application of a universal quantifier. 7. A Problem with Nomologicals As we saw in our discussion of Gallimore's Problem, an NTV defender is forced to deny that indicative conditionals follow logically from the corresponding nomologicals. Thus (9a), a nomological truth, cannot entail (9fo). (9) a. Every piece of iron heated to 200°C turns red, b. If this piece of iron is heated to 200°C it will turn red.7 Indicative conditionals also cannot be regarded by NTV as logically stronger than material conditionals. This is not quite for the same reason, since a truth-valueless sentence could be held to entail a true 7 Though for a different reason—he does not accept NTV—McDermott (1996) also denies the validity of Universal Instantiation here. He does adopt a three-valued logic.

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one; but the falsity of the corresponding material conditional would strangely fail to make the indicative conditional false. Of course, this is just to say that a conditional can have a true antecedent and a false consequent without being itself false, and since I reject Modus Ponens I officially agree with that claim, but on different grounds; more conventionally minded logicians should find the idea repugnant. The upshot is that NTV simply precludes the neat and attractive picture of indicative conditionals as intermediate in logical strength between strict conditionals and material conditionals. 8. Trouble with the Notion of Validity Indicative conditionals figure in deductively valid arguments, and in invalid ones. Indeed, one might hold that it is the very business of indicative conditionals to figure in arguments, and that if there were no arguments there would be no conditionals. NTV makes all that hard to understand, for deductive validity is defined in terms of truth values (as the impossibility of true premises and false conclusion, or as the non-existence of a model in which premises are true but conclusion false). Anticipating the difficulty, Adams originally tried to formulate a definition of a validity surrogate, 'reasonableness' of inference, in probabilistic terms. Appiah (1985: ch. 10) has examined and criticized Adams's attempt, but sympathetically develops his own conditional logic without appeal to truth. Possibly it succeeds; at any rate I shall not try to fault it here. (See also Beall, 2000.) My present argument against NTV is only that, when one abandons truth value for indicative conditionals, the problem of reinventing validity is non-trivial. 9. Subjective versus Objective Modal Concepts Stalnaker (1984: 112) points out that ... the contrast between [indicative] and [subjunctive] conditionals can be seen as a special case of a wider contrast between subjective and objective modal concepts. Possibility can be compatibility with knowledge or compatibility with objective necessities. Probability can be subjective degree of belief or objective chance. Certainty begins as an attitude or epistemic state, but can also be some kind of objective necessity. ('From that point, it was certain that the Shah would be deposed, although no one recognized it at the time.') The contrast between 'if he killed the Pope' and 'if he had killed the Pope' parallels

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the contrast between 'the Pope may have been killed' and 'the Pope might have been killed'. Stalnaker goes on to observe that, historically, the objective modal concepts have been felt to be more problematic than the subjective/ epistemic ones, and that empiricists and pragmatists, at least, have tried to explicate the former in terms of the latter, regarding the objective concepts 'either as illusory reflections or as legitimate extensions of their subjective analogues'. (Of course, my Event theory itself is a metaphysical idealization of an originally epistemic notion.) Whether or not one applauds that strategy, there seems to be a systematic if hardly transparent relation between the objective and the subjective concepts, and nowhere else in the modal family is that relation manifested by truth-valuelessness of the relevant subjective statements. On the contrary; the initially dubious objective partner is usually lashed to the subjective statement whose truth condition is better understood. 10. Deflationism8 Deflationist and minimalist theories of truth itself—descendants of Ramsey's and Ayer's Redundancy theory, which had it that to call a sentence or utterance true is not to predicate a special property of that sentence or utterance, but merely to repeat it or to endorse it—has made a strong comeback in recent years (see e.g. Horwich, 1990; Grover, 1992; Brandom, 1993). And it has been widely pointed out that if such a view of truth is correct, then expressivisms and other anti-realisms about subject-matters which have traditionally attracted anti-realism, such as morality and aesthetics, should not be expressed as claims of truth-valuelessness. For example, the Emotivists held that moral judgments are not true or false, but merely express conative attitudes of those who utter them. But no one has ever doubted that a moral judgment can be repeated and endorsed. So, if to call an utterance 'true' is merely to endorse or repeat that utterance, it follows that moral judgments can be true. 8

This point was suggested to me by JC Beall and Greg Restall. So far as I am aware, the first meta-ethicist to make this point was Smart (1984). A. J. Ayer (1946) notoriously defended emotivism. But as noted above, he also held a Redundancy theory of truth, in another chapter of the very same work. This is either a flat selfcontradiction or as near to one as matters. I know of no one else who has noticed this. 9

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So too with NTV. Conditionals can be repeated and endorsed; so anyone who holds a deflationary theory of truth must reject NTV. I do not myself accept any version of deflationism,10 but lots of people do. Let us turn to the arguments for NTV.

Rebutting the Case for NTV 1. In expounding NTV, Stalnaker (1984: 108) poses a rhetorical question on Gibbard's behalf. If an indicative conditional expresses a proposition distinct from that expressed by the relevant material conditional, the proposition is stronger than the material conditional. But then what additional information is conveyed, over and above the material conditional? Stalnaker concedes to Gibbard that 'it is difficult to see' what information that is. If there is no such determinate information, the indicative does not express a proposition stronger than the material conditional. But since (as Gibbard and Stalnaker agree) the indicative conditional is not the material conditional itself, it expresses no proposition at all; hence NTV. Rhetorical or not, the question of what additional information the indicative conditional conveys is easily answered by our Event theory. For on that theory the material conditional is the special case in which a speaker's domain of circumstances is restricted to the actual. Thus, the extra information conveyed by an ordinary stronger indicative is that, not only in every relevant actual antecedent circumstance, but also in every relevant non-actual circumstance that is a contextually real possibility, does the consequent hold. 2. Responding to Lewis's mention of the embedding problem, Gibbard argues (1981: 234-6) the very surprising thesis that if indicative conditionals express propositions and if they embed in the way(s) we would normally expect them to, then they are material conditionals. If Gibbard is right about this, and if we are right in continuing to deny that indicative conditionals are material conditionals, then either they do not express propositions at all or they do not have the embedding feature that is our current ground for holding that they do express propositions. (Gibbard himself does deny that indicatives are truth-functional, and holds that an apparently embedded indicative either makes no real sense at all or poorly expresses 10

See Bar-On etal. (2000).

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some grammatically non-conditional state of affairs such as a thing's having a disposition. A similar position is taken by Woods (1997).) One reason Gibbard's thesis is so surprising is that we have a number of non-material conditionals truth-defined in the literature, such as Stalnaker's, that certainly express propositions and embed (whether or not any of them is in fact expressed by English 'if'). So we need to look at Gibbard's ingenious argument for the thesis. It begins with the equivalence schema A > (B > C) = (A & B) > C, which Gibbard says 'seems... to be a logical truth' for indicatives (1981: 234). He assumes, further, that (i) A > B entails A D B and that (ii) if A entails B then the conditional A > B is necessarily true. Now, consider the formula (G) (A D B) > (A > B). By the equivalence schema, (G) is equivalent to ((A D B) & A) > B. By (ii) (since ((A D B) & A) entails B), that formula is necessarily true; so (G) is necessarily true as well. By (i), (G) entails (G*) (A D B) D (A > B), and so (G*) must be necessarily true. But the necessitation of (G*) is tantamount to the thesis that, assuming A > B expresses any proposition at all and is embeddable, it is no stronger than A D B; Q E D . Of course, I reject (i), since I reject Modus Ponens; but it would not be a good political tactic to attack NTV by attacking Modus Ponens— a bit like discouraging teenage pregnancy by attacking motherhood— so I shall not make an issue of (i). Rather, why should we accept the equivalence schema itself? Stalnaker's conditional does not sustain it; nor (far more importantly) does mine. So neither of us is going to grant Gibbard's suggestion that the equivalence is a logical truth for indicatives. Gibbard himself concedes in a footnote that his equivalence principle commits him to the logical truth of A > (B > A) (since (A & B) > A is surely a logical truth); he does not mind that consequence, despite its having instances like 'If Harry runs fifteen miles this afternoon, then if he is killed in a swimming accident this morning, he will run fifteen miles this afternoon.' So Gibbard's opponents have independent reason to deny him the equivalence principle.11 11 For fuller discussion, see Kremer (1987). A simpler version of Gibbard's argument, attributed to Geoffrey Hunter, is presented by Clark (1971): if A and B jointly entail C, then A alone entails B > C; therefore, since D and D D E jointly entail E, D D E alone entails D > E for any relevant use of '>'. Naturally, I reject the Hunter-Clark principle. Suppose my friend Bob is in fact going to retire next year. Let A be 'My friend Bob will retire next year v In 2004 the planet Ynool will spontaneously explode, causing a rain of blood over Fairbanks, Alaska", which is true only because its left disjunct is. Let B be 'My friend Bob will not retire next year". Those two sentences together entail 'In 2004 the planet Ynool will spontaneously

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3. Gibbard offers a fascinating example, which I shall call the Riverboat Puzzle, designed to show conclusively that one must accept NTV if one is to preserve Conditional Noncontradiction (~((A > B) & (A > ~B))). I have an alternative exegesis of the example, but I shall defer that discussion until Chapter 8, after I have surveyed several theories of the 'indicative'/'subjunctive' distinction. 4. Appiah makes a gradual, cumulative case for NTV, the gist of which is that (pace Grice, Lewis, and Jackson) truth conditions do no work in explaining the assertibility of indicatives as described by Adams and indeed a complete and adequate conditional logic can be formulated entirely in terms of assertibility without reference to truth. I shall briefly address this claim in the next section, after setting out Adams's famous generalization regarding the assertibility of indicatives. Appiah adds (1985: sec. 9.7) that indicatives behave abnormally within the scope of the truth-functional connectives 'not' and 'or', as would not be expected of sentences with characteristic truth conditions. Certainly there are some interesting problems in this area. But the problems concern either syntax (especially disambiguation), or assertibility itself rather than truth value, or claims Appiah makes as to the nonsensicalness of certain embedded constructions, which claims I reject; so I see in them no support for NTV. 6. Dorothy Edgington (1986) offers an ingenious and complex argument. In outline, it is that (a) indicatives are not truth-functional but (b) they do not have non-material truth conditions either; it follows that they do not have truth conditions at all. Since (a) is plausible (again pace Grice, Lewis, and Jackson), Edgington's defense of (b) is the crux. Attacking the hypothesis of non-material truth conditions, Edgington in effect elaborates Stalnaker's rhetorical question: if an indicative conditional expresses a proposition distinct from that expressed by the relevant material conditional, what additional information is conveyed, over and above the material conditional? She divides the hypothesis into four subcases, corresponding to the four lines of the horseshoe's truth-table definition. The first subcase (p. 22) is that in explode, causing a rain of blood over Fairbanks, Alaska". But it certainly is not true that 'My friend Bob will retire next year v In 2004 the planet Ynool will spontaneously explode causing a rain of blood over Fairbanks, Alaska" entails 'If my friend Bob does not retire next year, then in 2004 the planet Ynool will spontaneously explode, causing a rain of blood over Fairbanks, Alaska", because the former is true and the latter is false.

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which antecedent and consequent are both true; she considers the hypothesis ('Assumption 1') that'[a] conditional ["If A, B"] has truth conditions which are not truth-functional when "A" and "B" are both true'. Assumption 1, Edgington says, has the 'consequence' Q: 'Someone may be sure that A is true and sure that B is true, yet not have enough information to decide whether "If A, B" is true; one may consistently be agnostic about the conditional while being sure that its components are true (as for "A before B").' I put quotation marks around 'consequence' because Edgington herself hedges the logical relation: Ci 'does not quite follow merely from the assumption of nontruth-functionality. There are exceptions to claims of the same form. But the exceptions are special cases, which do not cast doubt on the case of conditionals' (p. 22, italics original). (She reviews two such exceptions and argues convincingly that conditionals are analogous to neither.) Now she insists that Q is false: Admittedly, the conditional 'If A, B' is not of much interest to someone who is sure that both 'A' and 'B' are true. But he can hardly doubt or deny that if A, B, in this epistemic state. Establishing that the antecedent and consequent are true is surely one incontrovertible way of verifying a conditional, (p. 24) (She backs up this appeal to intuition by endorsing a version of Adams's generalization aforementioned, about indicatives, assertibility, and probability, on which see below.) If Q is false and is also a consequence or near-consequence of Assumption 1, then Assumption 1 is false; hence the conditional is truth-functional for the case of true antecedent and consequent, if it has a truth condition at all. Edgington then proceeds to the second subcase, that of true antecedent and false consequent. A parallel Assumption 2 is made and parallel €2 derived. Not surprisingly, Edgington rejects €2 on the grounds that, if one is certain that A and certain that ~B, one can hardly be less certain that 'If A, B' is false. So if the conditional has a truth value, that truth-value is determined (to be F) in the case of A true and B false. (Here, as before, I could contest this immediately as a tell-tale manifestation of Modus Ponens credulousness, but I shall mind my manners.) Going through the remaining two subcases, Edgington makes arguments similar to her first one (the Q-and-anti-Ci argument),

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though more complicated. I shall not expound them, because I think the criticism I shall make of Edgington's first argument adapts to blunt them as well. My criticism is that, contrary to appearances, Q is not at all a consequence of Assumption 1. Assumption 1 is simply the claim of non-material truth conditions. As such, it may entail something nonspecific about people's epistemic attitudes, for example, that someone could believe that A and B are true while failing to believe their conditional. (Which certainly someone could, because people often do.) But it does not entail Q; for Q is specifically about certainty or being sure and, for all Edgington has shown, certainty may be a special case. That is, there may be something about the epistemic attitude of certainty in particular that makes Ci false despite the truth of Assumption 1. The inference from Assumption 1 to Q is not validthough-subject-to-hedges; it is simply not formally valid. And more trenchantly, if the Event theory is correct, there is indeed something special about certainty: certainty directly and dramatically restricts the parameter R, by making some possibilities non-real. Suppose I am certain that A and I am certain that B. Now consider the conditional A > B, explicated as 'In every A-event that is a real and relevant possibility, B'. If I am certain that B, ~B is not a real possibility for me; so there is no ~B event 8 R. Thus, no A event that is a real possibility is one in which ~B, and if it is a relevant possibility it will be one in which B. That is why the conditional will be accepted when enunciated by someone who is certain of both antecedent and consequent.12 But again, this is a special case, because it is only the certainty that entirely rids the conditional's reference-class of ~Bevents. That is a concrete—and highly pertinent—example of why we cannot infer the falsity of Assumption 1. 7. Edgington gives a further though thematically related argument against NTV (1986: 27-8), the idea again being that, although the 12

Actually this might be taken as an objection to the Event theory itself, because some theorists have refused to grant that certainty of A and B suffices for acceptance of A > B: e. see Pendlebury, 1989, Mellor, 1993, and Read, 1995.1 have mixed feelings about this, even though my own theory has predicted Edgington's result. Suppose I am entirely sure, a la Moore, that I now have hands at the ends of my arms. I am also entirely sure that the United States won the Battle of Midway (by a fluke, actually, on 4 June 1942). Is Edgington right in proclaiming that I 'can hardly doubt or deny" that if I now have hands at the ends of my arms, the United States won the Battle of Midway? Admittedly I am a philosopher and there is much that I can doubt, but I do not think the foregoing conditional should be obvious to anyone.

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truth-functional theory is false considered as an account of truth conditions, it is true of people's epistemic states. Suppose you and I do not know the truth value either of A or of B. Along comes someone who does know both truth values. This person secretively withholds them from us, but does vouchsafe that ~(A & ~B). This is enough for me to conclude that if A, B. Now, ~(A & ~B) does not entail 'If A, B'. That is [would be] the truth-functional account, with all its difficulties. But belief that ~(A & ~B) in the absence of belief that ~A is sufficient for belief that if A, B...No non-truth-functional account [of the conditional's truth condition] can accommodate that fact. (Italics original) So once again, indicative conditionals have neither truth-functional truth conditions nor non-truth-functional truth conditions. But is Edgington right about what we should conclude? If we are told that ~ (A & ~B) and nothing more, especially if we know that our informant knows the specific truth values of A and B but is refusing to reveal them to us, we must wonder about the informant's grounds. Suppose s/he knows that ~(A & ~B) only because s/he knows that ~A. Then A > B does not follow, and since we do not know that knowledge that ~A is not the informant's ground, we should not ourselves conclude, at least not in one step, that if A, B.

The New Horseshoe Theory Impressed by some of Adams's ideas about indicative conditionals and probability, Lewis (1976) and Frank Jackson (1979,1987) have urged a compromise between NTVand truth-conditional semantics; Bennett (1988) presents it as an attractive option, though he does not officially adopt it; Thomson (1990) seems to have come upon it independently. The compromise is to concede that indicatives have truth conditions, but also (a) to maintain that, despite all appearances, indicatives are after all material conditionals rather than anything stronger and/or intensional, and (b) to insist that indicatives are still very special, in that their inferential and conversational roles go by the Ramsey Test or something like it and bear only distant relations to their horseshoe truth conditions. Thus this New Horseshoe Theory agrees with NTV that for indicative conditionals assertibility is sui generis or at least does not go by likelihood of truth, and that what is important about indicative conditionals is assertibility rather than truth.

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The NTV literature was inspired by Adams's Generalization: Normal speakers' tendency to assert or assent to an indicative conditional A > C varies directly with the conditional probability Pr(C/A). Adams (1965, 1975) provides a few bits of evidence in support of the Generalization, and as yet, no one has seriously contested it. The Generalization needs explaining, because normally we would expect a speaker's tendency to assent to a sentence S to vary with S's own subjective probability for that speaker. The first, obvious explanation was voiced by Richard Jeffrey (1964), Brian Ellis (1969), and most trenchantly Robert Stalnaker (1970): (Jeffrey's Hypothesis) An indicative conditional's own subjective probability is the conditional probability of its consequent upon its antecedent; Pr(A > C) = Pr(C/A). This is a neat, clean, and attractive explanation of Adams's Generalization. But by a series of trivialization proofs Lewis (1976) has shown it to be false: a small set of innocuous assumptions entails that no language of which the Hypothesis is true could assign non-zero probability to more than two mutually incompatible propositions, that is, could be more than four-valued.13 Lewis goes on to consider the alternative explanation suggested by Adams's own discussion: (E) NTV is true, and indicative conditionals have merely assertibility-conditions that line up with Adams's conditional probabilities. As I said before, anyone who wants to sustain (E) has to reinterpret talk of'probability' in such away as to split it off from probability of truth, since on Adams's view a sentence can be 'probable' or assertible even though it can be neither true nor false. Lewis agrees that such a reinterpretation could be done fairly cheaply, but he points out that to do it would neither help to explain Adams's Generalization nor lend even oblique aid or comfort to Jeffrey's Hypothesis. In view of the latter point, we cannot suppose that the 'assertibility' of a conditional matches its own subjective probability. So it turns out that Adams's 13 Appiah (1985) contests one premise of Lewis's argument, but allows that a revised version formulated by Carlstrom and Hill (1978) circumvents his objection by not relying on that premise.

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notion of 'assertibility' is sui generis—'assertibility' for Adams is just whatever property indicative conditionals have that makes us assert or assent to them. Thus, even if we were to reinterpret Jeffrey's Hypothesis as a thesis about assertibility rather than about probability of truth, it would be no explanation, but would merely repeat the Generalization. Following Grice (1989, first published 1967) Lewis now suggests a version of the New Horseshoe Theory: (L) Indicative conditionals are in fact material conditionals, but Grice's Maxim of Quantity makes some true conditionals conversationally unacceptable [and some false conditionals conversationally mandatory—WGL]; the subjective probability of a conditional A > C minus the conversational 'assertibility diminution' calculated by Lewis equals a conversational 'assertibility' that is also equal to Pr(C/A). Any New Horseshoe theorist must explain the alleged divergence of assertibility from material truth condition. According to (L), what is wrong with asserting A > C on the basis of ~A (despite its automatic truth given ~A) is that the speaker would mislead by saying something significantly weaker than is warranted. But Lewis raises an objection of his own to (L) (1976: 138-9): that parallel considerations ought to hold for conditionals with true consequents, but they do not. The argument Lewis directs at false antecedents does not apply to true consequents. If C is highly assertible on probabilistic grounds, then so of course is A > C, but Lewis's own calculation procedure does not predict assertibility diminution here. At this point Lewis moves on, saying only that he 'think[s] it reasonable to hope that the discrepancies are not so many, or so difficult to explain, that they destroy the explanatory power of the hypothesis that the indicative conditional is truth-functional' (p. 139). Jackson (1987) makes a similar appeal to probabilistic 'robustness', but without relying on conversational maxims. His idea is that indicative 'if functions conventionally to signal the robustness of the (material) conditional with respect to its antecedent—crudely, that the speaker would go on accepting the conditional if he or she came to believe its antecedent. Jackson argues on this ground that naturallanguage speakers would have use for a binary sentence connective '*' such that A * C is assertible just in case Pr(C/A) is high. As Appiah (1985) points out, Jackson's conventional-implicature strategy forsakes Lewis's irenic idea that the assertibility of an indicative conditional depends on the conditional's (material) truth condi-

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tion; the truth condition plays no obvious explanatory role at all. Thus Jackson fails to explain Adams's Generalization if the Generalization is understood in terms of probability of truth, and (like Stalnaker) he fails to explain it non-trivially if 'probability' means just assertibility. Thus the Generalization remains unaccounted for.14 Perhaps we should now ask whether it is true, for that matter; though plausible on its face, it is by no means obvious. In fact, Edgington's epistemic arguments for NTV suggest a criticism of the Generalization itself. Suppose I believe each of two propositions that are not only probabilistically independent of each other but mutually irrelevant in topic; but I believe the first not at all strongly. For example, at the moment I am inclined to think that there is a piece of Monterey Jack cheese in the refrigerator, though I may well be wrong about that because someone may have eaten it, and I believe that Al Gore will win the next US Presidential election. I would not want to put money on the first proposition, but if forced to choose, it would be my choice. So the subjective probability I attach to the first is greater than .5 but not by much. Let us suppose that I am confident to degree .505 that there is a piece of Monterey Jack cheese. But I am considerably more so, say .85, that Gore will win. Since the two propositions are probabilistically independent, the conditional 14 Lewis's and Jackson's attempts to explain away the appearances of non-truth-functionality by predicting a divergence between assertibility-conditions and truth conditions are further criticized, to good effect, by Edgington (1986,1995) and by Woods (1997: ch. 4). We might try a final suggestion for explaining Adams's Generalization. 'The assertibility of a conditional is in fact controlled by perceived nearness of worlds. Now, probability is also a matter of nearness of worlds: the further away from our world one has to go in order to find a world in which ~p, the more probable P is for us here. If so, and if (say) Stalnaker's semantics for conditionals is correct, then given a true conditional A > C, the subjective probability of A & C will exceed that of A & ~C by some amount, and it follows trivially that Pr(C/A) will exceed Pr(~C/A) by a corresponding amount. Thus, I will find a conditional to be assertible just when I perceive a Stalnaker truth condition to be satisfied, and it is in just such cases that the relevant conditional probability will exceed .5 for us; that is why Adams's Generalization holds.' This argument would need a lot more spelling out; in particular, one would have to explicate and defend its two major premises. However these things might be done, two problems would remain. First, the argument would have to avoid vindicating Jeffrey's Hypothesis (since the latter is already known to be false), and I cannot offhand see how it would do that. Second, the argument assimilates assertibility (in whatever sense) and probability both to nearness or perceived nearness of worlds, and such assimilations are impugned by the kinds of cases considered by Gibbard and Harper in their landmark article (1981) on the difference between causally and epistemically expected utilities. Epistemic 'nearness' and causal similarity are just not the same, even though they have the same superficial logic. So I doubt that the foregoing suggestion would do the trick even if it were clear.

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probability of the second given the first is equal to its own probability, .85. According to Adams's Generalization, then, I should believe to degree .85 that if there is a piece of Monterey Jack cheese in the refrigerator, then Gore will win the next US Presidential election. I do not think any ordinary speaker of English, uninfected by truthfunctional logic and by discussions of conditionals couched from the beginning in probability theory, would give much credence to the sentence, 'If there is a piece of Monterey Jack cheese in the refrigerator, then Gore will win the next U.S. Presidential election', even if that speaker shared my weak beliefs in its antecedent and consequent individually. Incidentally, I have a general reason for deploring the custom of approaching the semantics of conditionals from the direction of probability theory. It is a historical accident that the early philosophical work on conditionals was done by logicians who were interested in probability theory and to some extent in philosophy of science. However useful probability-defined conditional operators may be in technical contexts to which probability theory is already appropriate—say in quantum mechanics or in formal decision theory or in computer modelling of one kind or another—it is well known that, for good or ill, almost nothing in the human mind works by representation of probability theory in the formal sense. Unless we happen to have been supplied by nature or by artifice with a partition of possibilities, as when shooting craps or playing poker, we do not draw inferences according to the probability calculus (Nisbett and Ross, 1980), and arguably we should not (Cohen, 1981; Harman, 1986); and even when we should, this is a matter of technical epistemology, not (or not at all obviously) of the semantics of our native language. So it would be very surprising if the semantics of naturallanguage conditionals reflected the probability calculus in any simple way. I shall not either pursue the Lewis-Jackson-Appiah dialectic15 or further dispute Adams's Generalization, for I have three criticisms of my own to make against the New Horseshoe Theory. The first is 15 Except to note that Appiah has the last word, a further argument for NTV: if Jeffrey's Hypothesis is false, then we must demand a special exception to ASS, the principle that assertibility follows probability when a sentence has a truth condition. But the only two attempts to motivate such an exception (Lewis and Jackson) fail. Thus probably there is no exception; indicatives do not have truth conditions.

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that, as I have argued in Chapter 1, English incorporates no binary sentential connective expressed by 'if. The horseshoe is a binary sentential connective; therefore English 'if is not the horseshoe. The horseshoe idea is syntactically just untenable. Yet a reply is available to the Horseshoe theorist. The theory can be understood weakly, as saying only that indicative conditionals are material in their truth conditions, not anything about syntax. The Horseshoe theorist can simply accept our syntax, if the truth conditions can be made to come out material. And they can. For as we saw in Chapter 2, our conditionals collapse into the horseshoe if we restrict our 'event' quantifier to the actual. Indeed, this weak way of formulating the Horseshoe theory has the advantage of unifying the syntax and semantics of indicatives and subjunctives while explaining the well-known semantic differences (cf. Chapter 8). Indicatives and subjunctives are just alike, the Horseshoe theorist may say, except that indicatives' quantifiers are restricted to the actual while subjunctives' quantifiers roam fairly freely. I rejoin only that indicatives are plainly not so restricted in English. (10) a. What if the TAs boycott the meeting? b. In that case we'll adjourn for lack of a quorum. The antecedent of such a conditional can be demonstrably nonactual, and the speaker clearly has in mind a range of possibilities which may or may not materialize. My second criticism of the Horseshoe theory is fairly obvious, but to date I have not seen it raised in the literature against Lewis or Jackson.15 The Lewis/Jackson method cannot handle the worst material-implication paradox of all, ~(A > C) / .'. A, ~C. At least, I see neither conversational nor conventional reason why one might assert an instance of the premise while denying either or both of the conclusions.17 No indicative semantics can be right that does not explain the outrageously evident invalidity of that inference pattern—the 16

Sanford (1989: 62) makes it against Grice. The linguist Doug Fuller has suggested to me that in fact this inference is valid and that the reason we find no instances of it in nature is that English for some reason affords no means of lexicalizing any instance of its premise. As I recall, his evidence for this suggestion was that it is hard to find any external-sounding negation of an English indicative conditional that is not heard equally well as the internal negation of that conditional. I am inclined to grant this, but notice that all it would actually prove is Conditional Excluded Middle for indicatives, not the (mysterious) inexpressibility of external negations of indicatives; the latter would need to be defended further in its own right. 17

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most obvious explanation being, of course, that it is as invalid as it looks. Thirdly, consider an example adapted by Sanford (1989: 61) from Cohen (1971): (11) If it is true both that if the Dean doesn't approve your raise, then I will resign the departmental chairmanship, and that the Dean does approve your raise, then as a chairman I am both idealistic and effective. On a truth-functional interpretation, the conditional embedded in (11) 's antecedent is redundant on the ensuing conjunct. Thus, assuming that A > (B & C) entails A > B, (11) should entail (12) If the Dean does approve your raise, then as a chairman I am idealistic. It is unobvious to say the least how the New Horseshoe Theory might explain away our clear intuitive rejection of that entailment, or (as Sanford argues) how it might explain the relevance of the embedded conditional to my alleged idealism. The Event theory can claim a number of further achievements and advantages that it has over other current theories of conditionals.18 But it is time to turn to a more detailed discussion of the particularly tricky 'even if, and then to the 'indicative'/'subjunctive' distinction. 18

e.g. the theory affords a precise and illuminating statement of the account of 'conditional perfection" sketched in Boer and Lycan (1973), as well as a particularly useful way of formulating different Reliabilist theories in epistemology; see Lycan (1984fe nn. 12, 21).

5

A Beautiful But False Theory of 'Even If 'Even if is a very troublesome locution, raising special and difficult questions in the semantics of conditionals. It is not often discussed by linguists and is generally either ignored or mishandled by philosophers. But my semantics is particularly well equipped to account for its special properties, for I am grammatically prepared to treat 'even if as the result of letting the word 'even' operate on a conditional antecedent; 'even' applies to 'if P' just as it does to 'when P' and to 'where P' (cf. 'even when', 'even where'). Thus my contention will be that 'even' in 'even if actually means 'even', just as (I have argued) 'only' in 'only if means 'only'. In consequence, a theory of 'even if should fall out of a plausible general theory of the semantics of'even', if one can be obtained. To my knowledge, Hazen and Slote (1979) and, following them, Bennett (1982) were the first to pursue this strategy;1 I shall discuss Bennett's subtle theory and compare it to one of my own.

Three Views of 'Even' Everyone knows that 'even' carries a strong connotation having to do with contextual presumptions or expectations and circumstances' contravening those expectations: (1) Even Grannie was sober. (2) Not a creature was stirring, not even a mouse. (1) suggests that the level of sobriety of some gathering was so great that Grannie, whom one would not expect to be sober, was sober; (2) suggests that the stillness on the occasion in question was so great 1

But Vic Dudman had advocated it for many years. It is to Dudman that I owe the immortal example (1) below.

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as to include all the mice—animals that one would normally expect to be moving about. Further examples illustrate that 'even' just as easily applies to constituents other than NPs: (3) For you, my dear, I would even eat haggis. (At least threeways ambiguous.) (4) It is fast, it is durable, it is even low in price. (5) She won steadily, in large sums, and even graciously. Indeed, everyone knows that the main function, probably the only function, of'even' is to carry that expectation-contravening connotation. But as with all 'connotations', dispute arises over whether the somehow communicated contrastive content is entailed by the sentence containing 'even', or is only implied or implicated by it in some less formal way. Let us set out some alternative general views of'even' that illustrate such differences, in ascending order of semantic respect for the word. The Minimal View At an extreme of 'radical pragmatics', one might hold that 'even' makes no semantical contribution whatever to a sentence in which it occurs and no contribution to anything that one might call locutionary meaning. It is semantically null, and serves only to express an attitude of mild surprise on the speaker's part (though the topic or focus of the surprise is marked by the syntactic scope of'even'). Thus, (1) would be understood as something like, 'Gosh, Grannie was sober!'2 The Conventional View This view posits conventional implicature (or what Lycan (1984a) calls 'lexical presumption'), which implicature originates precisely in the choice of the word 'even'. (Cf. 'but', 'too', and 'either' as in 'wasn't a genius either'.) Though 'even' contributes nothing to truth conditions strictly construed, a sentence containing it is inappropriately 2 Or I suppose someone might eke out the minimal view by invoking conversational implicature (a la Grice) to explain why 'even' serves to express counterexpectation. I know of no one who has done so. It would be totally implausible, since conversational implicatures are calculated on the basis of whole prepositional content, not triggered without calculation by special single words.

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lexicalized if the implied unexpectedness does not really obtain. (Bennett defends the conventional view.3) The Semantic View This view eschews all attempts to write off the 'connotation' of (even) as merely emotive, conversational, conventional, or otherwise pragmatic. The semantic view is that 'even' does affect truth conditions, in some way that the semantic theorist would have to go on to specify; the addition of 'even' to a sentence creates new genuine entailments that the original sentence did not have. But to my knowledge, no one had ever taken the semantic view prior to Lycan (1991). I doubt anyone would take the minimal view seriously. Ordinary speakers insist that (6) Grannie put on her coat and

(7) Even Grannie put on her coat differ in 'meaning', to say nothing of (8) a. Grannie even put on her coat b. Grannie put on even her coat c. Grannie put on even her coat. Though we professionals may care nothing for the ideas of ordinary speakers, even would-be 'rad-prag' linguists (who enshrine as little in truth-conditional semantics as possible) would feel some obligation to explain the contrastive implications generated by 'even' in specific pragmatic terms of some sort, presumably Gricean or relevancetheoretic.4 Finally, as we shall see, there are both syntactic and semantic reasons to assimilate 'even' to the obviously semantically valued quantifier 'only'. As I have said, the connotation seems specifically to be supplied by the meaning of the word 'even', and that intuitive feature is the mark of conventional implicature, lexical presumption, or semantic albeit lexical entailment outright. The conventional view is attractive. It 3

It was earlier enunciated by Karttunen and Peters (1979), and I know of no one who has contested it. For a recent defense, see Francescotti (1995). 4 For a relevance-theoretic account, see Delgado Lavin (1999).

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combines the healthy semantic skepticism of the minimal view with the semantic view's concession to common sense that the word 'even' itself actually means something and contributes a specific component of locutionary meaning to sentences in which it occurs. The conventional view is also impressively fleshed out by Bennett, who specifies in elegant detail what he thinks the choice of the word 'even' implicatively adds to a sentence into which it is inserted, and more recently as well by Kay (1990) and Barker (1994), ditto. Any defender of the Conventional view must specify that, of course. One would hold out for the semantic view only if one were dissatisfied with the conventional account as a view of the perceived difference that 'even' makes to 'meaning', or if one has actual syntactic or semantic evidence that 'even' affects truth conditions. And of course there is more than one possible truth-conditional theory of 'even'. Let us take a look at Bennett's account. I shall then go on to argue that there is some evidence for the semantic view as against the conventional, and that my own general theory of conditionals offers some semantical advice regarding 'even' generally.

Bennett's Theory Bennett contends that 'even' does not affect truth conditions, comparing it to the contribution of 'but' over and above 'and'. But he insists that it does make a highly systematic contribution to pragmatic assertibility. Whether true or false, a sentence containing 'even' will be assertible only if 'there is a neighbour sentence which is known, related, and less surprising' (1982: 406). This shorthand formulation needs considerable unpacking. If S is a sentence containing 'even', let S* be the result of deleting 'even' from S, and let S's 'neighbors' be other sentences that differ from S* only in the constituent that is intuitively the focus of'even' in S (bar whatever superficial grammatical changes may be required by the substitution). To take Bennett's own example. If S is (9) Even the children laughed at him 5 Instead of the linguists' term 'focus', Bennett uses the word 'scope' in a way he carefully defines (1982: 407). So far as I can tell, his notion of scope differs from that of focus only in one way, that I shall describe shortly. It is sharply distinct from the logicians' use of 'scope'.

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then S* is simply (10) The children laughed at him and neighbors include (11) a. Everybody laughed at him b. Nobody laughed at him c. His grandmother laughed at him d. Dick and Jane laughed at him e. The dog laughed at him and so on. Now, Bennett's assertibility condition for the sentence S is that there exist a neighbor Sj of S such that (1982: 405-6) (i) Sj is true, and mutually believed by speaker and hearer, and salient for them (e.g. it has just been authoritatively asserted); (ii) the truth of S* and that of Sj can naturally be seen as parts of a single more general truth; (iii) it is more surprising that S* is true than that Sj is true. (9) will thus be assertible only if there is some salient truth of the form 'X laughed at him' that can be seen as part of the same more general truth and is less surprising. Bennett's bare existential quantification—there need be only one salient neighbor—leaves his analysis open to an obvious sort of counterexample, in which there are two or more salient neighbors, still conspicuously less surprising than the relevant S*. But that objection does not immediately affect my own enterprise, and so I shall postpone consideration of it till the next chapter. For now let us move on and apply the analysis to conditionals containing 'even'. Bennett says that 'even if conditionals can be generated in either of two ways, depending on the focus of 'even' (he explicitly considers only subjunctive conditionals). In particular, 'even' has different effects when its focus contains an entire conditional from those it has when its focus is merely a conditional antecedent or smaller constituent. The first way of generating an 'even if conditional is to apply 'even' to an S* whose Sj is already a conditional. Let S* be (12) If he drank just a little she would fire him, said of a puritanical boss (1982: 410). The relevant Sj, which licenses the assertion of the resulting S,

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Beautiful But False Theory of 'Even If (13) Even if he drank just a little she would fire him,

would probably be (14) If he drank a lot she would fire him, the focus of'even' in (13) being 'just a little'. When the Sj is already a conditional in this way, Bennett calls S a 'standing-"if'" conditional. But sometimes, Bennett says, 'the relevant Sj is not a conditional, [and] the move from Sj to Sis a move into conditionally' (1982:410). When the Sj is not in this way already a conditional, Bennett calls S an 'introduced-"if"' conditional. (In such a case the 'if falls within the focus of 'even', as Bennett says it does not in standing-'if conditionals.) Here things get a bit tricky, for at first it is hard to see how a non-conditional Sj could be related as a 'neighbor' to a conditional S*; the 'neighbor' relation works by substitution of grammatical constituents. Bennett's answer is that sometimes for his purposes a constituent is 'null, empty, a mere absence from the sentence' (1982: 407). His example is one in which 'I stand looking at the raging waters of the river, and the ruins of the bridge, and I say (S) "Even if the bridge were standing I would not cross"'. Here S* is of course (15) If the bridge were standing I would not cross, and Bennett says the relevant neighbor Sj is simply (16) I will not cross. S* results from Sj by substitution of the conditional antecedent for a (I suppose, the) null constituent; it is 'formed... by sheer addition, rather than by replacement' (1982: 411). Two questions arise immediately, (i) How is Bennett's 'relatedness' condition satisfied? (ii) Since the idea of a 'neighbor' sentence is based on comparative judgments of expectedness, how can a conditional and its own free-standing consequent be related as neighbors, when there is no comparison between a conditional antecedent and nothing at all? Question (i) is that of how (15) and (16) 'can naturally be seen as parts of a single more general truth'. Bennett says (1982:411) only that 'a wide range of conditions is inimical to my crossing the river'. If that is the 'single more general truth', I do not offhand see how either a counterfactual, S*, or the categorically factual Sj are 'parts of it, at least not in the way that the children laughing and the grandmother laughing are parts of the general fact of everyone's laughing. I suppose

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the counterfactual may be counted by courtesy as 'part of the inimical conditions because its categorical basis lies in them, but the fact of my not crossing is part of the inimical conditions only if we deliberately assume that it is a fact and that I do not cross despite the inimical conditions. (To assume that would doom Bennett's main explanatory project to circularity—see below.5) Question (ii) is more pressing. The idea of a 'neighbor' sentence is intuitively grounded in that of a natural reference-class of items. In Bennett's example, (10) has as its true neighbors all and only sentences of the form 'X laughed at him', where 'X' is replaced by names of people or groups who did laugh at him, the idea being that from among the people or groups who did laugh, the children had been less likely to laugh than were the others. (12), when the focus of'even' applying to it is still 'just a little', defines a reference-class of amounts he might drink, and so forth. But there seems to be no such reference-class defined by (15) and (16). The conditional antecedent certainly suggests a natural reference-class of conditions under which I would not cross, but the categorical (16) does not differ from the conditional by substitution of another member of the same reference-class; it states what it states unconditionally.7 Bennett seems to intend that the 'null condition' should be counted as a member of the reference-class of conditions. But how might that be understood? We need, remember, to compare degrees of expectedness, which is easy enough with conditional antecedents; it is more expected that if he drank a lot she would fire him than that if he drank just a little she would fire him. But which is more expected, that if the bridge were standing I would not cross or that I would not cross, period? (Perhaps we should understand (17) I would not cross as elliptical for (18) I would not cross under any conditions, which at least gives us 'no conditions' as an explicit member of the relevant reference-class of envisaged conditions. But my categorically not crossing under any conditions is a priori less likely than is just my 6 Perhaps what 'unifies' S* and Sj is natural law: the conditions are so inimical that crossing is a physical impossibility. Fine, but we want our treatment of 'even if to apply to conditionals that are not fully nomically necessary, as well. 7 Nor, as Michael Hand has reminded me, is there any syntactic trace of a deleted or otherwise inexplicit conditional antecedent.

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not crossing if the bridge were standing, and so Bennett's condition (iii) would not be satisfied.) Let us call this general difficulty of understanding the 'neighbor' relation for 'introduced-"if conditionals the 'Problem of Comparison'. The problem has its roots in a decision made earlier by Bennett in formulating his general theory of 'even'. Consider (19) Conflicts of interest make him angry. Indeed, even allegations of conflicts of interest make him angry. (20) The Soviet authorities put dissidents into mental hospitals. They put even the relatives of dissidents into mental hospitals. (21) There has never been a miracle. There has never even been prima facie evidence o/a miracle. (Bennett 1982: 407) Intuitively, to me, the respective foci of'even' in (19)-(21) are 'allegations of conflicts of interest', 'the relatives of dissidents', and 'prima facie evidence of a miracle', and the S*s underlying the respective second sentences result from substituting those phrases for the corresponding simpler constituents in the respective first sentences, the SjS. Bennett denies this. He stipulates instead that the second sentences result from the first sentences by 'sheer enlargement' (1982: 408), substitution of 'allegations of, 'the relatives of, and 'prima facie evidence of for 'null parts' of the SjS. He gives no reason for making this choice, save to note that it 'will matter later on'. The reason I find the choice counterintuitive is again that I think of 'even' as expressing a comparison of expectedness within a context ually indicated reference-class, and the Sj-S* 'neighbor' relation as grounded in the same. But Bennett's interpretation of the relation abandons that idea. We cannot compare the expectednesses of allegations, of relatives, or of prima facie evidence with that of nothingness. What we are comparing is allegations of conflict with conflict, the relatives of dissidents with the dissidents themselves, and so on. If we try to respect that idea and restore it to Bennett's analysis, what happens to the Problem of Comparison regarding conditionals? (15) and its genuine neighbors would have to be seen as grounded in a reference-class whose members were being compared as to the expectedness of their corresponding neighbors. And, as above, it is easy to see what sorts of items those members would be: conditions which might or might not have obtained, the neighbors being sentences of

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the form 'If condition e obtained, I would not cross'. The spirit of Bennett's analysis of 'even if conditionals is unimpaired, for those conditions form a unified class, of circumstances under which I would not cross the river; and among the neighbors defined by the members of that class, some are less expected or more surprising than others, and so the more surprising neighbors rate an 'even'.8 An important qualifying note: though all this talk of'expectedness', 'likelihood', 'surprisingness', etc., is standard in the literature, beginning perhaps with Fillmore (1965), it is misleading. Whatever scalar notion really is in play here is not always so forthrightly epistemic. Kay (1990) has produced clear counterexamples to the idea that the focus of'even' must denote something unexpected or unlikely in the ordinary epistemological sense. Indeed, sentences containing 'even' can be pragmatically ambiguous as regards what scale is assumed. Certainly, it seems that extremity relative to some scale is required, but the question of what sorts of scale are mobilized in what contexts remains complicated. For brevity, though perhaps perniciously, I shall continue to use the vague epistemic terms. The issue does not in particular affect the application of 'even' to 'if.

The Consequent-Entailment Question We have seen that the idea of 'even' generating a reference-class is consonant with the main points of Bennett's analysis. What, then, is impaired by my rejection of Bennett's unintuitive notion of'scope' as comprehending 'null parts', and why did he say his choice would 'matter later on'? The answer is important for my own forthcoming theory of'even if. It is that a main purpose of his paper is to explain an oddity or puzzling phenomenon concerning 'even if, which oddity will be causing trouble for my own account as well. The oddity is that, although 'Q even if P' has the superficial aspect of a conditional and although it seems grammatically to be simply the result of applying 'even' to an ordinary conditional, it does not seem 8 One might have reservations about the notion of a 'reference'-class in a case where th scope of 'even' is an entire clause. I am assuming the intuitive anti-Fregean idea (cf. Barwis and Perry, 1983) that even if sentences strictly denote truth values, there is also a sense in which at least embedded sentences refer to conditions, situations, or states of affairs. Indeed my general theory of conditionals embodies this presupposition.

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intuitively to be conditional in meaning. A speaker who asserts 'Q even if P' is typically felt to have asserted that Q—unconditionally. Mackie (1973), Pollock (1976), and Lycan (1984b) have claimed, more aggressively, that on its standard use 'Q even if P' entails Q, though there seems to be a less central use on which it does not. What, then, is the role of'even if P'? This I take to be a pre-theoretical puzzle for any theory of conditionals of either mood. I have my own view of the matter and shall expound it shortly, but for now let us continue to study Bennett's analysis. Bennett points out, following Pollock's own concession (1976: 2931), that the example of the puritanical boss is one in which the consequent is (obviously) not entailed. (13) can be true whether or not the employee ever does drink or ever does get fired. Notice that this is a focus phenomenon. Its intended reading is that on which 'even' operates on 'just a little' as opposed to 'a lot', but if we take the whole conditional antecedent as the focus, there is also a reading that seems to entail or imply his being fired: not even a (tee-)totally unexpected act on his part of drinking-just-a-little would save him from being fired (by an anti-puritanical boss). What distinguishes 'even if conditionals that entail or imply their consequents from those that uncontroversially do not? Bennett's ingenious answer is that the former are 'introduced-"if"' conditionals and the latter are not. Recall that, on his view, an 'even if conditional is on strict lexical grounds properly assertible only if there is a relevant Sj that is true, and on his problematic account of introduced-'if conditionals, the relevant Sj's are simply the conditionals' consequents. Thus one cannot say 'even' unless the consequent is true, even though the relevant S* does not itself semantically entail the consequent. That is why some 'even if conditionals, the introduced-'if' ones, are felt to imply their consequents uncancellably even though in fact they never entail them. This explanation is marred by our problems (i) and (ii) aforementioned. The first was the difficulty of seeing how Bennett's bridge case exemplified 'relatedness'. We saw that it might do so if we hamhandedly assumed it to be a 'general fact' that inimical conditions simply prevent me from crossing the bridge no matter what. But, as I predicted, that particular assumption would be useless in the present explanatory context, for it begs the question: our only motive for accepting it is our desire now to make the bridge case one in which the consequent is uncancellably implied.

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The second problem was the Problem of Comparison. Bennett's answer to the Consequent-Entailment Question depends unfortunately on his idiosyncratic stipulation about the 'neighbor' relation, and it turns out that that stipulation was motivated only by its ability to yield that answer to the Consequent-Entailment Question. Thus, despite its ingeniousness, Bennett's theory gets us no further forward on the Consequent-Entailment Question in particular. Let us turn to the account that falls out of the Event theory of conditionals. Though I had no such intention in devising it, the Event theory of 'even if supports a qualified version of the ConsequentEntailment claim. And if correct it explains a good deal. The theory explains (a) why 'Q even if P' is felt to assert that Q, (b) wherein 'Q even if P' is conditional in form despite its seeming to embody a flat assertion, (c) the uneasy feeling of redundancy or superfluity that accompanies recognition of the foregoing two facts, and (d) the actual positive role of'even if P'—all at one stroke. The Event analysis is, remember, (A) ( CER ) (In(e,Q) & (f eR )(In(f,P) D In(f,Q))) Here are the explanations, (a) 'Q even if P' is felt to assert that Q because (according to (A)) its first conjunct says in effect that in any ('envisaged') event, Q. (b) 'Q even if P' is conditional in form in that its other conjunct is a conditional (to which 'even' is applied), (c) The feeling of superfluity is brought on by the fact that the conditional conjunct posited by the Event theory is redundant, being entailed by the previous conjunct. The Event theory's explanation of (d) turns on the function of the parameter R. Suppose the speaker were merely to assert some reflection of (B) (e ER )(In(e,Q)). Now, what the speaker had asserted (what specific proposition he or she had expressed) would depend on the exact value of R, since the formula as displayed is an open sentence until the parameter has been assigned a denotatum in the context. And a hearer who is concerned to grasp the speaker's meaning exactly must know the correct value of R. But that value is something that that hearer would have to work out from the context, employing the almost inarticulate pragmatic rules (whatever they may be) that we use in computing the valuation function for demonstratives and other

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indexicals. Those rules are irreparably vague. Now suppose the speaker is anxious that the hearer fully understand what proposition is being expressed: it would be a good idea to save the hearer the trouble and risk of this pragmatic guessing by making explicit, if s/he can, what had been left merely implicit in the context. And to do this, I submit on behalf of the event analysis, is the function of 'even ifP'. (A) is equivalent to (C) (e ER )(In(e,QJ) & (e ER )(In(e,P) D In(e,Q)), whose second conjunct ensures that among the events 8 R are at least one in which P and at least one in which ~P. Thus, the redundant conjunct serves to assure the hearer more explicitly that circumstances in which (= 'the event that') P are envisaged by the speaker in the context in question. Thus, rather than letting her/his utterance go at (heuristically) In any relevant circumstance that is a 'real' possibility relative to this occasion, Q, the speaker is saying the more explicit In any relevant circumstance that is a 'real' possibility relative to this occasion, and I specifically count the circumstance that P as such a circumstance, Q. The redundancy of 'Q even if P' is just the price that the speaker and hearer pay in extra time and computation for the advantage of greater clarity and ease of communication.9 All that is splendid, but so far it ignores the datum of Pollock's that started Bennett off in the first place. What has our account to say of (13), on its intended reading? My official analysans would be (13*) (e eR )(In(e, she fires him) & (f eR )(In(f, he drinks just a little) D In(f, she fires him))), which is equivalent to (13**) (e ER )(In(e, she fires him)) & (e ER )(In(f, he drinks just a little) D In(e, she fires him)). This is fine for the unintended reading pointed out above, but will not do for Pollock's. Our analysis must somehow be modified to afford focus distinctions like Bennett's. 9 This explanation substantively assumes that the values of R as it modifies both of the quantifiers in my analysans for 'Q even if P' are one and the same, i.e. that R does not take one value for the first quantifier and then a second, distinct value for the second quantifier. But I see nothing objectionable about this; we should expect that the speaker would be envisaging one and the same set of relevant circumstances throughout her/his utterance.

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Note one further feature of my Chapter 2 treatment of 'even if. Unlike Bennett, I have bought into the semantic view of 'even', since the truth condition I assigned to 'Q even if P' differs sharply from that which I assigned to 'Q if P' alone. And I did this without special argument, offering only the plausibility of a paraphrase. My tasks, then, are two, if the spirit of the Event theory is to be preserved in our theory of'even if. I must make room for focus, in the manner of Bennett. And I must either defend or abandon my allegiance to the semantic view of 'even'.

The Beautiful But Penultimate Theory of 'Even If Let us begin by reconsidering my original analysans as a manifestation of the behavior of'even' in general.10 I paraphrased 'Q even if P' as 'Q in any circumstance, including any in which P', while the simpler 'Q if P' comes from the correspondingly simpler 'Q in any circumstance in which P'. What has 'even' semantically added? Seemingly, it has added (i) implicit reference to a contextually specified wider class (here, of real-and-relevant circumstances generally, not just those in which P), and (ii) a universal quantification over the members of that class. That suggests a semantic analysis of 'even' generally, based on our earlier intuitive idea of a 'natural reference-class' within which we distinguish degrees of expectedness. Where Sis a sentence containing 'even', Cis the constituent11 of S and of its corresponding S* that is the focus of'even' in S, unsaturated dashes ' ' indicate the result of subtracting 'even' and C from S, and G is a contextually determined class containing at least 10

Despite my boasts then and now that, on my view, 'even' in 'even if means 'even', Lycan (1984fe) did nothing to show that my original analysans is only a special case of the normal behavior of 'even'. And as we will see in the next chapter Stephen Barker has argued powerfully that my boasts are overdone. 11 I join Bennett in ignoring multiple 'even's and nested 'even's, for simplicity; on those, see especially Kay (1990). I also cannot here investigate the interaction of 'even' with negation, though that and the parallel behavior of 'only' are both fascinating and relevant to the present issues. Horn (1969) called attention to apparently presuppositional phenomena in this regard; 'not' in 'not even' and 'not only' is obviously not the logician's pristine 'external' negation. (See also Ducrot, 1973; Fauconnier, 1976, and again Kay, 1990.) I could not go into my disagreements with Horn without a lengthy digression on the nature of 'presupposition'. But I would note that differential interaction with negation does nothing to embarrass the claim I shall be defending as to the semantic closeness of 'even' and 'only'; for by anyone's lights, 'only" has a negative element impacted within it, and 'even' has not.

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one member 7^ C: S is true iff every member x of G including the referent of C is such that —x—. As in our original analysis of 'even if, the point of the otherwise redundant 'including the referent of C' is to make explicit the fact that the referent of C is indeed a member of G also. G is the 'natural reference-class' I have urged upon Bennett, within which comparisons of expectedness are being made. Like Bennett, I do not build the comparisons themselves into our official truth condition, but consider them as conventionally implicated or lexically presumed by the choice of 'even'. Let us apply this analysis to our opening examples: (1) is true iff everyone in the group was sober, including Grannie. (3) is true iff for you I would eat anything (within reason), including haggis—or on its other readings is true iff for you I would do anything (within reason) including eating haggis, or iff for you I would do anything to haggis including eating it. (4) is true iff the thing in question is fast and durable and has all the other good-making properties (that one might reasonably envisage) including that of being low in price. (5) is true iff she won in every contextually desirable way including graciously. And, joy of joys, (2) is true iff every one of the creatures including the mice remained motionless—here the 'wider class' G is mentioned explicitly. All these semantic proposals are plausible12 (though we shall see later on that they are flawed). Moreover our analysis affords us a way of attending to focus distinctions. Recall Grannie and the coat. (6) and (7) do indeed now differ in truth condition, since the latter implicitly refers to a group and entails that everyone in that group put on his or her coat. (8a) is true iff Grannie did everything, including putting on her coat; (8b) is true iff Grannie put on everything including her coat; and (8c) is true iff Grannie put on everyone's coat including her own. This all seems right, so far. Let us now return to Pollock's example of the puritanical boss, which inspired Bennett's paper and caused trouble for my own initial analysis of 'even if. Recall that Pollock's sentence 12

If for the moment we ignore the difference between entailment and conventional implicature, this analysis is almost exactly that of Karttunen and Peters (1979). See also Barker (1991). Notice that the universal quantification here posited can be degenerate: Horn (1992) cites an example of Bruce Eraser's, 'Come on, Chris, eat up—even little Billy finished his cereal". Here the class G, that of other children at the table, may not extensionally be wider but include only Billy.

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(13) Even if he drank just a little she would fire him has an unintended reading on which (given an anti-puritanical boss) it does entail or imply that she would fire him. That is the reading on which the focus of 'even' is the conditional antecedent, and it fits perfectly with my initial analysis in Chapter 2 (she would fire him in any circumstance, including any circumstance in which he drank just a little). The problem was that (13) also has the intended, puritanical reading on which it obviously does not even suggest that she will in fact fire him. I suggested that this is a focus phenomenon. Our new analysis of'even' confirms that suggestion. For the new analysis lets us shift our attention to 'just a little' as the more likely focus for 'even'. On that focus assumption, our truth condition for Pollock's sentence is that, if he drank any amount, including just a little, she would fire him, or more formally, every amount including just a little is such that if he drank that amount, she would fire him.13 And this too comes out right. It seems our new semantic analysis has succeeded in making room for the needed focus distinctions, as, being semantic, it might have been expected to do. What about Bennett's example, (22) Even if the bridge were standing I would not cross? Bennett's problem was to account for (22)'s apparently entailing or implying that I would not cross; Bennett's solution depended on his idiosyncratic, arbitrary, and otherwise counterintuitive twist on the 'neighbor' relation. By contrast, my initial analysis handles the sentence perfectly: I would not cross the bridge in any (envisaged) circumstance, including any in which the bridge is standing. We now see that other readings of the sentence are both possible and accommodated by our new general theory of'even'. Suppose I am in fact going to cross and everyone assumes that. But it is wartime and we are discussing scenarios. The enemy might want to obliterate the area, and if so would watch out for survivors and still-standing structures, and on sight of any would saturation-bomb the river and anything crossing it. I say, (23) If the tall radio tower were still standing, I would not cross the river; for that matter, if the BOQ were standing I would 13

Formally, in comparison to (13*), where 'a' ranges over amounts, (13***) (a) (eeR) (In(e, he drinks a) D In(e, she fires him) & (eeR) (In(e, he drinks just a little) D In(e, she fires him)))'.

108

Beautiful But False Theory of 'Even If not cross; even if the bridge [a considerably lower structure than either the radio tower or the BOQ] were standing I would not cross.

This is true iff for any former local structure x including the bridge, I would not cross if x were standing (under the saturation-bombing circumstances). Or consider a case in which bridges and other familiar objects are behaving oddly and we do not entirely know what to expect. Let us suppose our own bridge is trustworthy and we are confident it will continue living up to the highest principles of bridgehood, but (as before) we are also envisaging unlikely scenarios. In one of these the bridge has played all sorts of tricks and is quite unpredictable. I say (24) If the bridge were submerged I would not cross; for that matter if the bridge were dancing and singing I would not cross; even if the bridge were standing I would not cross, which is true iff for any activity on the bridge's part including its (just, as usual) standing, I would not cross in the imagined circumstances. This appears to dispose of Pollock's and Bennett's problem. But the solution is not so simple. At this point we must acknowledge a trenchant point made by Barker (1994), that refines the Consequent-Entailment problem. He notes that there is a class of 'even if conditionals which focus the antecedents but which, in context, do not even seem to entail or assert their consequents; and the reason for this is important. Notice that until now I have spoken glibly of 'the reference-class' attaching to the use of an 'even if conditional in a context. But by my own account, context associates two distinct classes of items with such a use. There is the comparison class of conditions, 'G', collected by 'even' as in any use of 'even', but there is also the more basic reference class R of 'real and relevant' circumstances needed to interpret the original conditional to which 'even' has been applied. Barker rightly complains that Lycan (1991) neglected the distinction. At least, I simply assumed that the conditional's reference class R was a subclass of the comparison class of'even'. On that assumption, it is true that an 'even if conditional in which 'even' focuses the whole antecedent will entail or assert its consequent. But the assumption does not always hold; a possibility can be both relevant and epistemically 'real' without being in G, and context can make this clear. (This will

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be illustrated in Chapter 6, when Barker's point becomes especially pertinent.) Accordingly, the formula I associated with 'P even if Q' in Chapter 2 cannot be taken as the full logical form of that schema, but only as a prominent special case. Barker paraphrases the 'even' away as 'Every situation/in G, including P, is such that (if/obtains, Q)', and then gives the full logical form as 'Every situation/in G, including P, is such that Q in any situation e of R in which /obtains' (1994: 251; I have adapted his original formulation to the schematic letters P and Q, comparison class G, and reference-class R). The latter in symbols is c (f E G)((e E R )(In(e,P) D In(e,Q)) & (e ER )(In(e,f) D In(e,Q)))', from which, if but only if R is assumed to be a subset of G, our original formula (e ER )(In(e,Q) & (f ER )(In(f,P) D In(f,Q)) can be derived.14 It remains to show independent reason why we should suppose that any version of the semantic view is correct, and why in particular we should think that 'even' actually reflects a universal quantifier in logical form, rather than being tied to the relevant comparison class by some merely pragmatic means. To my knowledge, no one save Lycan (1991) and Barker (1991) has ever made, entertained, or even tolerated the latter suggestion.15 But I shall give three arguments in its favor. First,1 semantically empty words are rare in natural languages. There are of course one-word utterances such as 'Hello', 'Damn', and 'Ouch', that are language-specific but arguably have no truth conditional semantics. There are also vocables that can be interpolated into 14 The original formula probably does represent the truth condition of the closely related sentence schema, 'If P, still Q', as in 'If you pass the exam, you will still fail the course". (Barker (1991) argues against the equivalence of'Even if P, Q' and 'If P, still Q', though presumably 'Even if P, still Q' is equivalent to the latter.) (Barker (1991, 1994) offers his own theory of 'even'. Like mine, it is a quantifier theory, though Barker accepts the conventional view rather than the semantic view. His theory has at least one or two advantages over mine, and one day I should duke it out with him.) Points parallel to Barker's about the two referenceclasses would have to be made about 'only if as well, if we want to take 'P only if Q' strictly as the result of modifying the conditional 'P if Q' (which, notice, would enforce the biconditional interpretation of 'only if). 'Only* induces a comparison class G in addition to the reference class R underlying 'if. The full logical form of 'P only if Q' would have to be rendered as something like '(e eR )(In(e,Q) D In(e,P)) & (f eG ) (e eR )[((In(e,f) D In(e,P)) D In(f,Q)]', from which I believe'(e eR )(In(e,P) D In(e,Q))' can be derived, but again only if R is assumed to be a subset of G. 15 There is a passing hint of it in Rivero (1972: 202): 'the semantic effect of even is "in all possible worlds"'. 16 I owe this and the next one to Geis, in conversation.

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structured sentences but arguably add nothing to truth conditions, such as 'oh' and 'say' ('Oh, shut up'; 'There are maybe, oh, four of them'; 'Let's do that, say, five or six times'). But such vocables require commas, presumably because they are discourse markers of some sort rather than genuine constituents of the sentences 'in' which they occur. By contrast, 'even' needs no commas. Few other English words are as comfortably embedded within sentential structure but are semantically empty.17 Second, we have already seen some evidence that 'even if involves a universal quantifier. Notice too that it paraphrases some more explicitly quantificational expressions: (25) You can give me your letter; I have to go to the Post Office anyway any case. case in any in any event. (25)'s second clause is well paraphrased by (26): (26) I have to go to the Post Office even if you don't give me your letter. 'Even' seems to make just the same concessive contribution as do 'anyway' and the rest. My third argument is more straightforward and I think compelling, though it is overlooked by philosophers everywhere:18 'even' is very closely akin to 'only' in its grammatical behavior and in its range of hospitable syntactic environments. Both words are 'floaters', in that they can occur in almost any grammatical position: Even

Only

1 hit him in the eye yesterday.

17 Actually, I would argue that in its estimative use, 'say' abbreviates the more obviously truth-conditioned 'let us say'. And I would adopt the same strategy in regard to words like 'too' and 'instead': 'too' means 'as well as X', and 'instead' means 'in the stead of X'. There is a class of expletives, paradigmatically swear words, that are arguably purely expressive rather than truth-conditional in meaning, as in 'That goddam cat has thrown up right in our stereo headphones'. (It would take a very radical anti-pragmaticist to insist that 'goddam cat' actually means 'cat that has been damned by God'.) As before, a proponent of the minimal view might maintain that 'even' should be assimilated to such expletives. I cannot refute that suggestion, but the expletives are more obviously and somewhat ritualistically emotive. 18 But see the linguists Horn (1969), Geis (1973), McCawley( 1974,1986), Rooth (1985), andBrugman (1986).

Beautiful But False Theory of 'Even If even only

I

I hit

111

hit him in the eye yesterday

even only

him in the eye yesterday.

even . only

I hit him

*?I hit him in

in the eye yesterday.

even . only

I hit him in the eye

the eye yesterday. even . only

yesterday.

I hit him in the eye, yesterday

even. . only

(But *?The library is closed on

even only

Sunday (Rooth, 1985: 93).

Neither 'only' nor 'even' can occur comfortably within certain simple PPs.) The similarity is all the more remarkable when one considers that very few words in English can float so freely.19 Moreover, when they float, 'even' and 'only' generate parallel patterns of focus ambiguity: Even

Only Not

Grannie was sober. (Univocal.)

even . only

Grannie liked the movie. (Univocal.)

19 And, when they float, they generate similar focus ambiguities. Other floaters are 'just' (usually a synonym of'only"), 'at least'/'at most", 'maybe', 'too', and 'also'. Notice that all have reasonably clear quantificational or otherwise referential values. A referee of Lycan (1991) suggested the addition of the hedges 'kinda' and 'sorta' to this list, but such hedges cannot normally focus proper names: *'Kinda John sang'. The same referee also pointed out a difference between 'even' and 'only' that needs explaining: 'even', but not 'only", can focus an item to its left (without special intonation or other emphasis).

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Beautiful But False Theory of 'Even If

For you, my dear, I would

ven ] ° '

eat haggis. (Same ambiguity

for 'only' as for 'even'.) Even Only

it he drank just a little,

she would would she

fire him (Par-

allel ambiguity again. The order inversion in the consequent is a negative polarity item, caused by the negative element within 'only'.) Edna

gven ° '

showed uop. (Parallel ambiguity between the

subject as focus and the predicate as focus.) John's mother ridiculed

gven I °nl7

him. (Univocal. Note that ad-

verbs cannot similarly intervene between V and NP, as in *'John's mother ridiculed recently him' (Rooth, 1988: 89); 'only' and 'even' are not adverbs.) The moral is that 'even' and 'only' are syntactic soulmates. Their surface distribution is uncannily alike.20 And 'only' is uncontroversially a quantifier,21 restricted in context to a salient class of items. It would be very surprising if 'only' had so robust and classical a semantic value while 'even' had no semantic value at all. In fact, once one gets used to the idea that both words determine a context ually natural reference-class relative to focus and that the reference20 Though not, strictly, identical, for each has other peripheral uses. 'Only yesterday" can mean 'as recently as yesterday" as well as 'on no day other than yesterday", and 'even' has no parallel use unless an archaic one that, oddly, means the same thing. 'Only* can occur as a shriek or uniqueness marker in definite descriptions, as in 'My only brother has been arrested", and there is no parallel use for 'even'; I suggest that is due to the negated-identity semantic meaning of 'only', obviously not shared by 'even'. 21 Uncontroversially among philosophers and logicians, at least. Someone—more likely a linguist than a logician—might assimilate 'only' to 'even', and argue that all that is entailed by 'Only Susan left' is that Susan left, while no one else's leaving is only conventionally implicated. (Recall our brief discussion of this in Ch. 2. n. 24.) But such a view is implausible. If there were an entailment/implicature asymmetry, it would cut in the other direction, i.e. it would be entailed that no one other than Susan left, and merely implicated that she did (as e.g. in Horn, 1969). Also, standard conventional implicatures are contrastive or otherwise attitudinative, not structural. An apodeictic relation between a sentence and a distinctively related quantified formula is semantic.

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classes are exactly the same everywhere, it is easy to see how the two words differ as quantifiers over that class. An 'only'-sentence is true iff none but the mentioned member of the reference class satisfies the schema that results from deleting only itself and the mention, while an 'even'-sentence is true iff every member of the reference-class including the mentioned member satisfies that schema.22 In brief, 'only' means 'none except', 'even' means 'everything including'. The two are logical contraries up to the mentioned member.23 In the Venn diagram, Gis the contextually indicated reference-class; S represents the matrix; shading indicates the emptiness of a class; x indicates occupancy; m indicates the mentioned member. ' Only m is S'

' Even m is S'

The argument is, then: (i) 'only' and 'even' are syntactic soulmates, in that they show identical distribution patterns over an extraordinary variety of syntactic environments; (ii) each of the two determines a 'natural reference-class' of items, and in a given syntactic environment both determine the same class, without fail; (iii) 'only' is uncontroversially a universal quantifier whose domain is the class in 22 Recall the truth condition for 'even' presented above. The corresponding truth condition for 'only' is as follows. Where S is a sentence containing 'only', Cis the constituent of S and of its corresponding S* that is the focus of 'only' in S, unsaturated dashes ' ' indicate the result of subtracting 'only' and C from S, and G is a contextually determined class containing at least one member ^ C: S is true iff no member x of G except the referent of C is such that —x—. (In putting forward this formulation, I have not tried to deal with the obligatoriness of internal negation, e.g. by splitting the analysans into assertion and presupposition. Again—cf. n. 12—my preferred treatment of negation would be a long story.) 23 Horn (1969: 106) saw a similar contrareity relationship, but expressed it in terms of the then going semantical distinction between assertion and presupposition: 'even... asserts what only presupposes and presupposes the negation of what only asserts'. The detail of Horn's thesis is criticized by Kay (1990: 86-7). Stevan Hamad has also observed in conversation that in English, Hungarian, and other languages, 'even' is fairly well paraphrased by 'not only non-', if the second negation is taken to apply promiscuously to any possible focus.

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question; (iv) when 'even' is accordingly though unprecedentedly interpreted as the near-contrary universal quantifier, the resulting paraphrases of typical 'even'-sentences are compellingly attractive; therefore, irresistibly, (v) 'even' is that near-contrary universal quantifier, and the semantic view is vindicated. Notice that, if that conclusion is correct, it reinforces the case for my general thesis that 'if'-clauses quantify over a domain of items, in light of the simple fact that 'even' applies to 'if exactly as 'only' does. There are other operators as well whose function is to indicate contrasts within the membership of a contextually indicated reference class, such as 'especially'. (27) a. Everyone was embarrassed, especially Ned. b. Ned especially was embarrassed. (Tacitly calls attention to a group.) Significantly, 'especially' applies to 'if: (28) a. A grizzly will chase you, if he isn't tired and if he's hungry and especially if you're carrying meat. b. A grizzly will chase you, especially if you're carrying meat. It would be great to stop here and pop the cork. But I must address a number of potential counterexamples to our account of'even'. Three of them will prove crucial, and require significant and rueful revisions.

6

An Unbeautiful But Less Easily Refutable Theory of 'Even If Four Apparent Counterexamples to the Beautiful Theory A first counterexample is discussed at some length by Bennett: the use of 'even' as an intensifier of comparatives, as in (1) Bill is even taller than John. (1) of course has several readings on which it fits our analysis and Bennett's alike (those in which it means that even John is shorter than Bill, that among Bill's accomplishments is even managing to be taller than John, etc.). But (1) can and would often mean that although John is tall, Bill is taller. Bennett argues convincingly that this ambiguity is not a focus ambiguity like the others—notice that on the comparative-intensifying reading, 'even' cannot be made a tag, as in (2) Bill is taller than John, even, —and he claims it represents what is simply if unexpectedly a different lexical use of'even'. He notes that French distinguishes it ('encore') from the use that concerns me ('meme').1 Someone impressed by the Beautiful analysis might think of isolating a reference-class of degrees oftallness, but I see no satisfactory way of following this through; the best I can do by way of a truth condition is: every (envisaged) degree of tallness including John's is such that 1 And cf. Italian 'anche' vs. 'ancora', German 'auch' vs. 'je', and to some degree Dutch 'zelfs' and 'nog'. Bennett's own example of the comparative-intensifying use is 'My wife's satisfaction was even greater than mine' (1982:408). The separateness of that use of'even' is supported by the ambiguity of his own example itself, parallel to that of our sentence (1). On its comparative-intensifying reading it entails that my satisfaction was great. But consider also the case in which my wife's satisfaction had a number of interesting properties: being timely and being hard-won, which were expected, but also being greater than my satisfaction, as was unexpected, even though my satisfaction in this case was zero. I think perhaps Kay's (1990) theory of 'even' might manage to subsume the comparative-intensifier use, but I shall not pursue that here. Barker (1991) claims to subsume it under his quantificational theory, but his claim is, I think, refuted by Berckmans (1993: 592-4).

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Bill's tallness has (at least) it. Though plausible, this does not carry the requisite implication that both John and Bill qualify as tall, period (that their degrees of tallness fall within the high range). Consequently I agree with Bennett that the comparative-intensifying use of'even' is simply a different though paronymous lexical use of'even'.2 The second apparent counterexample is (3) You have to be 11 or 12 or even 13 to get your ears pierced. Construed as a comment on the ages at which various children are allowed by their parents to get their ears pierced, (3) means roughly that some parents make their children wait until they (the children) are 11, some require that they be 12, and some require, even more stringently, that they be 13. Here again, appeal to a reference-class does not seem to help fit the example into our general analysis of'even'. The obvious reference-class is that of ages at which the relevant children are allowed by their parents to get their ears pierced. But does (3) mean anything of the form, 'Every age at which any of the relevant children is to be allowed by their parents to get their ears pierced, including age 13, is F'? The best instance of this construal I can come up with is to replace 'F' by 'at least 11 and is required by some parent', 13 being less expected to be required than is 11 or 12. This is awkward at best. I would be unashamed to leave (3) officially unsolved, since (3)'s modal operator and funny surface disjunction make (3) an especially puzzling sentence to begin with, even discounting the focus of 'even'. But Jonathan Bennett has suggested to me that (3) can be seen as an instance of the disparate comparative-intensifying use. Each of the ages is felt (by the speaker) to be pretty advanced; one could not say (4) *You have to be 1 or 2 or even 3 to get your ears pierced. And (3) is plausibly glossed by 'You have to be pretty old to get your ears pierced—11 or 12 or even 13'. Notice also that the surface disjuncts are ineliminable: (5) *You have to be even 13 to get your ears pierced makes no sense on its own. I think that is because the comparativeintensifying use of'even' is of necessity comparative: at least two items 2 A perhaps related use is the slightly archaic 'even as", as in 'Gaius was brought down by his overweening pride, even as his father had been brought down thirty years before", which is not contrastive at all, but equivalent to 'just as" or 'exactly as". 3 I owe this example to Jane Lycan, spontaneously in conversation.

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must be mentioned and compared, one of which has a positive scalar property and the other has the same property to a greater degree. So I gratefully accept Bennett's suggestion. It may be wrong; note that 'even' in (3) translates into French using 'meme' rather than 'encore', though that may be because there is no explicit comparative term. And the details of (3) would be both difficult and fascinating in any case, but (3) is no great threat for now. The third counterexample is our friend (12) from Chapter 3, renumbered here: (6) I'll be polite even if you insult me, but I won't be polite if you insult my wife. My analysans for that sentence is (6*) (e ER ) (In(e, I am polite) & (f eR )(In(f, you insult me) D In(f, I am polite)) & (geR) (In(g, you insult my wife) D In(g, ~(I am polite))). This formula is not itself a contradiction, but it entails that there is no event 8 R in which you insult my wife, which then leads to contradiction, once the Antecedent Requirement ensures via the third conjunct that there is such an event. Some response is required. In Lycan (1984&) I made the move of claiming that even though R had not changed its value from its first occurrence to its second, it did change its value from the first and second conjuncts to the third. The idea was that an utterer of (6), while uttering the first two conjuncts, did not envisage his hearer's insulting his wife, but suddenly came to envisage it and therefore uttered the third conjunct. The plausibility of this increases if we choose not to require the inclusion of all actual relevant events in R since, on my analysis under that requirement, (6) would entail that the hearer will not in fact insult the speaker's wife, which seems wrong. If we drop the Reality Requirement (Chapter 3), this consequence is avoided. The intuitive content of (6) could then be expressed as, 'I do not as things are envisage any real and relevant possibility that I will not be polite, not even one in which you insult me, but if I now make myself envisage one in which you insult my wife, I will not be polite in any such event'. So we have a bit more motivation for choosing not to impose the Reality Requirement.4 4

To drop the Requirement will force revision of our solution to the ConsequentEntailment problem; see below.

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As we saw, with the Reality Requirement stands or falls Modus Ponens. If Modus Ponens seems a high price to pay for (6), notice as in Chapter 3 that (6) creates a pre-theoretic difficulty for Modus Ponens, quite apart from the Event theory. Again, suppose I token (6) and you do proceed to insult both me and my wife, whereupon I am very impolite. Then although (6) was presumably true, its first surface conjunct Til be polite (even) if you insult me' has a true antecedent and a false consequent. Nor is the problem generated by the presence of 'even'. Still, the present treatment is somewhat stilted and I would like to do better. Our problem is not the semantic view of 'even', but the fact that a speaker can imply a global constraint on his or her conduct in one conjunct and then make an exception to the constraint in the next. In light of our discussion of Pollock's example, we might think of now trying to make Gibbard's datum into a focus phenomenon also. But that is unpromising. 'Even' occurs only once in Gibbard's sentence, and so cannot change its focus in the course of the example. And whether we take the focus of 'even' to be the first conjunct's whole antecedent or just 'me' (qua representative of the class of potential insultees), the second conjunct seems to contradict the first just as before. I cannot for now improve on my earlier parameter-shift hypothesis. However, I can make it a bit more plausible by pointing out that intrasentential parameter shift is far from unknown in English. Here as in Chapter 3, the parameter-shift hypothesis may look odd if one takes a very literal view of 'envisaging'; it is psychologically unlikely that anyone could utter (6) without actually having considered the possibility that the hearer might insult his wife. But remember that 'envisaging' as I have conceived it is in part a stylized matter of conversational pose. And there are plenty of examples of single sentences within which quantifier restriction classes are widened, without any actual doxastic change occurring episodically in the speaker. Recall (7) Subway Club with everything and also hot peppers, please. Or:

(8) I'd do anything to get into that fraternity, Sigma Phi Nothing, but of course nothing actually against the law. And a further example, attributed to Yogi Berra, in reference to a New York restaurant:

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(9) Nobody goes there; it's too crowded. (Admittedly (9) is an oxymoron, but its meaning in context is clear and unparadoxical.5) Notice too that ordinary 'even' sentences exhibit the widening feature: (10) I'll eat anything on pizza, even squid or bull's testicles, but not a brick or a crowbar [or the number 7 either]. I would be willing to leave the Gibbard situation at that. But an alternative possibility will be suggested, indeed required, by an adequate response to the last of our four problem cases. That fourth apparent counterexample strikes right at the heart of my novel semantic analysis of'even'. I contend that 'even' is a universal quantifier. But universal quantifiers have the habit of being, well, universal. Thus on my view, within the reference-class presupposed by any given use of 'even', there can be no exceptions. Yet 'even' does seem to admit exceptions. Suppose that, of a large group of people invited to a certain party, all are very likely to attend. Gonzo and Bluto, in particular, are party animals and virtually certain to go. However, as it turns out, nearly everyone ends up staying home on the night in question, because there is an outbreak of stomach flu and not even Gonzo and Bluto feel very well. Bluto succumbs, but Gonzo manages to drag himself to the party none the less, finding himself alone with the chagrined host and a forlorn stack of party hats. The problem is caused by Bluto. It is that (11) Even Bluto stayed home seems entirely assertible in the case described, Bluto being the least likely to have stayed home of those who did stay home. But my Beautiful theory analyzes that sentence as 'Everyone stayed home, including Bluto', which is falsified by the intrepid attendance of Gonzo. In fact, as was argued by Kay (1990), the tale of Bluto and Gonzo is only one of a large array of counterexamples to the popular 5 One of my favorite cognate examples, though the restriction class is narrowed rather than widened: ' "The thing is, you see," he said, gesturing at the twenty-or thirty-strong mixture of races, colours, creeds and no doubt other variables that sprawled or lurched in the far from extensive area close by the bar, "that nobody ever comes in here."' (Kingsley Amis, The Folks that Live on theHill (London: Hutchinson, 1990), 134).

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idea that 'even' is an 'end-of-scale' marker. Our present penultimate account follows most of the literature in assuming that the mentioned member of the reference-class of 'even' must be the most extreme, least 'expected' member to occupy the matrix at hand (e.g. Fauconnier, 1976). But witness Kay's further examples (1990: 89-90): (82) Not only did Mary win her first round match, she even made it to the semi-finals. (83) The administration was so bewildered that they even had lieutenant colonels making major policy decisions. Acceptability of (82) does not depend on the presence of some very special kind of context in which reaching the semi-finals, as against winning the tournament, is in some appropriate sense end-of-scale. In (83) it is clear that having majors, captains, or sergeants making major policy decisions would provide the basis for even more extreme assertions: lieutenant colonel is not an end-of-scale item here. It may be true that the semi-finals were the highest stage of the tournament that Mary did win, and that lieutenant colonels were the lowest-ranking military personnel who were in fact making decisions, but it does not follow that either were respectively end-of-scale relative to contextual expectation or envisaging. The problem is, then, part of a general difficulty for our understanding of'even'. The general difficulty is that of determining exactly where and how the conventionally implicated contrast of likelihood cuts into the reference-class in question. And the Gibbard problem is a special case of it as well. The Contrast within the Reference-Class Bennett's theory incurs that difficulty in a more obvious way. Consider a variation on the previous example. As before, almost all the invitees are very likely to attend the party. Again Gonzo and Bluto are certain to go. However, Clarence is quite shy and virtually never goes to parties, and James is virtually autistic, refusing ever to have anything to do with them. Now this time, the flu outbreak disables everyone, even Gonzo, and everyone stays home; Clarence and James had no inclination to go anyway. But since James was even less likely to go than was Clarence, Bennett's analysis would license (12) Even Clarence stayed home,

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which is intuitively not assertible here since it was never doubted that Clarence would stay home. One might think of revising Bennett's analysis by requiring that not just one but every 'known' and 'related' neighbor of S be less surprising than S*. But that would be essentially a reversion to my own present account, and so too strong. As we have seen, one could properly token (11) even if one knew that (as in the original version) Gonzo had managed to attend. One way to avoid the counterexample would be to modify my analysans by substituting a weaker quantifier than the universal, such as many. Thus 'Even Grannie was sober' would be taken to mean, 'Many members of the group were sober, including Grannie', and 'For you I would even eat haggis' would mean 'There are many things I would eat for you, including haggis', or on the other readings 'There are many things I would do for you, including eating haggis', 'There are many things I would do to haggis for you, including eating it', etc. (How many counts as 'many' in each case would, of course, be contextually relativized to the reference class.) For 'even if conditionals, our official analysis would accordingly be weakened to 'Q in many events, including all events in which P', or (M) (MANY e ER )(In(e,Q) & (f eR )(In(f,P) D In(f,Q))). This treatment would of course solve the Gibbard problem as well, for Gibbard's sentence (6) would now be entirely consistent as it stands and there would be no need to posit a mid-sentence parameter shift; the wider of the two reference-classes would be in force from the beginning. Yet the weakened analysis is still not satisfactory. For it does not explain the initial plausibility of the universally quantified paraphrases. Those paraphrases, both of plain 'even' sentences and of 'even if conditionals, are accepted at first hearing by all my informants, and continue to sound right to everyone until counterexample cases such as Gibbard's, Kay's, or my Gonzo example are discovered by theorists. (Pollock's counterexample to Consequent-Entailment does not count, for it turned on a focus distinction unrelated to the Gibbard/Gonzo/Kay problem.) Moreover, ordinarily when a sentence reflects a 'many' quantifier, there is no such illusion of universality. No one would even initially accept universal paraphrases of (13) Jeanne often forgets to eat

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It is hard to doubt that 'even' involves universal quantification in some way. Moreover, to posit only a 'many' quantifier would lose touch entirely with the Consequent-Entailment problem. For the 'many' quantifier does not guarantee that any actual event falls within its range (even if the Reality Requirement applies and guarantees the inclusion of some actual events in R); thus (M) carries no implication of Q. I take illumination of the Consequent-Entailment problem to be a sine qua non for a theory of 'even if'.5 A deeper problem of contrast within the reference-class is that some enumerative uses of 'even' seem entirely non-scalar and do not induce any credible universal generalizations.7 Berckmans (1993: 601) offers the following attested examples. (15) A vouvray, an Australian chardonnay or even a good vintage champagne would go well with scallops in creamy leek sauce. (16) Carol Nelson, a basket weaver, teaches others to dye fabric and dried grass using the juices of beets, berries and even onion skins. Obviously (15) does not imply that every wine whatever would go with the scallops, but neither does it suggest any particular narrower 6 The same objection applies to a suggestion that can be extrapolated from an observation of Kay's (1990:90 n. 32): One might try restricting our quantifier to the group of things satisfying the containing matrix. Thus one might think of understanding (11) as meaning just that the group of people who stayed home included (as was unlikely) Bluto. As it stands, that interpretation would logically not exclude the possibility that the group had only one member, and it was only Bluto who stayed home; and we need to preserve the idea that a sizeable group did stay home, which group included Bluto along with some people more likely to have stayed. But to do that, we could just stipulate it to be conventionally implicated or lexically presumed that significantly many stayed home, glossing (11) redundantly as 'Everyone (of the significant number) who stayed home stayed home, including Bluto (as an extreme case)', which is of course equivalent to the existential quantification 'Some (significant number of) people stayed home, including Bluto (as an extreme case)'. The objection again is that when applied to conditional antecedents, this redundancy treatment of 'even' would make the Consequent-Entailment phenomenon a mystery. 'I'll leave even if you leave' would mean just, 'Some (significant number of) circumstances are ones in which I leave, including all those in which you do', which neither entails nor even strongly suggests that I will, in fact, leave. 7 Vic Dudman has protested to me in correspondence that 'even' generates no quantificational entailments at all, not even that of the constituent item's not being alone. He may be right; we should entertain that possibility. But my intuitions go sharply against it, and so do those of all my other informants.

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class of wines, all of which would. Similarly, (16) does not imply that Nelson teaches others to use either every juice there is or every juice that meets some particular further condition.

Preserving Universal Quantification (First Attempt) I can think of two further possible means for preserving the idea that 'even' is a universal quantifier. One, the more conservative, is to return to and generalize my original treatment of Gibbard's sentence (6). For (6) I posited a mid-sentence widening of the reference-class, stylized rather than psychological. Let us now extrapolate that idea to 'even' toutcourt. Our non-conditional problem sentences were (10) ('I'll eat anything on pizza...') and (11) ('Even Bluto stayed home' where the indefatigable Gonzo managed to attend the party). The former seems an obvious example of reference-class widening, the first class including only edibles, however dubious. The latter is less obvious, since only people are involved throughout. But it is not badly glossed by 'Everyone but the most totally outrageous invitees, including Bluto, stayed home' (not counting the most totally outrageous invitee, Gonzo). There is still a narrower class, contextually 'within reason', within the wider specified class that still does not include every item in the universe or even every human being; for the conversational purposes of the moment, Gonzo is put beyond the pale. And quantification is universal over the narrower class, before sometimes being widened in mid-sentence. But this conservative treatment is not so good for Kay's examples, as he anticipated in the passage I have quoted above. (82)'s second conjunct is not so well glossed by 'Mary won everything but what would be completely preposterous, including the semi-finals'; no more is (83)'s embedded clause by 'The administration had everyone within reason making major decisions, including lieutenant colonels'. For it is implausible to think that the degree of extremity to be counted as 'preposterous' or complementarily 'within reason' was all that precisely fixed by context in advance; to assume that such limits were so fixed seems to beg the question in favor of our conservative account. As Kay says, we have no independent reason to suppose that 'some very special kind [or rather, feature] of context' fixes the domain of our putatively extra-restricted quantifier just where we would now like to deploy our 'even'.

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I agree that there need be no pre-set boundary encircling the 'expected', reasonable, non-extreme, non-preposterous, or the like. I am less convinced of the unsuitableness of the new 'within reason' paraphrases; for the phrase 'within reason' is itself highly contextrelative, and might be supposed to slide along with 'even'. Thus 'even' could be taken just to mean 'every... within reason, including...', the application of 'within reason' being controlled, not antecedently, but by the speaker's preference of the moment. Since the phrase 'within reason' is often used adventitiously to the point of caprice, the present idea seems tenable, but it is still somewhat ad hoc. Kay's own solution to our problem of setting the contrast within the reference-class is piquant. If I read him correctly, he suggests that context determines a single less extreme or more 'expected' member of the reference-class, with which 'even' now contrasts the newly mentioned member. (But that determination and contrast proceed only byway of a prior difference in semantic or pragmatic informativeness between the sentence containing 'even' and an antecedently determined 'context proposition' about the more expected member, 'informativeness' being a matter of contextual entailment relative to a 'scalar model', in a sense Kay carefully develops.8) In Bennettian terms, there is a single neighbor !Sj determined in context along with a scalar model, and S* contextually entails !Sj relative to that model. My beloved Beautiful theory falls out of Kay's account as a special case, namely, that in which the 'context proposition' !Sj happens to be a universal quantification: if everyone was sober, including Grannie as the extreme case, then for Kay, 'Grannie was sober' contextually entails 'Everyone was sober in a scalar model of expected sobriety that ranks Grannie last' (pp. 80-1). But Kay's theory is ostensibly broader, countenancing pairwise comparisons that are made without semantical quantification over a group. I have two objections to Kay's idea, one internal, one external. The internal objection is that context does not always determine a single contrasting proposition or class member, any more than it does a 'reasonable' or 'non-preposterous' set of expected members. Kay's discussion concentrates (though not exclusively) on examples in which pairwise comparisons are fairly explicit in the discourse. But 8

Kay's theory, stated at the level of whole propositions, makes no mention of referenceclasses; but as we shall see, nothing in his discussion suggests the needlessness of that notion.

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sentences containing 'even' can also initiate discourses out of the blue. Consider the following sentences specifically as doing that. (17) I am going to get to Sydney next August, even if the ticket costs $5,000. (18) Even Jenner couldn't jump that. (Said regarding a high bar that someone has left in an impossibly elevated position, Jenner being an Olympic athlete.) (19) I'd give even a hand or a foot to be able to sing like that. Granted, for each of (17)-(19), we can think of some appropriate single items of favorable comparison ($2,500; the high-school track star; a little finger). And, if challenged, a partisan of Kay's view could always choose one that was not too badly motivated. But no such item is psychologically real in the speaker at the time of uttering. The speaker is really making only a general comparison of the focused things with the respectively normal ranges of items in the referenceclass. We could try to stipulate a default 'context proposition' for such cases, say in terms of a 'normal' or 'typical' member of the referenceclass, but there is no reason to think any such single proposition is psychologically real either.9 Assuming the correctness of this last criticism, I do not yet see the advantage of Kay's view over my last suggestion about a sliding use of 'within reason'. Nor has Kay given us reason to abandon our independently defended semantic idea of quantification over a group, since his own account itself posits a group of items immanent to each scalar model (and I can see no example in his paper that does not at least loosely determine such a group10). My external objection to Kay's theory is that, when applied to 'even if, it flouts the Consequent-Entailment problem. (20) I'll stay even if Geoff starts throwing up, uttered without qualification, is felt to entail that the speaker will stay. But now how does Kay's analysis apply to conditionals? Let us waive my internal objection and suppose that someone has provided a single salient 'context proposition' for (20), say by having asked, 9 Berckmans (1993) offers a two-pronged positive theory of 'even', one prong of which resembles Kay's account; I am not sure whether it succumbs to the present objection. 10 The example least obviously likely to generate a reference-class is probably 'He worked hard and the boss wasn't even there' (attributed by Kay to Oswald Ducrot). But I take it the relevant class is that of conditions under which he would (or would not) work hard.

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'Will you stay if Dick starts telling his damn parrot jokes?' According to Kay, (20)'s 'even' is lexically correct iff the S* or corresponding 'text proposition', 'I'll stay if Geoff starts throwing up', contextually entails (21) I'll stay if Dick starts telling his damn parrot jokes relative to the appropriate scalar model. And, assuming the scalar model ranks Geoff's throwing up as more extreme than Dick's telling his parrot jokes, that condition is satisfied. But merely the truth of (20)'s 'text proposition' plus the satisfaction of that lexical condition does not entail, or even appear to entail, that I will stay. Kay's 'even' is justified eo ipso by the contextual extremity of Geoff s throwing up relative to Dick's telling the jokes, and that is all there is to it. So Kay has not explained why (20) does by itself seem to entail that, and indeed has (so far) predicted that (20) does not entail it. One might argue on Gibbard's grounds that (20) just does not have the entailment in question, for (22) is consistent: (22) I'll stay even if Geoff starts throwing up, but not if Shi'ite terrorists break in with combat weapons. And that is correct; 'even if conditionals do not categorically entail their consequents—not even on my own original theory, if the Reality Requirement is abandoned. But we still need to explain why they are heard as implying their consequents in contexts where the focus of 'even' is the whole conditional antecedent and they are uttered flatly, without further explicit or tacit comment. Kay's apparatus suggests no explanation. (He might think of invoking the Rule of Strength, = Grice's Maxim of Quantity, and claiming that a co-operative speaker would not utter (20) if that speaker were contemplating a more extreme condition under which s/he might stay; but that would be to say that 'contemplating' or envisaging sets a contextual limit on the lexical appropriateness of'even', which is precisely what Kay is concerned to deny.) So let us continue to pursue the semantic idea. But a further example of Berckmans's further embarrasses the Within-Reason theory. He appeals (1993: 591) to the 'so... that even' construction: (23) a. His quiz average was so low that even a perfect final could not save him. b. The denazification was organized so sloppily initially that even Eichmann and Mengele escaped.

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(23a) sustains the Beautiful theory; at least, it is well paraphrased by 'His quiz average was so low that nothing, a perfect final included, could save him'. But (23 b) implies neither that all the Nazis escaped nor, more to the point, that every member of some narrower 'within reason' group did. (Still, it implies some generalization past Eichmann and Mengele, or what would the 'even' be doing there?)

Preserving Universal Quantification (Second Attempt) Thus discouraged, I turn to my second strategy for preserving the status of 'even' as a universal quantifier. That more daring line is to hypothesize that 'even' means, not 'every... including...' but 'every .. .plus' Thus, 'Even Grannie was sober' would mean, more elaborately, that everyone whom you would expect to be sober was sober and Grannie was also. Unlike our original formulation, this one leaves it open that someone besides Grannie was unexpectedly sober as well. Likewise, (11) ('Even Bluto stayed home') would be consistent with Gonzo's having attended, so long as Gonzo was not expected to stay home either. And Gibbard's sentence (6) would be understood as Til be polite in any expected circumstance plus any in which you insult me, but not in one in which you insult my wife', neither insult being expected.11 Let us see whether this proposal preserves my original solution to the Consequent-Entailment problem. On the Chapter 2 analysis of'Q even if P', that form entails (e E R)(In(e,Q)) as a conjunct, but now according to the Plus theory, R ranges just over the real and relevant possibilities that are also 'expected'. And the restriction is threatening. For the actual may be unexpected; thus the Plus theory predicts that 'Q even if P' does not entail Q. But it is no longer clear that the entailment holds in real life. For any 'even if claim can always be counterexampled in the Gibbardian manner of (22),12 and so one might argue that, what with the possibility of an outlandish defeater always hovering in the background, 11

There are languages in which the word translated as 'also' is also used to mean 'even', especially in conditionals: Italian 'anche', German 'auch'; cf. Haiman (1986), Konig (1986). But Spanish 'incluso' seems to favor the Beautiful theory. 12 Arguably a comma can block such counterexamples, as in 'I'll stay, even if Geoff starts throwing up'. But only if the comma is understood as non-cancellably conjoining a flat nonconditional assertion with a conditional.

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such a conditional's consequent is never flatly asserted, much less semantically entailed; thus our original approach to ConsequentEntailment would have been impugned by Gibbard in any case. Actually the appeal to Gibbard does not, on its own, refute the entailment claim. For if the Reality Requirement is imposed, a sentence like Gibbard's (6) or our (22) still does entail its first consequent (along with the proposition that its second, more extreme antecedent is false). But I have urged dropping the Reality Requirement, and if we do so, our analysis thereby ceases to uphold Consequent-Entailment in any case. Sans Reality Requirement, our original account runs into the very same problem, that the actual outcome may evade our reference-class. Our question is, then, how the original approach can be adapted either to the loss of the Reality Requirement or to the Plus theory. And I think the direction is clear: on the Plus version of the original theory, 'Q even if P' does still entail (e E R)(In(e,Q)), where R ranges over the 'expected' real and relevant possibilities. Thus one who asserts 'Q even if P' would be unconditionally placing the event that Q in the 'expected' category. That is not quite to assert Q without qualification, but it is at least nearly to assert Q, and without overt qualification, and with the added emphasis of citing a circumstance that would not upset Q even though one might think it inimical to Q. Moreover, the theoretical availability of Gibbardian counterexamples does not conclusively show that Q is not asserted, for a detailed theory of asserting may rule that in appropriate contexts propositions can be asserted even when they are not strictly entailed by the sentences uttered. And all that, I suggest, is why 'Q even if P' is heard as asserting Q, even though it does not, after all, entail Q. (A parallel but stronger argument could be made for the logically more inclusive original notion of an 'envisaged' possibility.) I shall cease to speak of ConsequentEntailment and substitute 'Consequent-Assertion'. However, Barker's (1994) criticism, mentioned in Chapter 5, applies at this point. He argued correctly that even when 'even' focuses the whole antecedent, an 'even if conditional does not entail or assert its consequent unless the reference-class R is a subclass of 'even's comparison class G. For the Plus theory, the latter requirement amounts to the condition that every real and relevant possibility is also an 'expected' event. But of course a possibility can be both relevant and epistemically 'real' without being positively expected. Here is Barker's example (1994: 251). Suppose that the party is expected to be very pleasant all around, but someone raises a purely

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hypothetical question regarding things that would, were they to happen contrary to expectation, make me leave. I answer, 'If Mary starts arguing with me, I'll leave; if Fred starts screaming, I'll leave; even if you leave (though I always detested having you around), I'll leave.' In the context, that last 'even if conditional does not imply its consequent. So the Consequent-Assertion phenomenon is less general than I had tacitly supposed.13 Still, we have explained what needed explaining: not why some conditionals entail their consequents, because strictly they do not entail them, but rather why some are felt to assert their consequents when others are not. (I do think the use of indicatives here is unnatural. In real life, if someone were to raise such a hypothetical question, I would answer in the subjunctive, precisely because the new antecedents, though made 'real' possibilities by the raising of the question, are still not at all expected: 'If Mary were to start arguing, I'd leave'.) But there is a deeper problem.14 As Barker advised, I am now explicitly predicting that we get Consequent-Assertion when and only when R is a subclass of G, and the locus of expectedness is the members of G themselves. Unfortunately, regarding expectedness, that is not the prediction that falls most naturally out of my general account of'even'. If we render 'Even m is F' as '(x) ((x is expected to be F D x is F) & m is F)', then 'P even if Q' with focus on the antecedent should come out as '(f)(It is expected that (e E R)(In(e,Q) D In(e,P)) & (e E R) (In(e,f) D In(e,P)))'. That is, it should be the conditional states of affairs Q > P that get compared with respect to expectedness, not the members of G themselves. We should be saying that ConsequentAssertion obtains when and only when all the envisaged events e are such that 'e > Q' is expected, not when they are themselves expected. And that is trouble. For the set of conditionals generated by taking the 'expected' events as antecedents in 'If..., I'll leave' is not the same set as the set of expected conditional states of affairs; because when taken as antecedents, the completely unexpected events that would most firmly lead to my leaving make for the most highly expected whole conditionals: 'If there's a fire, I'll leave', 'If someone tries to kill 13

The Plus theory might encourage one to think that in an 'even if conditional, the antecedent £ R is never a member of G, because it is never 'expected'. But the latter does not follow. Though it would normally implicate otherwise, 'All the expected members plus N are F' is entirely consistent with X's being expected too. 14 Especially warm thanks to Michael McDermott for getting me to see this, which took him several long-suffering e-mails.

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me, I'll leave', 'If a burning airplane is falling toward the house, I'll leave'. So it seems there will be counterexamples to the formula, 'Consequent-Assertion obtains when and only when all the envisaged events e are also such that "e > Q" is expected.' 'I will leave if there's a fire; I will leave even if someone tries to kill me' does not assert its consequent in a Barker-type context, but for every envisaged e, 'e > I'll leave' is expected. One might argue that even in that context there are some envisaged events that give unexpected conditional states of affairs; perhaps I envisage enjoying the party, and the conditional 'If I enjoy the party I'll leave' is unexpected. But that would mean there is never Consequent-Assertion, not even for the original Til leave even if you leave' where all the envisaged events are also expected (or take 'If I go to the party, I'll leave', which is unexpected). Here is what I think, unsatisfactory though it is. Although it does look as though the foregoing is what the Event theory ought to say about Consequent-Assertion if it is to be a straightforward application of my general account of 'even', something has gone wrong with the way 'even' applies to whole antecedents. My earlier mismatched formulation, that compares the events themselves with respect to expectedness, still strikes me as natural in itself, that is, as a way of applying 'even' to whole antecedents; and it gives the right answers. So I am inclined to stick with it, acknowledging that it is a departure from the way one would think my account of 'even' applied to whole antecedent focus. I may yet think of an independent way of motivating that departure. The Plus hypothesis eliminates our third and fourth counterexamples at one stroke, without the slight artificiality of supposing that the reference-class widens in mid-sentence. It also deals with (15), (16), and (23fe), which it paraphrases respectively as A vouvray, an Australian chardonnay, and every wine you would expect to go well with scallops in creamy leek sauce, plus a good vintage champagne, would go well with scallops in creamy leek sauce', 'Carol Nelson, a basket weaver, teaches others to dye fabric and dried grass using the juices of beets, berries and every other juice you would expect plus that of onion skins', and 'The denazification was organized so sloppily initially that every Nazi you would expect to escape did and so did Eichmann and Mengele'. These glosses are not implausible, though the last still suffers from unclarity about a particular set of Nazis' being expected to escape.

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But the Plus theory has an offsetting drawback: it divorces the comparison-class of 'even' from that of 'only'. Originally, both words ranged over the same contextually specified group of items, as depicted in the Venn diagram on p 113. 'Only', of course, continues to do so, but 'even' is now being restricted to a proper subset of the group, containing just the 'expected' members. After our lavish appreciation of the parallel between 'even' and 'only', it is painful to have to grant that the parallel fails at this one focal point. (Note that the Within-Reason theory shares the same defect. That is not obvious at first glance, since one might naturally suppose that 'Every... within reason, including...' and 'No... within reason but...' ranged over the same class in the same context. But amid the Bluto/Gonzo imbroglio, one might truly and in one breath utter (24) Even Bluto stayed home; only Gonzo attended. Thus the two classes cannot be the same.) Also, some readers will find the simple paraphrases that result from the 'plus' variation somewhat unnatural: 'Everyone plus Grannie was sober'; 'I would do anything for you, plus eating haggis'; 'I will stay in any circumstance, plus any in which Geoff starts throwing up'. Though these are not all bad, they still strike me as being somewhat less natural than our original 'any... including' paraphrases. Moreover, since the final theory still features universal quantification, a further counterexample hunt is invited regarding the contrast within the comparison class. Suppose (to start again from the original Bluto-Gonzo example) someone who would have been expected to stay home did not do so, for some reason, and in fact attended the party along with Gonzo. Could we still assert 'Even Bluto stayed home'? Not, I think, without qualification—a qualification freshly exempting the renegade from the narrow expectation class: 'Even Bluto stayed home—though actually, Geoff found some Dramamine and mixed it with codeine and got there eventually.'15 Or suppose that only Gonzo was expected to turn up, but Bluto heroically overcame the flu and attended also. The Plus theory authorizes 'Even Bluto made it', even though Bluto was, after Gonzo, the next most likely reveller. I am inclined to think such counterexamples work, and the 15 From David Sanford: 'It is fast, it is durable, it is even low in price; unfortunately, it does a really poor job of cutting grass. It doesn't cut the grass at all, actually; it just tears at the grass and mangles it."

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contrast-location problem persists. Readers who agree are invited to solve the problem on their own, and I will pay for the champagne if they succeed. Finally, the Plus theory faces two further attacks by Berckmans.

Berckmans's Existential and Prepositional Examples Berckmans (1993: 603) notes that explicitly existential quantifications can induce 'even', as in (25) Some of the most loyal White House officials weren't with the president on this one, even Sununu and Baker weren't. Scowcroft, of course, stood behind his leader. Berckmans argues that if 'even' universally quantifies over a comparison-class, that class must be only a proper subset of the contextual domain of the opening existential quantifier. He offers a 'plus' paraphrase (1993: 603): (25') Some of the most loyal White House officials weren't with the president on this one, and of all those that one expects to be with the president, none were with the president, plus Sununu and Baker. Scowcroft, of course, stood behind his leader. The idea seems to be that 'plus' marks a difference in expectedness between the unnamed officials in virtue of whose behavior the opening existential quantification holds, and Sununu and Baker who are less expected; but at the same time Scowcroft stands as a counterexample to the universal generalization that none of the expected members was with the president. So if a narrower universal generalization is true and expressed by 'even', its members must be 'expected' in a stronger sense or to a stronger degree than the already expected officials originally indicated though unnamed. But notice that the two-domain intepretation is not forced upon us. There can be just one class of expected officials, that is, of those who would have been expected to be with the president. Try this rewording of (25'): (25") Of all those that one expects to be with the president on this one, none were with the president, including some of

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the most loyal White House officials, plus Sununu and Baker. Scowcroft, of course, stood behind his leader. (25") seems entirely consistent with (25') and with (25). And it collects only the one comparison-class. It maybe complained that, if (25") is a correct paraphrase of (25), it follows that (25) is redundant—since 'Some... weren't' is already contextually entailed by 'none were'. (And on its face, (25) is not redundant.) But in fact that does not quite follow, because both (25")'s 'including' clause and (25)'s opening existential quantification include the predicate 'most loyal', which is not semantically entailed by the universal quantification posited by the Plus theory of 'even' alone. The objector may protest that, since obviously the most loyal officials would be expected to be with the president, they are already pragmatically included in the comparison-class, and so both (25") and (25) would be pragmatically redundant. Very well, but if we grant the premise that 'obviously' the most loyal officials are expected to be with the president, then it seems to me that (25) is pragmatically redundant in that way. If 'even Sununu and Baker' defected, then it follows in the context that some of the most loyal officials did, especially since (as Berckmans emphasizes) their names occur in apposition to that quantifier phrase. So as yet we have seen no convincing argument that (25) would force the Plus theory to posit an ad hoc split between grades of expectedness. We must turn to Berckmans's second type of counterexample.15 He points out that 'even' has a recalcitrant use, in the context of prepositional phrases referring to times or places, that does not seem to involve universal quantification. His two leading examples are (1993: 598): (26) Evans kissed Mary even before he knew her name. (27) He was executed even after the queen herself made a plea to spare his life. (As intended by Berckmans, each of these recounts a particular dated event, rather than generalizing over time intervals.) (26) does not seem to mean anything of the form, 'Evans kissed Mary in every way [Adv^ly, Adv2-ly, etc.], plus before he knew her name', nor (27) 'He was executed in every way [Advi-ly, Adv2-ly, etc.], plus after the queen herself made a plea...' 16

Such sentences had been noticed by Fraser (1971).

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In what follows I shall confine my discussion to (26). The use of 'after' in (27) does not seem to me genuinely temporal; the point of (27) is not, like that of (26), temporal sequence or comparative earliness/lateness. Rather, (27) seems equivalent to the concessive conjunction 'He was executed {although /despite the fact that} the queen herself had made a plea to spare his life'. A more clearly temporal example using 'after' would be Berckmans' sentence (28) Even after the ground attack was in full swing, many Iraqis didn't believe the land war had actually started (1993: 600 n. 17); my remarks about (26) will apply to (28) as well. Berckmans anticipates two responses on my part, each worth our consideration. First, he speculates that I might try to assimilate (26) (as I did (3) above) to the comparative-intensifying use. Understanding 'before' as meaning 'earlier than', a speaker of (26) may mean that although Evans's learning Mary's name occurred early on in their relationship, Evans's kissing her occurred still earlier. This is not implausible; each of the events is felt to be early. One could not happily say (29) ??Evans kissed Mary even before they had had their fourth child. Berckmans grants that (26) can have the comparative-intensifying meaning, but he insists that (26) also need not have it and, as intended, does not. He does not say why he thinks that. Perhaps he believes the characteristic entailment is missing. On its comparativeintensifying reading, (1) ('Bill is even taller than John') entails that both Bill and John are tall. Does (26) entail that both Evans's learning Mary's name and his kissing her were early? I am not sure. Perhaps not semantically, for (30) Evans kissed Mary even before he knew her name, but he learned her name late in their relationship is not obviously a contradiction—though I think it is anomalous. More discouraging is the fact that (26) lacks two useful marks of the comparative-intensifying use, noted above. It translates into French not using 'encore', but using 'meme'. And it tags: 'Evans kissed Mary before he knew her name, even'. Those dissimilarities may not be fatal, since as with (3), they maybe due to the tacitness of the comparative 'earlier than' in (26), but they make one unconfident of the present strategy.

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Berckmans's second anticipated response is that the object of even' in (26) is not a time, but rather a comparison class of standard personal-relationship-establishing events, the idea being that kissing Mary is a more extreme or less expected such event than is learning her name. Thus 'even before' would be reread as 'before even', and (26) would be paraphrased as something like, 'Evans kissed Mary before any of the standard personal-relationship-establishing things had happened between them, including his learning her name'. That is not bad. Eva Delgado (personal communication) has suggested a syntactically more plausible version of this strategy. Retain the evident focus of 'even' as being the whole prepositional phrase, and let the comparison class be of adverbial items that we might call 'beforenesses' or 'prioritudes', thus: {occurring before seeing her, occurring before knowing her name, occurring before having a conversation with her, occurring before asking her out, occurring before getting engaged to her,...}. Remember that 'even' can focus phrases of any kind, not just phrases which correspond semantically to individuals or types, and some fanciful ontology must follow; 'prioritudes' are something like comparatively or otherwise relationally specified time intervals. On this view and according to the Plus theory, (26) would mean that Evans kissed Mary in every expected prioritude plus that of occurring before he knew her name.17 Berckmans (1993: 600) makes a trenchant rejoinder that unfortunately applies to Delgado's variant as well as to his own offering. However intuitive the comparison-classes and however seemingly natural the paraphrases, the vital quantificational element of the Plus theory generates an unacceptable implication, and it is a big one. The quantification in (26) would be over all the expected standard personal-relationship-establishing events, or all the corresponding 'prioritudes'. But temporal 'X before Y' entails both X and Y; so (26) would then entail that all the expected events occurred and/or prioritudes obtained. And (26) does not entail that. Indeed, although (26) seems to entail both that Evans kissed Mary and that Evans went 17

Delgado also floated the alternate suggestion that 'even' might collect the class of comparative temporal relations: {before, simultaneous with, soon after, long after,... (. This does generate a possible reading of (26), but the stress would have to be on 'before' rather than on 'knew her name'; also, one would have to gerrymander the notion of expectedness, since in the context, extended relations such as forty years after would be less likely or expected even than before.

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on to learn her name, (26) does not entail that anything further passed between them. Evans might then have lost interest (or died of joy or been brained by a jealous husband), without even an exchange of business cards. There is of course a non-factive use of 'before', on which 'X before Y' does not entail Y in actuality: 'We left before we started a riot'; 'The technician opened the safety valve just before the explosion (thereby preventing it)'. There seems to be an implicit modal: (26) may be true when Evans never did in fact learn Mary's name, but only if read as 'Evans kissed Mary before he [subjunctively] had even learned her name'. The quantifier might then be taken to range over non-actual events or prioritudes that might reasonably have been expected. There is precedent. 'Even' can compare its focus to nonactuals; 'Not even a Lilliputian (much less a hobbit, a dwarf or a 10-year-old boy) could get through that hole'; 'Even Superman would have trouble lifting the World Trade Center'.18 On the other hand, (26) seems genuinely ambiguous as between its non-factive and a more ordinary factive reading (this is perhaps more obvious if we delete 'even'). If so, then the factive reading remains a counterexample to the general Plus theory of'even'. (As Stephen Barker has suggested in conversation, it is not obvious that there is a strictly factive reading of 'before'. It may be that, across the board, instances of 'X before Y' only conversationally implicate Y. But it is not plausible to deny that 'X after Y' entails Y, so (28) remains a problem.) I said a counterexample to the generalPlus theory because, once we isolate the factive use of'before' and 'after', it is possible that the use of 'even' Berckmans has identified is a special use. He himself notes that the present problem for the quantifier theory is distinctive to 'prepositional phrases referring to times or places', and the only such examples I find convincing are those involving temporal 'even before' 18

And here is a piquant example from Carl Bernstein and Bob Woodward's All the President's Men (New York: Simon & Schuster 1975, 132). Woodward quotes the anonymous Deep Throat: 'Mitchell conducted his own—he called it an investigation—for about ten days after June 17. And he was going crazy. He found all sorts of new things which astounded even him." Here, it may seem that no one but Mitchell need actually have been astounded. (His subordinates already knew about all the dirty tricks, indeed because they had planned them, and we can suppose hypothetically that no one else ever found out.) The 'even' still seems appropriate because of a counterfactual population of ignorant people who would more easily have been astounded than Mitchell (John Dean, Hugh Sloan, probably Nixon himself...).

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and 'even after', such as (26) and (28).19 //that is so—admittedly I have no independent syntactic evidence that it is—then perhaps we may exempt them from the general or prototypical analysis of 'even', and the Plus theory could remain intact even though hedged once again. In particular, since there seems to be no analogous example involving 'if, the Plus theory of 'even if would be unimpeded.20 But there is a remaining problem. Eraser's sentence (31) Come on, Chris, eat up—even little Billy finished his cereal (mentioned in n. 12 to Chapter 5) is supposed to be true even if Chris and Billy are the only relevant diners. This is consistent with the Beautiful and the Within-Reason theories, assuming our comparison-class may have only one member, but it seems a counterexample to the Plus theory; the comparison-class cannot be null. (31) does not strike me as a very good sentence if there are no other diners, though of course I am firmly in the grip of the universal quantification view. At the very least (31) suggests a comparisonclass of children who are not present and may be only hypothetical— not that that would help the Plus theory as stated, which requires a class of actual kids who have finished their cereal. Perhaps (31) makes the Within-Reason theory look a bit better than before. Each of our two possible retreats from my counterexampled Beautiful theory (the Within-Reason theory and the Plus theory) is repulsive, for the aesthetic reason I have mentioned, but must be considered in light of the clear counterexamples to the Beautiful account. Worse, each of the theories faces objections that an impartial observer might reasonably consider fatal; at best, the universal quantification account is staggering under a weight of anomalies. Why, then, should anyone keep straining to save some version of that view? 19 His two further examples (1993:601 n. 18) are(fe) 'I never felt the earthquake, and I was even in San Francisco when it happened" and (d) 'I didn't notice anything peculiar about her singing, and I was even on stage with her". But each of these does collect a set of relevant geographical areas: respectively {in the continental United States; on the West Coast; in California;... ( and {in the same town; in the same neighborhood; in the same building; in the room;... (. And Berckmans's objection to the universal-quantifier analysis of (26) does not apply here, for each of (b) and (d) does entail that the speaker was in every expected member of its comparison class. 20 As noted in n. 8 above, Berckmans offers his own theory of 'even', and it is a quantificational theory, although Berckmans posits an ambiguity as between universal and existential quantification. As in Barker's case, I must eventually come to a showdown with Berckmans.

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Because of Chapter 5's arguments for the thesis that if 'only' is a quantifier, then so is 'even'. Those arguments still seem to me all but conclusive. Of course, we should consider Modus Tollens, and be prepared to rethink the assumption that 'only' is a universal quantifier, but that assumption is hard to reject. It maybe that 'even' is paronymous—that it has a number of closely related but distinct uses, which simply cannot be captured by any single theory. In fact, a priori that seems quite likely. So far as I can see, 'only' is not paronymous in that way, but there may be some reason why 'even' may have diffused on its own. In any case, I fervently urge anyone to do better than I have here.

7

The 'Indicative'/'Subjunctive' Distinction My purposes in this chapter are to make some progress in delineating the semantical distinction between indicative and subjunctive conditionals (as they have been called) and to provide further evidence for the semantics defended so far.

Straights and Boxarrows In Chapter 4 I mentioned some strong affinities between indicative and subjunctive conditionals, and it is obvious that the semantical analysis to which our syntactic considerations have led us is strikingly close to Stalnaker's selection-functional idea, common to the Ramsey Test and the similarity-of-worlds approach to conditionals. (As I have said, most of its main advantages over previous versions of the selection-functional idea stem from its not treating surface conditional connectives as being syntactically primitive.) Yet there are wellknown cases, due to Adams (1965) and others, in which an indicative conditional and its corresponding subjunctive seem to differ sharply in truth value. (1) a. If Oswald did not shoot Kennedy, someone else did. b. If Oswald had not shot Kennedy, someone else would have.1 (la) is uncontroversially true; (\b) is accepted only by conspiracy theorists. (Of course Adams himself does not think (la) is true, because he champions NTV. But he thinks (la) is 'assertible' while (Ifo) is not.) What, then, is the difference between an 'indicative' conditional and its corresponding 'subjunctive'? This is a large issue on which a 1

Adams (1970: 90); cf. Lewis (1973: 3).

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number of excellent works have been written (particularly Stalnaker, 1975;Slote, 1978; Davis, 1979; and Gibbard, 1981). But before joining the issue in earnest, I should follow Dudman (1983, 1984a) and Bennett (1988) in recognizing that the terminology of 'indicative' and 'subjunctive' is ill-chosen. The members of an Adams-pair (as I shall call them) do at first seem to differ as between indicative and subjunctive mood, but V. H. Dudman has handily shown that grammatical mood per se has little or nothing to do with the semantical and other differences more interestingly exemplified by Adams-pairs. And in contemporary syntactic descriptions of English, mood plays no systematic role. The real differences between the members of an Adams-pair have more to do with tense (e.g. 'If he has left,...' vs. 'If he had left,...') and modal auxiliaries and aspect ('If..., someone else did' vs. 'If..., someone else would have); nothing seems to be gained syntactically by saying that the members of an Adams-pair also differ in mood. Moreover, Dudman argues, there is no semantic difference between a future-referring 'indicative' and its corresponding subjunctive; they should be co-classified.2 Against the letter of Dudman's positive account, Bennett argues that serious taxonomic questions remain, and I heartily agree. I will not try to answer those questions here, but a terminological decision must be made. 'Indicative'/'subjunctive' is absolutely standard and well understood, but also incorrect. (On account of its familiarity and its causing no semantic harm, I would be inclined to stick with it still; but the respecting of grammatical distinctions is a central theme of this book.) Bennett advocates the otherwise meaningless 'straight' and 'corner', but somewhat tendentiously, because he independently thinks that 'straight' conditionals are in fact material conditionals and 'corner' conditionals are Stalnaker-'indicative' and Lewis conditionals combined. Since I strongly dispute Bennett's semantical view of the distinction and rather join Stalnaker in holding the difference to be pragmatic, I shall from here on out accept Bennett's term 'straight' but employ the new and genuinely neutral (though deliberately reminiscent) term 'boxarrow' in place of 'subjunctive.' Straight/boxarrow Adams-pairs are very clearly recognizable even though the distinction lacks a secure theoretical characterization. 2 I doubt this semantical claim. I am not persuaded that 'If Oswald does not shoot Kennedy, someone else will", said before the occasion, is strictly synonymous with 'If Oswald had not shot Kennedy, someone else would have" said afterward, even though I shall argue below that they are very close in meaning. It seems very likely that they will differ parametrically.

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A further refinement is needed. Within the class of grammatically indicative conditionals are contained several distinct subgroups of 'if'-containing sentences that are not intuitively conditional at all, in the sense of expressing conditionhood or dependency of any sort, and some of those sentences fail to exhibit even the most elementary and uncontroversial semantic and pragmatic features of paradigm conditionals. Those features I take to be: (i) dependency, of whatever sort and however loose, between consequent and antecedent; (ii) epistemically, the inferability of consequent from antecedent plus contextual assumptions of some sort; (iii) a fairly clear indication of tense and time relationships; (iv) pronominalization by 'then'; and (v) illocutionary assertion of neither antecedent nor consequent. I know of at least five subclasses of technically indicative but intuitively nonconditional 'conditionals' that distance themselves from features (i)-(v). They are discussed at length in the Appendix; I mention them here only to note that my ensuing remarks about straight conditionals are not meant to apply to the nonconditional conditionals. Let us turn more directly to some diverse semantical ways of characterizing the distinction between straight conditionals and boxarrows, that have been suggested by various authors. The Players I offer a brief catalogue. Adams (1965, 1975) Straights lack truth value; they have sui generis 'assertibility' values that follow the Ramsey test probabilistically construed. Adams gives no definite account of boxarrows.3 Lewis (1973) Straights are material conditionals; appearances to the contrary are to be explained away by Gricean pragmatics. Boxarrows of course get the 3 In ch 4 of Adams (1975) he argues tentatively that boxarrows do not have truth values either. He also explores, but does not adopt, the hypothesis that boxarrowness functions as a kind of'epistemic past tense", and that the assertibility of a boxarrow goes by the assertibility that the corresponding straights would have had if actually or hypothetically uttered on a prior occasion.

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standard Lewis semantics, with 'similarity' interpreted adventitiously as in Lewis (1979). Stalnaker (1975) Straights obey the original Stalnaker semantics and a special pragmatic constraint. The constraint is that 'if the conditional is being evaluated at a world in the context set, then the world selected must, if possible, be within the context set as well' (p. 199), where the 'context set' is the set of worlds compatible with what is mutually presupposed (whether or not actually believed) by speaker and hearer. Boxarrows obey the original Stalnaker semantics but not the pragmatic constraint. Davis (1979) Straights are Lewisian 'similarity' conditionals computed in terms of overall similarity of worlds. Boxarrows are the same except for being computed in terms of similarity of worlds with respect to their histories up to the 'reference-times' of the conditionals' antecedents (intuitively, up to the times their antecedents are 'about', the time (if any) of the state of affairs that would make the conditional's antecedent true) .4 Gibbard (1981) Straights are truth-valueless and 'assertible' by Ramsey Test, a la Adams. Boxarrows are 'similarity' conditionals computed in terms of up-to-antecedent-reference-time similarity only, a la Davis. Each of these proposals has significant advantages, rightly claimed for them by their respective proponents.5 It would take some time to 4 See Slote (1978); Dudman (1984a); and especially Davis (1979: 552 ff). Pendlebury (1989) does an interesting variation on this approach. This truth condition for boxarrows was, as Davis says, anticipated by Bennett (1974), but not in the context of the straight/ boxarrow distinction. Bennett has since (1988) come to accept either NTVor (if one insists) the Horseshoe account of straights; thus the combined position would be close to Gibbard's (below). 5 Gauker (1987) also offers an ingenious characterization of the straight/boxarrow distinction, in terms of a notion of 'assertibility' that differs from both Adams's and Jackson's. Unfortunately, the proposal saddles straights with two of the paradoxes of material implication and with Antecedent-Strengthening, on a notion of Validity' defined in terms of 'assertibility' rather than of truth. Moreover Transitivity comes out valid in the

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sort through everything and score up all the pros and cons. Instead of doing that, in the rest of this section I shall ignore both NTV and the New Horseshoe view that straight conditionals are after all material conditionals (relying on the arguments given in Chapter 4); I shall make my own suggestion about the straight/boxarrow distinction in accord with the semantics developed in Chapters 2 and 3, and newly test all the different proposals against each of several considerations that have received fairly little attention in the literature. The rejection of NTV and of the Horseshoe theory leaves only Stalnaker and Davis as live contenders to date. But after setting out my own hypothesis, I shall conduct a general survey based on three more subtle considerations.

The Distinction and the Event Theory My account of the straight-boxarrow relation falls naturally out of the Event theory. What seems clear ab initio is that a straight conditional and its corresponding boxarrow are or would be tokened with different sets of relevant and/or envisaged possibilities in mind. The difference is characteristic and systematic enough that it splits the individually various values of R into two general types. A conditional token whose associated value of R is of the first type is lexicalized straightly; a conditional token whose associated value of R is of the second type is lexicalized boxarrowly.5 Thus, a straight conditional and its corresponding boxarrow have the same logical form but differ in the types of value that their respective parameters can take, and this is why they can differ in truth value. Let us hazard a quick guess regarding the two types of referenceclass, based on (1) and the following three further examples. (2) a. If it's nighttime now, I'm having a very strange visual delusion. (Said while looking out the window during the day.) same sense for both straights and boxarrows. Of course, Gauker defends these results against received opinion. 6 I believe the mechanism here is what Boer and Lycan (1976) and Lycan (1984fo) called 'lexical presumption". In particular, Boer and Lycan argued that the 'subjunctive mood" is not a mood at all. Mood is in all other cases a matter of standard illocutionary force (declarative, interrogative, imperative, etc.); no standard type of speech act corresponds to subjunctivity. There is other evidence as well.

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(Imagine (3 a) as uttered by one who has heard the tail end of Carter's concession speech but did not catch to whom Carter conceded. Yet this same speaker thinks of Anderson as a very weak third, and so rejects (3fe).) (4) a. If Christine didn't marry Ted, she married his twin brother. (Said by one who personally witnessed the wedding, there being marginal suspicion of a switch of bridegrooms.) b. If Christine hadn't married Ted, she would have married his twin brother. In uttering (Ifl), a speaker in effect holds the fact of Kennedy's assassination fixed, and eo ipso envisages no circumstance in which Kennedy escaped being shot. By contrast, (1 b) seems false to anyone who is not a conspiracy theorist because in evaluating (1 b) we do not hold the assassination fixed; given the totality of circumstances in our ken prior to the shooting, we had no particular reason to suppose that an assassination would occur, and so in considering circumstances in which Oswald did not shoot Kennedy we easily—more easily than not—envisage some in which Kennedy remained unhurt. (2a) and (2b) differ similarly. In uttering (2a), I hold fixed the daylightsuffused experiences I am having and envisage no circumstance in which I am having them during the nighttime but am not having a delusion, while in uttering (2V) I envisage only nighttime circumstances that are in all other ways epistemically normal; since I am not given to having strange visual delusions and the thought would not occur to me, none of these circumstances are ones in which I am thus deluded. Likewise, in uttering (3a), the speaker does not envisage a Carter victory, since s/he knows that Carter has already conceded; but in considering (3b), of course the speaker does envisage Carter's winning since s/he considers it far more likely than an Anderson victory. And in uttering (4a) I hold fixed the bridegroom's striking visual appearance, while in considering (4fo) I would envisage circumstances in which Christine tolerated other physiognomies. 7

Allan Gibbard, in conversation.

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The following generalization is tempting, though crude and vague (or perhaps because crude and vague): A conditional is lexicalized straightly when its utterer holds fixed some salient fact that is looming large in his or her epistemic field, a fact that is presumably though not necessarily 'common ground' (in Stalnaker's phrase) between utterer and audience. A conditional is lexicalized boxarrowly when its utterer means to prescind from contextually salient facts and consider a generally wider range of alternative possibilities constrained only by broader and perhaps more idealized epistemic considerations. (I said only 'generally wider range' because I do not mean to suggest that R for a straight is always a subclass of R for the corresponding boxarrow.8 Sometimes it will be, but often it will not.) For (la), the 'salient fact' is that of Kennedy's having been assassinated; for (2a), the salient fact is that of my having the vivid daylight experiences. Both get held fixed, making (la) and (2a) true. What is distinctive about the boxarrows (Ib) and (2b), I think, is that their respective consequents would be quite remote—not easily envisaged against the background of the antecedent suppositions combined with the known facts leading up to those suppositions' referencetimes— but for the salient facts that underwrite their corresponding straights. Supposing just that Oswald did not shoot Kennedy, and not being given the historical fact of the assassination, we would have no particular reason to envisage someone else's shooting Kennedy. Supposing just that it is nighttime, and not being given the fact of my having daylight experiences, I would have no reason at all to suppose that I would shortly be having delusions. Likewise for (3): the salient fact is Carter's having conceded, but for which we would have no reason to envisage an Anderson victory. (4) confirms the idea even more clearly. But for the bridegroom's known visual aspect in the actual situation, we would have no reason on earth to suppose that Ted had a twin brother, much less that Christine marries that person in any circumstance in which she fails to marry Ted himself. It seems, then, that a boxarrow conditional with antecedent A and consequent C differs most obviously from straight A > C when the possibility of C, given A and the background information leading up 8 It would follow from that suggestion that every boxarrow entails its corresponding straight. Counterexample by Michael McDermott (in correspondence): 'If Oswald hadn't killed Kennedy, no one would have" does not entail 'If Oswald didn't kill Kennedy no one did'.

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to A's reference-time, would be remote but for the 'salient fact' that makes straight A > C true. Let us apply this protohypothesis to a further example. J. L. Mackie (1973:115ff.) suggests that instances of accidental generalizations yield straight-boxarrow mismatches: (5) a. If x is in my pocket, x is silver. b. If x were in my pocket, x would be silver. Mackie contends that (5 a) is true of a typical coin, say, but (5b) might well be false. However, against Mackie, Davis (1979: 547-8) maintains that nonsilver coins do not satisfy (5a); (6) is not true, for example: (6) If this penny is in my pocket, it is silver. I believe Mackie's suggestion is true for some instances of (5) and false for others, in a way that is predicted by the protohypothesis. I agree with Davis about (6), and I think the reason (6) is false is that an utterer of (6) would normally be ostending a penny, making it a 'salient fact' that the penny is copper rather than silver.10 Thus, what is true is not (6) but (7) (Even) if this penny is in my pocket, it is copper. But now change our mode of reference to the penny, or rather its mode of presentation to us. Suppose a puckish friend enters the room and says she is thinking of a particular coin in here that she calls 'Arthur'; I am to guess things about it. In this case I would be perfectly right to say (8) If Arthur is in my pocket, he is silver. For in this utterance context, the salient fact is not the (unknown) composition of the coin but that all the coins I know of in this room, 9 The idea that some fact or facts are held fixed in evaluating a straight conditional but let rip in evaluating a boxarrow is hardly revolutionary. Indeed, it is an obvious special case of the view that the straight/boxarrow distinction is at bottom a difference between two designated similarity relations. All that I claim as distinctive about it is its picking out 'the facts heldfixed",or the relevant respect of similarity, in epistemic rather than metaphysica terms. In this respect, as before, my view goes back to Stalnaker's original suggestion (1968: 102), abandoned by Stalnaker himself almost without remark, on the same page. 10 Of course, (6) would be an odd sentence to utter, since speaker and hearer know and know that they both know that the penny is not in the pocket; indeed, (6) violates Stalnaker's pragmatic constraint on straights. But we can imagine someone's just having suggested (for whatever reason) that the speaker is hallucinating the penny.

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namely, the ones in my pocket, are silver. This adjudication of the intuitive disagreement between Mackie and Davis is a pleasing protoconfirmation. Note again the oddity of (la) mentioned in Chapter 4: (la) is not simply a conditional, but is, in virtue of its internal structure, redundantly equivalent to the non-conditional 'Someone shot Kennedy'. This equivalence should be predicted by any adequate account. What has mine to say? Our official representation of (la) is (la*) (C E R) (In(e, Oswald didn't shoot Kennedy) D In(e, Someone distinct from Oswald shot Kennedy)). Given the severe requirement for straight lexicalization, that R contain no circumstance which lacks the salient fact of Kennedy's being shot, (la*) is tantamount to (la+) (C E R) (In(e, Kennedy was shot) & (In(e, Oswald didn't shoot Kennedy) D In(e, Someone distinct from Oswald shot Kennedy))). (la+) is redundant, and logically equivalent to (S) (C E R) (In(e, Kennedy was shot)), and (S) is indeed equivalent to 'Someone shot Kennedy', since every circumstance in which Kennedy was shot must be included in R. As we saw in Chapter 4, some other theories of straights do not preserve the equivalence, and in my view that embarrasses them very badly. A similar point can be based on Mackie's example (la). Put back in terms of our official semantics, then, my thesis is that what distinguishes straights from boxarrows is their holding fixed of a contextually determined 'salient fact'. Once the salient fact is determined, the 'holding fixed' is quite strict: Every circumstance 8 R must include it, for I do not envisage otherwise—every real and relevant possibility is one in which the salient fact obtains. But in virtue of what is a 'salient' fact salient? Lycan (1984c) used the term 'striking fact'. But that suggests that the fact would itself have to be remarkable or extraordinary in some way, and it does not. (David Sanford's example: 'If Henry did not put his socks in the hamper, someone else did'/'If Henry had not put his socks in the hamper, someone else would have'. Obviously there is nothing remarkable or extraordinary about Henry's putting his socks in the hamper, at least if Henry is like most of us.)

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Nor, I think, is 'salience' a purely epistemological notion. Michael McDermott has reported to me that he personally considers it a striking and salient fact that Oswald acted alone; yet he does not assent to (9) If Oswald didn't shoot Kennedy, no one did. On whatever grounds, I do not intuitively count Oswald's acting alone (assuming he did act alone) as a 'salient' fact in my sense. I suppose that may be in part because even if McDermott detests conspiracy theories, he must admit that it is less certain for him (and for almost any speaker, though not for the few people who know or knew the truth about the assassination) that Oswald acted alone than that Kennedy was shot. But I think it is less epistemic and more a matter of conversational salience. To test that suggestion, we might think of a conversation between two people who know very well that Oswald acted alone and for whom that fact is at the moment looming conversationally very large ('Why didn't the fool recruit some backup? Why didn't he?'). The trouble is that the two people would still be presupposing that Kennedy was shot, so they would be envisaging events in which Oswald acted alone but Kennedy was shot, from which it follows that Oswald, hence someone, hence not no one, shot Kennedy. That is the reason why McDermott cannot assent to (9). But now suppose our two people do not know whether Kennedy was shot. (They are in an inner room of the Texas Book Depository and they heard Oswald fire, but they also knew that he was a lousy shot.) Then while they obsess about Oswald's failure to recruit backup, they would assent to (9). No doubt my protohypothesis will be counterexampled, so far as it is clear enough to admit of testing at all. But let us compare the plausibility of our rival hypotheses with regard to each of four semantical phenomena, the first being the quartet of examples which inspired my own impressionistic hypothesis.

Adams's, Gibbard's, and Mackie's Examples I shall consult each of our five theorists in turn, assessing that theorist's presumed treatment of each of the five examples.

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Adams For Adams, (la) is assertible if Pr(Someone else shot Kennedy/Oswald didn't shoot Kennedy) > Pr(No one else shot Kennedy/Oswald didn't shoot Kennedy). Adams argues that although 'there still remains some chance, possibly remote, that Oswald was not Kennedy's assassin' (p. 91), there remains no chance (practically speaking) that Kennedy was not shot, by someone; so (la)'s corresponding conditional probability is high and one would be rational to make the corresponding conditional bet. That is all there is to it; either (la) has no truth value at all, or its truth value is irrelevant to its logical behavior. Adams offers no positive suggestion as to why the boxarrow (1 b) is contrastingly not assertible; he observes only (i) that boxarrows do not carry 'commitments to action [= to betting]' in the way he says straights do, and (ii) that some boxarrows' justifications depend on the justified assumption of their antecedents' falsity, so that if I were to find out that their antecedents were true after all, I would have to withdraw the conditionals themselves rather than acquiescing in their consequents (this never happens with straights). Nor does Adams speculate as to boxarrows' truth conditions, since he is disinclined to think that they have any. (2a) is assertible for Adams if Pr(I'm having a strange delusion/It's nighttime now) > Pr(I'm not having a strange delusion/It's nighttime now). This case illustrates particularly well a further difficulty for Adams's theory: the epistemic context-dependence of his conditional probabilities. Normally I would think that (2a)'s antecedent and consequent propositions by themselves (that it is nighttime and that I am having a delusion) are probabilistically independent of each other, unless I am mentally disturbed and my malady has something to do with the time of day. In order to make the first of the conditional probabilities come out higher than the second, as Adams needs and intends, I have to add the background knowledge that, in general, when it is nighttime the sun does not shine and that, specifically, the sun is shining now. If I am allowed to count this in, then Adams predicts the right result for (2a). But the qualification raises questions about how we are to determine what background information we are allowed to and/or forced to count, and a theory of the straight/ boxarrow distinction is supposed to answer such questions rather than raising them.

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And so with (3) and (4); these cases illustrate the same relativity to background information, even more vividly. (3a) is assertible if Pr(Anderson won/Reagan didn't win) > Pr(Anderson didn't win/ Reagan didn't win). But my estimate of those two conditional probabilities depends entirely on my believing or not believing that Carter is still in contention. (4a) is assertible if Pr(Christine married Ted's twin brother/Christine didn't marry Ted) > Pr(Christine didn't marry Ted's twin brother/Christine didn't marry Ted). Since very few of us have twin brothers at all, the second probability would be far greater than the first for most people. Even for a speaker who witnessed the ceremony, the first probability is only as high as is warranted by the auxiliary assumption that if male person A strongly resembles person B, A is likely to be B's twin brother. Of course, Adams will say, (3a) is assertible only by someone who knows Carter has conceded, and (4a) only by someone who witnessed the ceremony and on the basis of the groom's visual resemblance to Ted, precisely for the reason I have given; where is the surprise in that? But recall that Adams is concerned only for assertibility in his sense, while I, having scorned NTV, am still seeking truth. Our quest is for truth conditions, and our problem here is that an ordinary sentence's truth condition should not be so radically relative to the speaker's background knowledge. (Though as we shall see in the next chapter, Allan Gibbard argues dramatically that if straights do have truthvalues that are not simply those determined by Horseshoe semantics, the truth-values are indeed radically relative to the speaker's background knowledge.) For Adams (5a) is assertible if Pr(x is silver/x is in my pocket) > Pr(x is not silver/x is in my pocket). It is hard to see how to assign such probabilities unless the variable's range is restricted to coins; but if I do make that restriction and also assume I know that all the coins in the pocket are silver, the first of the two probabilities degenerates to 1, and so (5a) is maximally assertible. (6) is assertible if Pr(This penny is silver/This penny is in my pocket) > Pr(This penny is not silver/This penny is in my pocket), which fails grandly because of the vanishingly low prior probability of 'This penny is silver.' (8) is assertible if Pr(Arthur is silver/Arthur is in my pocket) > Pr(Arthur is not silver/Arthur is in my pocket), that is, highly assertible so long as I know that all the coins in my pocket are silver. So Adams's theory does very well by the Mackie data.

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Lewis Lewis says (la) is true because (la)'s antecedent is false, let alone being true because of its equivalence to the obvious 'Someone shot Kennedy'. Unfortunately, he is committed to saying that 'If Oswald did not shoot Kennedy, no one else did either' is also true for the same reason, even though that falsehood is incompatible with 'Someone shot Kennedy'. Even more unfortunately, for Lewis (la) and the latter falsehood alike are entailed by the (presumably though not uncontroversially) true 'Oswald shot Kennedy'. This is a rout, even if the falsehood is ruled unassertible for Gricean reasons. (1 b) is of course false on standard Lewis semantics. (2a) too comes out true simply by having a false antecedent. This is again small comfort, since like (Ifl)'s, (2a)'s ostensible contrary, 'If it's nighttime now, then I'm not having any strange delusion', comes out true as well for exactly the same reason. I am not sure how (2b) would come out on the potentially very complicated set of criteria limned in Lewis (1979), but since Lewis's custom is simply to readjust his 'similarity' criteria in response to any counterexample, we may suppose he would handle the present case by hook or by crook. (3 a) is automatically true if Reagan won, and false if someone other than Reagan or Anderson did. That is not so bad. (3b) is false on standard Lewisian grounds. Thus Lewis does well by (3). Parallel observations hold for Lewis and (4). As before, Mackie's (5a) comes out true for any object x by virtue of the accidental generalization, and so Lewis unfortunately sanctions Davis's (6) and our (7) alike. (8) comes out true also, which is fine, and (8)'s boxarrow counterpart is handled properly by Lewis's boxarrow semantics. Stalnaker For Stalnaker, we can evaluate (1 a) only if we are supposing that we do not know whether Oswald shot Kennedy; we are considering some worlds in which he did not and some worlds in which he did. Now, at the closest of those within the 'context set' in which he did not, did someone else shoot Kennedy? Yes, certainly, for we all know Kenned was shot— nowhere within the context set does he fail to be shot. But at the closest world tout court (inside or outside the context set), if we are not conspiracy theorists, no one shoots him; hence the falsity of (Ib).

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To evaluate (2a), we consider some worlds in which it is not nighttime and some worlds in which it is. At the closest of those in which it is and which is still an open possibility for us, am I having a strange delusion? I suppose Stalnaker would want to argue that relative to present presuppositions, it is easier to mess up my particular visual system than to change the laws of astronomy (or at least the arrangement of the heavens) in such a way that the sun shines at night; I know that the sun does not shine at night, but once the possibility of delusion has been raised, I must consider it. So (2a) comes out true. By contrast, (2b) is evaluated according to nearness tout court, since the boxarrow construction suspends our usual presumption that only worlds in the context set are to be considered. At the closest world (period) in which it is nighttime, am I having a strange delusion? No, because all I have to do to make it nighttime now is to slip our time-line forward or back a bit;:: there is no need to mess about with particular facts or (in particular) to rearrange my perceptual apparatus—so Stalnaker might reason, at any rate. Then (2b) comes out false, as desired. Stalnaker does excellently by (3). His pragmatic constraint fortifies (3a) against encroaching Carter worlds, while (3b) is unfettered and all Anderson worlds remain remote. Concerning (4), did Christine marry Ted's twin brother at the closest of the still 'open' worlds in which Christine did not marry Ted? I have imagined (4a) as asserted when there are such worlds but when it is known what the groom looked like, so the question is just that of whether in the closest world in which the groom looks like that, the groom is also Ted's twin brother or not. It seems to me that the truth of (4a) does more or less hang on that question. Mackie's (5a) can be evaluated only if I leave it open whether the coin x is in my pocket. Davis's (6) does not leave that open, since the ostended penny is visibly not in my pocket, but our puckish friend's (8) deliberately does. So, for Stalnaker, (6) is anomalous12 rather than flatly false as Davis would have it; (7) is likewise anomalous rather than somewhat degenerately true (though (7)'s parenthesized 'even' 11

One can raise nasty metaphysical problems about worlds differing only in their time frames. But let us draw a veil here. 12 Stalnaker says that if a superficially straight conditional's antecedent is presupposed false, the conditional is both infelicitous to utter and inappropriately lexicalized. But (unless I have missed it) he says nothing of that conditional's semantic status; I do not know whether it is supposed to be truth-valueless, false, or for that matter still possibly true.

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might raise complications); (8) is appropriately true since I know that all the coins in my pocket are silver; and (8)'s corresponding boxarrow, 'If Arthur were in my pocket, he would be silver', is true or false depending on Arthur's actual composition, since it would be easier to relocate him in my pocket than to change that composition. Stalnaker too handles Mackie's data well. Davis Regarding (la), Davis argues against Lewis that owing to the worldwide momentousness of the assassination, a world with merely a different assassin is actually closer to ours than is a world without the assassination. Thus, since Davis claims Stalnaker-Lewis semantics holds for straights, (la) should be evaluated as true. But boxarrows are to be assessed in terms of a similarity relation restricted to times previous to their antecedents' reference-times, and in our world, up to the time of the assassination itself, there were no confederates, regardless of the assassination's later consequences; so, Davis concludes, (1 b) is false as it should be. If the reasoning tentatively attributed to Stalnaker concerning (2b) is sound, Davis's theory is in trouble here, since Davis evaluates straight conditionals according to overall similarity of worlds and so (2 a) should come out false for him. What about (2fo)? Davis evaluates boxarrow conditionals according to similarity up-to-the-antecedent's-reference-time, that reference-time in this case being the moment of utterance. So the two types of world we are comparing will be worlds in which it is nighttime and I am having a delusion vs. worlds in which it is nighttime and I am not. Here again, even if we are considering similarity only up to the present moment, the latter seems nearer than the former, so it seems (2b) comes out appropriately false. On the other hand, the argument for this that I attributed to Stalnaker was based on the relative ease of shifting a world's time-line, and this complicates the comparison of two worlds with respect to their corresponding temporal segments, since shifting time-lines will make it harder to say which temporal segments do correspond. This example opens the door to an interesting area for new inquiry. Davis runs into trouble over (3). Counting by overall similarity, the nearest Anderson world is easily beaten out by the nearest Carter world, so Davis is forced to reject (3a) as false. To evaluate (3b), counting by similarity-up-to-reference-time, we would have to

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know whether the election was decided before Carter's concession or Reagan's victory was only hastened by the concession. If the concession came significantly after the victory was decided, then similarity up to the time of the victory might leave it open whether Carter or Anderson might prevail (things may have begun to go wrong for Carter only very late). I shall not try to sort out the details here, but only note that the relation of reference-time to time of utterance may be vexed, and on Davis's view the truth value of the corresponding boxarrow should accordingly be uncertain, which in this case it is not. Evaluating (4a) according to overall similarity of worlds, and assuming that Ted in fact has no twin brother, I have to decide whether a world in which Christine does not marry Ted and in which she marries a twin brother of his is on the whole closer to our world than is one in which she does not marry Ted but marries someone else. So far as comparative-similarity judgments can be obvious, it seems obvious to us that Christine's simply marrying someone other than Ted would require a far less drastic departure from the actual world than would the introduction of a (here) fictional twin brother. (Remember that in comparing by overall similarity, we are not bound to hold the groom's visual appearance fixed.) Thus (4a) unhappily comes out false on Davis's view. In evaluating (4b) Davis holds fixed the history of this world up to the wedding pronouncement, so our question is that of whether for purposes of similarity the bridegroom, looking as he actually looks, should be Ted's twin brother or not. That depends as before on whether lookalikes are most often closely blood-related, but also on people's family trees and how they might be rearranged; vicious imponderables abound. There being no clear similarity judgment here, it seems to me that Davis's boxarrow should come out neuter, while in fact (4b) is false. So Davis does poorly by (4), striking out on the straight (4a) and giving a dubious result for the boxarrow (4fe). I have already noted and adjudicated Davis's response to Mackie. Gibbard As I said in the case of Adams, the Ramsey Test predicts the right results for (la) and for (2a), but (2a) also illustrates the tricky relativity of Adams's conditional probabilities to background knowledge. Turning to (2b), Gibbard's treatment is the same as Davis's, and raises the same issue about comparison of worlds with respect to

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corresponding temporal segments when one world's time-line has been shifted. Gibbard inherits Adams's questionable treatment of (3a), pairing it with Davis's unfortunate result for (3b); so he does not score highly against (3). His results for (4) are no better: (4a) gives him the same trouble as did (3a) (Adams's inappropriate evidence-relativity), and he is stuck with Davis's dubious verdict on (4fo). Like Adams, Gibbard handles Mackie's straights well, and like Lewis and Davis both (since here the reference-time makes no difference to the example), Gibbard correctly predicts the truth or falsity of (7)'s boxarrow counterpart depending on the actual composition of the coin. None of the foregoing treatments of (1)—(8) is unproblematic, though Stalnaker's has come off better than the rest. I have found our own treatment less objectionable, though perhaps only because it is vague and sketchy.

Morgenbesser's Anomaly Michael Slote (1978:27 n.) mentions a case put to him by Sidney Morgenbesser, which he says no known theory of counterfactuals can handle. Your friend offers you good odds that a fairly tossed coin—indeed, a coin whose toss outcome is genuinely random on account of quantum effects—will not come up heads. You decline the bet, your friend flips the coin anyway, and it comes up heads. Your friend says, 'If you had bet on heads, you'd have won'. We may imagine that before the flipping, your friend might also have said (for whatever reason), 'If you bet on heads, you'll win'. The counterfactual is felt to be true in this case, and the straight conditional may be as well. Let us see what our various theories have to say about them. Adams For Adams the straight conditional will be assertible just to the extent of Pr(You win/You bet on heads). Let the probability of your betting be b; then the relevant conditional probability will be (b x .5) divided by b = .5 exactly. This is not enough; the conditional probability of your winning fails to outweigh that of your losing, so (unless I

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misunderstand him) Adams's view predicts that the Morgenbesser straight is not assertible (nor is its contrary). Epistemically speaking that is right, but Adams leaves us no way of judging whether the straight is true. (As before, Adams has no theory of boxarrows' truth conditions.13) Lewis The straight comes out true for Lewis simply because it has a false antecedent. Morgenbesser's boxarrow comes out true also, I believe: A world at which the antecedent is true and at which the coin comes up heads seems (other things being equal) more similar to the actual world than any world at which you do bet but the coin does not come up heads, since in our world the coin does come up heads; the coin being random, there is no incongruity between your betting and the coin's coming up heads that would make such a world less like our world than a world exactly like it except for the coin's not coming up heads. Of course, betting and winning might have dramatic consequences for the world's future; in some Bet-and-Heads worlds a nuclear holocaust ensues; but I did say 'other things being equal.' (Actually we would have to thread our way through the complicated interpretation of'similarity' provided in Lewis (1979), but it does not seem that any of the complexities there would affect the needlessness of changing the actual outcome of the toss.14) Stalnaker It seems that on a Stalnaker semantics both conditionals come out straightforwardly true. In each case, the reasoning is the same as Lewis's for the boxarrow: Go to the nearest world at which you do bet on heads; since in our world the coin does come up heads and making our antecedent true has no tendency at all to affect that fact, 13 If he chose, Adams could appeal to Dudmaris thesis that future-referring straights are semantically identical to the corresponding boxarrows. Thus, if Morgenbesser's boxarrow is indeed true, that would explain why 'If you bet on heads, you'll win" was true when uttered prior to the coin flip. But this would require Adams to curtail his claim that straights never have truth value—or, more in keeping with Dudman's thesis, to deny that future 'indicatives' should be classified as straights. 14 However, Stephen Barker has argued at length (in correspondence) that the (1979) account drags Lewis into a dilemma over the Morgenbesser conditional, and that the problem is serious for him.

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our consequent should be true in the nearest antecedent world, and both our straight and our boxarrow are therefore true. (Why, then, does Slote say that he 'know(s) of no theory of counterfactuals that can adequately explain why such a statement seems natural and correct' (p. 27 n.)? It is a puzzle.15) Davis Davis computes straights according to overall similarity of worlds, so the Morgenbesser straight comes out true for him just as the boxarrow does for Lewis. Davis computes boxarrows according to similarity up to the antecedent's reference-time; does that make a difference? The reference-time in this case precedes the time of the coin flip, so similarity of worlds to ours as regards the flip itself does not count. To evaluate Morgenbesser's boxarrow, go to a world at which you do bet on heads and which differs minimally from our world up till that point. Is our consequent true at that world? Here there is no answer; the Stalnaker-Lewis-type semantics on the time-bound interpretation of 'similarity' does not rule on the truth of the consequent, because the laws of nature do not suffice to determine the outcome of the coin flip.15 Thus, Davis's analysis unhappily makes Morgenbesser's boxarrow either truth-valueless or false. Gibbard Here things turn out badly also. For the straight we get the same result as in Adams's case: the straight is not assertible, nor should it be, but we are afforded no way of saying that it is true, as it may seem to be, or that it is false if it is false. For Morgenbesser's boxarrow we get the same difficulty as for Davis. 15 Morgenbesser's case does cause a problem for Slote's own semantics, a cotenability semantics, because of the coin's randomness. The conditional's antecedent conjoined with the background conditions and the laws of nature does not determine the coin's coming up heads, because by hypothesis nothing does. Slote maybe reading his cotenability intuitions into Stalnaker semantics in some illicit way, or he would have seen (I presume) that similarity theories have no problem with the Morgenbesser example; but see also n. 16. 16 This may help to explain why Slote says what he does, since when he makes his remark he is already operating with a time-bound notion of antecedent conditions. It is true that a similarity semantics gives the wrong prediction when interpreted in the Slote-DavisGibbard time-bound way. But of course it does not follow that a similarity semantics gives the wrong prediction when interpreted in the original, intuitive way. Slote may simply be assuming that the original way is no longer a contender.

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We are left with a problem, then: Though a similarity semantics can predict the truth of both our conditionals correctly, it does so only by forfeiting the advantages of Slotean antecedent-time-binding, which Slote and Davis show to be considerable. This is a problem worth working on. Let us see what the Event theory has to say. My semantic representation common to Morgenbesser's straight and boxarrow is (C E R) (In(e, You bet on heads) D In(e, You win/won)) For straights, R is assumed to contain only circumstances which include the relevant 'salient fact', while for boxarrows R may be larger, since speaker and hearer are envisaging circumstances in which the salient fact does not obtain. Here the salient fact seems to be that the coin did come up heads. If I hold that fact fixed, Morgenbesser's straight comes out straightforwardly true, as it should. If I do not, the boxarrow question is merely that of whether every Bet circumstance that is a real and relevant possibility in the context is also a Win circumstance. Morgenbesser's boxarrow is true on my view if and only if that universal quantification holds. But the question reveals a temporal relativity in our notion of a 'real' possibility, corresponding here to the different possible utterance times. Suppose the friend in Morgenbesser's example says, prior to your decision, 'If you were to bet on heads, you would win'. (Never mind that the friend could have no possible justification for saying that.) At that time, before the random coin is flipped, there are plenty of envisaged relevant circumstances in which you bet but the coin comes up tails and you lose, so the friend's forward-looking boxarrow is false on my view (as would be 'If you were to bet on heads, you would lose', Conditional Excluded Middle being false for boxarrows). Bad news, it seems, since the boxarrow is supposed to be true. I believe the forward-looking boxarrow is not true, after all. The temptation to think it is comes from looking forward. That is, since from our eternal and omniscient point of view regarding all hypothetical cases I know all facts future to the cases' reference-times as well as past and present facts, I as external observer tend to think of outcomes as established structural parts of cases and accordingly of their negations as not being real possibilities. Since I know the coin is in fact going to come up heads, I think it will, and would, come up heads no matter what, so that any boxarrow whose consequent stands or falls with the coin's coming up heads will be true. But this is a fallacy. Even

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if the coin is in fact going to come up heads, each of the following antecedently uttered boxarrows would be false: 'If this coin were to be vaporized in midair during the flip, it would come up heads'; 'If this coin were two-tailed, it would come up heads'; 'If this coin were controlled by an evil genie who does anything needed to prevent coins' coming up heads, it would come up heads'; 'If this coin were controlled by an evil genie who does anything needed to prevent coins' coming up heads when someone has bet on heads, it would come up heads'. Likewise, I say, the forward-looking boxarrow is false, though I could be argued into relenting so far as truth-valuelessness. At the very least, it is no more true than Quine's 'If Bizet and Verdi had been compatriots, they would have been French'. (Of course it has a true semifactual reading.) Suppose that your friend speaks after your decision not to bet but before the flip: 'If you had bet, you'd win'. It seems to me that just the same reasoning holds—despite the actual future truth of the consequent, this conditional is false or at best truth-valueless, for the reasons just given. Similar remarks apply to the forward-looking straight; I believe it is not true either. The de facto truth of its consequent does not support forward-looking 'If this coin is vaporized in midair during the flip, it will come up heads' etc., so it should not be taken as automatically verifying 'If you bet on heads, you'll win' either. But now suppose that the flip is over and done with and the outcome is known to all. Your (fair-weather) friend only then utters 'If you had bet, you'd have won'. This conditional is the one that is undeniably and unmistakably true. But here is also where the temporal relativity of 'realness' of possibility shows itself. The outcome having just occurred, and being the speaker's evidence and reason for uttering the boxarrow at all, it is no longer a real possibility that the coin did not come up heads; so all circumstances 8 R are ones in which the coin did come up heads and so the heads-bettor won. The backward-looking boxarrow is accordingly true and obviously so, just as common sense demands. And so would the backward-looking straight be, if uttered by someone who did not know whether you had bet. Verdict: I have argued contra Slote that Lewis and Stalnaker succeed in predicting the truth of Morgenbesser's boxarrow. But they both predict the truth of the forward-looking straight as well. So if I am right in maintaining that that straight is false, my analysis as

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developed thus far gives a better overall account of Morgenbesser's case than does any of the others. My argument for the falsity of the forward-looking straight would also apply to the examples of McDermott's (1996) mentioned in footnote 15 of Chapter 2. The examples are forward-looking straights that predict the outcomes of die throws, for example, 'If it's even it will be a six'. McDermott maintains that such conditionals lack truth value if their antecedents are false but are true if their consequents and antecedents are both true. If he is right, the Event theory is counterexampled, since at the time of utterance, there are certainly envisaged Even circumstances that are not Six circumstances—necessarily so, since we assume the die is fair and two and four are each as likely as six. But I believe McDermott has committed the error scouted above, that is, of illicitly looking forward and holding the outcome fixed. In fact, he is led into doing this specifically by his chosen methodology, which advises us to ask who would win a bet given a stipulated outcome. Of course, once we know that the die has come up six, we assent to the backward-looking boxarrow (if, in this case, we are able to overlook the truth of its antecedent). As before, it does not follow that the original straight was true at the time it was uttered. For the record, I think McDermott's distinctive conditionals need special treatment, in part because of their consequents' membership in probabilistic partitions and in part because of the strong connection he makes with betting. He holds that a bet on one of them is a conditional bet, but denies that the assertion of one is a conditional assertion. I think both contentions are very plausible and must be reckoned with in a theory of conditional speech acts.

Conditional Excluded Middle The Law of Conditional Excluded Middle (GEM)—that is, (A > C) v (A >~C)—fails for boxarrow conditionals. (If GEM held, then the following variation on Quine's (1950) stock counterexample would have to be true, which it is not. (10) Either Bizet and Verdi would have been Italian if they had been compatriots, or they would have been non-Italian if they had been compatriots. (Neither disjunct is true.)

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But does GEM fail for straight conditionals? The point is open for discussion. Let us check which of our six characterizations of the straight/boxarrow distinction allow GEM for straight conditionals. (I shall be speaking throughout of 'robust' conditionals, leaving aside the further question of whether GEM holds for Davis's 'weak' ones.) Adams One might think that Adams does not have GEM, or rather its analogue stated in terms of 'assertibility', because of the cases in which the relevant conditional probabilities are equal to .5. Suppose that for us Pr(C/A) = Pr(~C/A) = .5; then according to Adams's Generalization I will assert neither A > C nor A >~C. However, if 'assertibility' continues to follow the classical probability calculus, the Disjunction rule applies: Pr(p v q) = Pr(p) + Pr(q) — Pr(p & q). Assuming Conditional Noncontradiction, Pr((A > C) & ~(A > C)) = 0; so Pr((A > C) v (A >~C)) = Pr(A > C) + Pr(A >~C) - 0 = .5 + .5 = 1. This is a probabilistic version of GEM. (I assume this is why Stalnaker (1981) maintains that a probabilistic semantics for conditionals favors his own conditional logic rather than Lewis's weaker one.) Lewis If straights are really material conditionals, then GEM certainly is true for them. GEM is of course false on Lewis's semantics for boxarrows. Stalnaker Notoriously, Stalnaker's official semantics upholds GEM for both straights and boxarrows, though using van Fraassen's method of supervaluations Stalnaker (1981) gives up bivalence.17 He does not, in either case, treat straights and boxarrows differentially.

17 Stalnaker (1970) offers a probabilistic semantics in which compounds of conditionals are interpreted, and in which CEM is valid. Assuming that a conditional's negation is assertible if the conditional's probability approaches 0, then in a probabilistic semantics of Adams's sort, ~(A > B) will entail (A >~B). (I am grateful to Stalnaker for beginning to straighten me out on this point.)

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Davis Here we should expect no difference of treatment, since for Davis the only difference between straights and boxarrows is pragmatic (the computation procedure for the similarity relation). Davis (1979) makes no explicit choice for Lewis's logic over Stalnaker's or vice versa. Gibbard Gibbard's treatment of straights is just like Adams's, it seems, so our remarks on Adams's proposal apply here too. (Actually, Gibbard (1981) takes the position that the question of CEM does not arise, since Adams's non-truth-valued Ramsey-Test conditionals do not admit of sentential embedding at all, while CEM can be stated only with embedding. But that does not settle the question of bivalence.) Since Gibbard, like Davis, takes no clear stand on Stalnaker vs. Lewis when he comes to boxarrows, I do not know how he stands on CEM for boxarrows. My own rendering of CEM is: (e ER ) (In(e,A) D In(e,B)) v (e ER )(In(e,A) D In(e,~B)) The truth of this depends on the pragmatics of the reference-class parameter. May there be circumstances 8 R in which A but in which neither B nor ~B? So far as I can see, both the Moderate and the Strict Relevance conditions permit this. Neither 'If I finish this chapter today, Norway will have an early autumn in 2001' nor 'If I finish this chapter today, Norway will not have an early autumn in 2001' is true on its ordinary understanding. On my semantics both are false, and so Conditional Excluded Middle fails for straights as well as for boxarrows. Thus I seem to be in the minority on this issue. That is good.

The Apparent Non-Existence of Future Adams-Pairs Each of our Adams-pairs (l)-(5) is either past or present tense. This is no accident. It is generally thought that there are no future-referring Adams-pairs; when a true future-referring conditional is in the

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indicative mood, its corresponding 'subjunctive' is true also. At least, no one has offered a counterexample to that generalization.18 Perhaps, then, our five players may be compared on the basis of their ability to explain the non-existence of future-referring Adams-pairs. But wait. As I have noted, Dudman argues that the apparent subjunctiveness of boxarrow conditionals is a tense phenomenon rather than a mood phenomenon (in particular, the 'would' that figures in boxarrows is not the subjunctive 'would' as in 'Would she were here', but is simply the past tense of'will'), and Dudman offers a forward-tense-shift theory of Adams-pairs according to which futurereferring straights are semantically equivalent to the corresponding boxarrows. This yields a ready explanation of the nonexistence of future-referring instances. Its doing so serves as a nice confirmation of the Dudman-Bennett view. Perhaps it removes the challenge from our more orthodox theories of the straight/boxarrow distinction, that award the distinction semantic or crisply marked pragmatic status, since each theorist can just appeal equally to Dudman's simple explanation, denying that future 'indicatives' should be classified as straights in the first place. Historically, though, none of the five players had at the time taken account of Dudman's argument; they intended their accounts to apply to future 'indicatives' as well as to nonfuture straights. So it may be worthwhile to see how well each succeeded in his own terms. Moreover, as Stephen Barker has argued to me in conversation, it is not so obvious that there are no future Adams-pairs. One thing that makes it seem obvious is that a future straight and its corresponding boxarrow do not differ in assertibility, and for a future-referring sentence considered from one's own current point of view, there is no difference between truth and assertibility. But (Barker points out) the latter psychological obstacle can be overcome by adopting a temporally omniscient viewpoint. Take a stock Adams-pair, such as (1) or (3), and futurize it by shifting its time line forward. Thus, imagine that in 1962, two overimaginative residents of Dallas, Steve and Dalene, have noticed a somewhat creepy person named L. H. Oswald; and in the Texan 18 There are special readings of the boxarrow that would make a boxarrow's truth value diverge from that of the corresponding straight. The most obvious example is the 'backtracker' reading. For example: 'If I pick up that beehive, the bees will sting me'/'If I were to pick up that beehive, the bees would not sting me, because I would not think of picking up a beehive if I had not first put on impregnable protective clothing."

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style of that period, they also fantasize about Kennedy's possibly being assassinated. Their anti-Kennedy fantasies grow to include Oswald, and ramify. At some point Steve says, 'If Oswald does not shoot Kennedy, someone else will.' (Of course this is loony; Steve has not the slightest evidence for it.) Dalene says, 'Yes, and if Oswald were not to shoot Kennedy, someone else would.' (At least as loony.) Steve's and Dalene's utterances may be equally assertible in their context. But, Barker suggests, they may also differ in truth value, because of the future facts about the actual assassination. Kennedy was in fact shot in 1963, which seems to make Steve's conditional (futurized ( l a ) ) de facto true even though Steve had not the slightest epistemic right to utter it at the time. But Dalene's conditional (futurized ( l b ) ) demands a conspiracy just as (1 b) did, and assuming there was no conspiracy, it is false. A future Adams-pair, it seems. I myself do not agree that Steve's conditional is true. Since straights are not material conditionals, it is not true simply by falsity of its antecedent; nor is it true in virtue of a conspiracy or any other reason for betting on its consequent based on its antecedent; nor is it a 'weak' conditional; nor (cf. the forward-looking Morgenbesser straight) is it true just because its consequent is. So I do not believe that Steve's and Dalene's sentences form an Adams-pair (though I do detect a slight difference: Steve's seems at least a bit less indefensible than Dalene's). (3) is an even clearer case, I think. Imagine that in the spring of 1980, a Republican optimist named Ted says, 'If Reagan doesn't win, Anderson will.' His comrade Ned adds, And if Reagan weren't to win, Anderson would.' The future fact is that Reagan did go on to win, by defeating Carter. Ned's boxarrow is clearly false, and I maintain that Ted's straight is false as well, for at the time he would have been right as well as evidentially licensed to say, 'If Reagan doesn't win, Carter will', which contradicts what he did say. (3) does not convert into a future Adams-pair. But not every one of our going theories concurs. Let us, after all, run through them. Adams For Adams straights are truth-valueless; so of course there are no future-referring Adams-pairs strictly speaking, but this is for an irrelevant reason. I do not know whether he might be able to mark a difference in assertibility between future straights and boxarrows. As I

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said, futurized (1 b) seems to me slightly less assertible than futurized (la) even though neither is positively assertible, but I have no great confidence in this. Adams will rightly dismiss futurized (3a) as unassertible. Lewis For Lewis straights are material conditionals, so there will be fairly dramatic future-referring Adams-pairs. Futurized (1) and (3) qualify; Lewis ratifies both Steve's conditional and Ted's. And suppose it is (in fact) false that Al Gore is going to win the 2000 U.S. Presidential election (either because he will not win the nomination in the first place or because he will lose the election to his opponent). Now consider the pair, 'If Gore wins the election, Hillary Clinton will divorce Bill Clinton, murder Gore's wife Tipper, and marry Gore herself on Inauguration Eve'/'If Gore were to win the election, Hillary Clinton would divorce Bill Clinton, murder Gore's wife Tipper, and marry Gore herself on Inauguration Eve'. Whether or not Ms Clinton will in fact do any of those things, Lewis must count the indicative as true in virtue of its antecedent's falsity; the subjunctive, I believe, is false. Stalnaker At the closest world within Steve and Dalene's 1962 'context set' in which Oswald does not shoot Kennedy, does someone else? Surely not. It is irrelevant that Kennedy does get shot (and by Oswald) later. And as originally, when the 'context set' is relaxed, the boxarrow comes out the same. Both futurized (la) and (\b) are false for Stalnaker, so they are no Adams-pair. Stalnaker does fine by futurized (3): His pragmatic constraint no longer protects futurized (3a) against Carter worlds. Davis As before, Davis maintains Stalnaker-Lewis semantics for straights, and also holds that a world with merely a different assassin is actually closer to ours than is a world without the assassination. So for Davis, futurized (la) comes out true—and not just degenerately, as for Lewis. But futurized (\b) is properly false as originally. Davis does

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better by futurized (3a) than by (3a), for futurized (3a) is indeed false. Regarding (3fe), his problem of the vexed relation of reference-time to time of utterance remains as before. Gibbard For him, futurized (la) is as for Adams but futurized (1 b) is as for Davis; that is not too bad, since futurized (la) is indeed not assertible and futurized (Ib) is indeed false. Like Adams, Gibbard will dismiss futurized (3a) as unassertible. He again inherits Davis's problem about (3b). The losers here, then, are Lewis and Davis, both in that they give wrong truth conditions and in that they predict future Adams-pairs when none seem to exist. Of course, either can just follow Dudman and reclassify future 'indicatives' as boxarrows, stipulating that their analyses of straights no longer apply to those sentences. But it is perhaps a liability of their views that they are forced to do that. I ended up perhaps slightly ahead of Stalnaker on our original set of data, and I believe ahead of him by the test of the Morgenbesser straight; one way or another, the remaining players are left further behind. GEM divides Stalnaker and me: he upholds it for straights, I do not. I think I am in the right on this, but not everyone will agree.

8

The Riverboat Puzzle Let us turn at last to Gibbard's (1981) riverboat cases. I shall speak of the Simple Version and the Anomalous Version. The Simple Version (p. 226) is as follows: Sly Pete and Mr. Thomas Stone are playing poker aboard a Mississippi River boat. Both Pete and Stone are good poker players, and Pete, in addition, is unscrupulous. Stone has bet up to the limit for the hand, and it is now up to Pete to call or fold. Zack has seen Stone's hand, which is quite good, and signalled its contents to Pete. (Call this moment to). Stone, suspecting something, demands that the room be cleared. Five minutes later, Zack is standing by the bar, confident that the hand has been played out but ignorant of its outcome. (Call this moment ti). He now entertains these two conditionals. [ 1 ] If Pete called, he won. [2] If Pete had called, he would have won. At ti, Zack accepts [ 1 ], because he knows that Pete is a crafty gambler wh knew Stone's hand; thus Zack knows that Pete would not have called unless he had a winning hand. [2], on the other hand, Zack regards as probably false. For he knows that Stone's hand was quite good, and therefore regards it as unlikely that Pete had a winning hand. Gibbard concludes that the straight (1) fits Adams's Ramsey-Test theory as regards assertibility. He adds that (1) has no clear truth condition: 'Suppose that in fact, as Zack suspects, Pete did not call, because he know [sic] he held a losing hand. It is not clear what then has to be true for [1] to be true' (p. 227). I have no serious disagreement with that, so let us move directly to the problem posed by the Anomalous Version (p. 231). The Puzzle

The Anomalous Version is like the Simple Version except for the presence of a second henchman, Jack, who moves around the table and sees Pete's own hand as well as Mr Stone's, before the room is 1

These were examples (27) and (28) in the original text.

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cleared. I then later receive two unsigned notes, one of which (in fact written by Zack) says as before 'If Pete called, he won.' The other note (in fact written by Jack) says 'If Pete called, he lost.' NB, Zack and Jack each have good evidence for their reports, the difference between their epistemic situations being that Jack has seen Pete's hand while Zack has not. Gibbard argues that if the two conditionals express propositions at all, they are both true; but if the law of Conditional Noncontradiction holds, they cannot both be true unless they are indexical and hold relative to distinct hidden parameters. So either they express indexical propositions or they do not express propositions (or have truth values) at all. Gibbard argues briefly against the former alternative and so chooses the latter: straight conditionals have assertibility values relative to their utterers' epistemic situations, but are not true or false. I believe Gibbard has smuggled his drastic conclusion into his preliminary thinking, in each of two ways. First, in offering his own analysis of the two opposing conditional reports, he has considered the reports only from the respective standpoints of their utterers' epistemic situations and let it go at that. He has not considered a transcendent point of view, as I shall bring out below. Second, the main premise of his argument (p. 231) that both reports are true if truth-valued begs the question also. It is that 'one sincerely asserts something false only if one is mistaken about something germane'. At the very least, that premise would not be granted by anyone who took a view opposed to his. Let me sketch such an opposing view, at the same time expanding on the previous point.

The Hard Line Here is the Hard Line. Let us remind ourselves of a key difference between assertibility and truth: that the former is relative to one's epistemic situation (assertible for/by whom?), while the latter ostensibly is not. To judge whether a sentence S is assertible for Jones in scenario T, we look at Jones's epistemic situation in T. To judge whether S is true in T, we simply look at the facts of T, assuming an omniscient point of view. Now, my complaint about Gibbard's analysis of the Anomalous Version is that he has concentrated on assertibility alone and has not even tried to judge truth in the way I have just

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mentioned. Suppose we do try. Unlike Zack and Jack themselves, we know all the facts of the riverboat situation. Relative to those facts, which of our two conditionals is the correct one? Given that Pete's hand was in fact worse than Stone's, I think we have to conclude with Jack that if Pete called, he lost. There is simply no sense in which it is true that if Pete called he won. The reason, and the only reason, that the latter conditional is assertible for Zack is that Zack is ignorant of the contents of Pete's hand. If he were to learn more, namely, the contents of Pete's hand, he would change his mind and assert the contrary conditional. He has, fully justifiably, asserted something false. (Bear in mind, of course, that Zack, Jack, and we all agree in believing that Pete did not call.) What about Gibbard's argument for the claim that Zack's report is true if truth-valued? Gibbard says, 'one sincerely asserts something false only when one is mistaken about something germane'. Zack has (according to the Hard Line) sincerely asserted something false, so is he mistaken about something germane? As Gibbard points out, Zack holds no false atomic beliefs. But (a) as we have seen, he is ignorant of a key fact, and (b) it would not follow in any case that his conditional was not itself false, since (I am assuming) the conditional is not truthfunctional and cannot obviously be made true by the atomic facts of the case alone. So we have been given no reason to accept Gibbard's premise rather than the Hard-Line judgment about the case (this is the second point above). That is the Hard Line. Everyone I have consulted finds it attractive; at least, everyone finds Jack's conditional easier to fall in with than Zack's. There seems to be a sense in which Jack's conditional is objectively true and Zack's is not. On the other hand, few of us sympathize with the Hard Line to the full extent of simply writing off Zack's conditional as a justified false belief; even though Gibbard's argument is unpersuasive, we feel however inarticulately that there is more to be said on Zack's behalf than that. What more might be said? 1. In a paradigm case of justified false belief, the believer's evidence is regarded by the omniscient observer as misleading. Thus, suppose (to take the first half of a standard Gettier case) Jones told me yesterday that he owns a Ford, and I saw him driving a Ford, and he even showed me his ownership papers. Hence I now believe that Jones owns a Ford. But I am wrong; Jones sold it early this morning. I have a

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justified false belief. My evidence misled me. But now consider Zack's case. Has his evidence misled him? It does not seem so, though I am not at all sure how we should cash out the notion of'misleading' that is in play here. But there is another way of trying to get at the difference. 2. As regards Jones, my belief is based on a background assumption that itself is reasonable but is falsified in this case: the assumption that if a person owns a Ford on Friday afternoon, s/he will own the same Ford on Saturday morning. (Or take a more extreme example of justified false belief: Smith believes he is sitting at his desk typing a paper; but actually he is being deceived by a mad scientist who has his (Smith's) brain in a vat and is stimulating it cleverly by means of implanted electrodes. In this example Smith is making the perfectly reasonable, but false, assumption that there are not any mad scientists who go around doing that, or at least that no such trick is being played on him personally at the time.) There seems to be no comparable reasonable-but-false assumption on Zack's part. It is not as though Zack would normallybe right (having the sort of evidence he does) in a case of this type. (Perhaps this is what Gibbard is trying to get at in his argument.) This is a difference, then, between Zack's case and a paradigm case of justified false belief, though I am unsure of its dialectical force. Maybe what is going on is as follows in 3. 3. One has a justified false belief on the basis of inference from truths only when one's evidence is non-deductive and one's inference is ampliative. (If one's premises are true and one's conclusion false, then the chain of reasoning that connects them is not deductively valid.) But it is not obvious that in the Anomalous riverboat case either henchman is making an ampliative, risk-inducing inference. Whatever the correct truth conditions for the relevant straight conditionals may in fact be, it is entirely possible that the facts of the case deductively determine whether those truth conditions are satisfied. Indeed, this must be true if one supposes that the truth of conditionals supervenes on categorical, non-conditional facts, as is quite plausible even if we deny that our conditionals are truth-functional. If all this is right, then Zack's conditional belief could be false only if he had miscomputed its truth condition or made a mistake in reasoning deductively to the conclusion that the truth condition is satisfied; in either case his false belief would not be a justified false belief. 4. In fact Zack actually offers a deductive argument for his conditional, or so we can suppose. He says to himself (Argument Z),

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Pete [since he is alert, intelligent, and fond of money2] did not call unless he had a better hand than Stone's. If Pete called and had a better hand than Stone's, he won. .'. If Pete called, he won. Both premises seem to be true and the argument seems valid. On the other hand, as we have seen, the validity of conditional arguments is a very chancy matter once one leaves the horseshoe behind and ventures out into English. Let us check to see how each of our five going proposals regarding straights versus boxarrows handles the Riverboat Puzzle. Adams As Gibbard maintains, Zack's conditional fits Adams's theory well; it is what Zack would conclude after performing the Ramsey Test. Jack' conditional seemingly fits too; if Jack were suddenly to learn that Pete had called, he would probably not doubt the testimony of his own senses, but would suppose that Pete had gone insane or some such. (Here too, however, there is plenty of scope for readjustment of background information.) Thus, Adams's theory predicts that each of our two conditionals is assertible by its utterer, and says nothing more. Lewis Both conditionals come out true, since Lewis thinks straight conditionals are truth-functional, but this is an uninteresting reason. That the Horseshoe theory fails to illuminate the Riverboat Puzzle is just one more nail in the coffin of the Horseshoe theory. Stalnaker For Stalnaker, Zack's conditional will be true if Pete wins rather than loses at the closest world at which he calls. Which is more similar to our world, one in which Pete calls and wins or one in which he calls and loses? To produce the former, we would have to change either 2

Gibbard tacitly assumes that Pete wants to win this hand in particular. I shall sustain that assumption throughout.

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Pete's hand or Stone's hand or the rules of poker; to produce the latter, we would have to change either Pete's skillful acquisitive psychology or the reliability of his henchmen's signal system. I should think the lesser change would be simply a change in Pete's or Stone's cards. If so, then for Stalnaker Zack's conditional would come out true, though not for any appropriate or relevant reason. Accordingly, Jack's conditional would come out false. On the other hand, remember Stalnaker's pragmatic constraint: 'when a speaker says "If A," then everything he is presupposing to hold in the actual situation is presupposed to hold in the hypothetical situation in which A is true'. This distinguishes fairly nicely between Zack's conditional and Jack's, if we suppose that Zack officially suspends judgment about the value of Pete's hand, while Jack presupposes that Pete's hand is a loser. We have to suppose that Pete's hand is also a loser in the antecedent world under investigation, according to the pragmatic constraint, so it may seem that Jack's conditional will manage to come out true for this reason. But if I understand Stalnaker correctly, he will want to mark Jack's conditional as anomalous in any case, since Jack also presupposes (along with Zack) that Pete would never call with a losing hand. According to what Stalnaker says (p. 200), Jack would have to lexicalize his speculations in theboxarrow mode, in which case his conditional comes out unproblematically true. Davis Davis computes straight conditionals according to overall nearness, so the reasoning I sketched in my first paragraph on Stalnaker should hold for Davis. Zack's conditional would come out true but for inappropriate reasons; Jack's would come out counterintuitively false. Gibbard Gibbard sides, of course, with Adams.

My Solution We may expect that the event semantics will illuminate the Riverboat Puzzle considerably, since the key difference between Zack and Jack is

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that the former treats the possibility of Pete's having a winning hand as a 'real' possibility while the latter does not, and our semantics trades precisely in contextual distinctions between 'real' and negligible possibilities. But it proves unexpectedly hard to apply the theory to the Riverboat case, mainly because of our unclarity as regards 'relevance' and because of the failure of bivalence within 'events'. Let us take Zack's and Jack's arguments in that order, and formalize them according to the event analysis. As Zack's premises we have: (Zl) ( e E R )(In(e,~B)Dln(e,~C)); (Z2) (e ER )(In(e, C & B ) D In(e,W)). Let us now choose an arbitrary event a (e R) in which Pete calls. By non-contradiction within events we have (3) ~In(fl,~C), from which together with (Zl) we may infer (4) ~In(o,~B). Now if, but only if, we are entitled to assume bivalence within the events in question here (we do not assume bivalence for events generally), (3), (4), and conjunctivity within events yield (5) In(a, C & B ) ,

and from (5) and (Z2) we obtain (6) In(a,W). Conditionalizing from (3) and generalizing (since a was an arbitrarily chosen event), we get our conclusion: (7) (e ER )(In(e,C) D In(e,W)). So if we are entitled to assume bivalence just for our restricted class of events, Zack's argument is sound. But what justification is there for making that assumption? This is unclear, and I do not have a good enough intuitive handle on my own notion of'relevance' to be able to provide a crushing answer; but I can offer two observations in defense of bivalence. First, if we understand our Strict Relevance Condition (see again Chapter 2) as extending to antecedents and consequents occurring in isolation (such as (3) and

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(4)), we may be justified in insisting that an event is not relevant unless it is one in which C, ~C, B, or ~B (we are already disallowing counterexamples to C = B as non-'real' or negligible possibilities). Second, intuitively, an event is not relevant here unless it is at least one in which Pete is playing a poker hand against someone. And by the nature of poker, if in e Pete is playing a poker hand and it is not the case that in e Pete does not have a better hand than his opponent, then Pete must in e have a better hand, for any hand would have to be either better, equal, or worse. NB, in order for the argument to go through even with the aid of local bivalence, we have to assume further that no parameter shift occurs in the course of the argument. On to Jack's reasoning. We have said that the key epistemic difference between Jack and Zack is that Jack, having seen Pete's hand, rules out Pete's having a winner as a real possibility. (This is an interesting point for epistemologists. Suppose Mr Stone's hand is a royal flush to the king of hearts. Then the likelihood of Pete's winning is lower on Zack's evidence than it might be on Jack's evidence in another case of this same type. From Zack's point of view the chance of Pete's having a winning hand is one in gazillions, yet we still count Pete's winning as a 'real' though tiny possibility. In another case there might be a larger (though still tiny) likelihood that Jack's eyes have deceived him, yet we still would not count Pete's winning as a 'real' possibility on that ground.3 So as a background assumption for Jack's argument we have (Jl) ~(e ER )In(e,B), which, given our still questionable bivalence assumption, is equivalent to (8) (e ER )In(e, ~B). Now, Jack has his counterpart of Jack's (72): (J2) (e E R )(In(e,C&~B)Dln(e,L)) We have to be careful about parameter shift here, since normally we would have expected Jack to share Zack's opinion (Zl); Jack does not regard it as a real possibility that Pete might call while holding a losing hand. But we do not want (J2) to be vacuously true, since (J2)'s conditional contrary would then be true as well and yield paradoxical 3

Disparities of this curious kind are discussed by Dretske (1971) and Harman (1973).

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results. I think we must look at the matter in this way: Normally Jack would not even consider (J2), since he would regard (J2)'s antecedent as being beyond the pale. But we persist and ask Jack to say, just for the sake of discussion, what will in fact happen if Pete calls and does not have a winning hand. In effect, we force Jack artificially to envisage at least one such event even though this is uncomfortable for him. On this interpretation, the argument depends on holding onto (Jl) while artificially suspending the equally certain presumption (9) ~(e E R )In(e,C&~B). Again let a be an arbitrarily chosen event 8 R in which Pete calls. Thus, (10) In(a,C). By (8) we have (11) In(o,C&~B), and the rest is trivial: (12) In(a,L). (From (J2) and (11)) (13) (e E R)(In(e,C) D In(e,L)). (Conditionalization from (10) and generalization on the arbitrarily chosen a) Thus we have an argument for Jack's conditional that is apparently about as convincing as our argument for Zack's. What about Conditional Noncontradiction? Despite appearances, Jack's conclusion (13) does not formally contradict Zack's (7) (even when we rewrite 'L' as '~W'), because we know that the parameter R takes a different value for Jack from the value it takes for Zack—Zack's restriction-class includes at least one event in which Pete has a better hand than Stone. But there is a remaining problem. Even if Jack's restriction-class is distinct from Zack's, they overlap considerably; for example, they both feature a number of events in which Pete does not call and loses. Consider any one of these overlap events (those included in both Jack's restriction-class and Zack's) in which Pete does call. Then (7) and (13) jointly entail that in that event Pete both wins and loses. We might reply that this just means there is no overlap event in which Pete calls, especially since Jack 'normally' does not envisage any such event at all after he has seen Pete's hand. But recall that (J2) has forced Jack to envisage such an event, however uncomfortably,

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and at least one is included in the restriction-class mentioned in (13). Presumably what saves the situation is that an event of that type, for Jack, is always going to be one in which Pete does not have a winning hand, while for Zack an event in which Pete calls is never one in which he does not have a winning hand (since Zack has not been conversationally forced, as Jack has, to envisage any lapse in Pete's rationality). If we take this line we can maintain our compatibilism concerning Zack's and Jack's conclusions, rendering the law of Conditional Noncontradiction inapplicable.4 All the foregoing rests on some questionable assumptions. There is a further problem as well: Everyone with whom I have discussed this case agrees that there is at least a sense in which Jack's conditional is objectively true at the expense of Zack's; for example, if Zack and Jack meet, Jack will persuade Zack that he (Jack) is right, and, as we saw above, an omniscient observer has to take Jack's side against Zack. Yet it seems our treatment does not reflect that asymmetry; it is too irenic. So something has been left out. Notice that if, per impossibile, it turned out that Pete did call in the end, we would not (most of us) want to continue maintaining that Zack and Jack had both been right; Conditional Noncontradiction would cut in, or it ought to. This takes us back to the issue raised in Chapter 3 about the Reality Requirement and Modus Ponens. If we 4 For a related compatibilist discussion based on Stalnaker's semantics, see Kremer (1987). There are a number of different 'compatibilist' solutions to the Riverboat Puzzle (I am calling a 'compatibilist' solution any treatment according to which Zack and Jack are both right and yet Conditional Noncontradiction is not violated). One is mine, or one like mine, on which a hidden parameter changes its value from Zack's conditional to Jack's. Another is Gibbard's own, on which the semantic values of straight conditionals themselves are relativized to utterers and Conditional Noncontradiction is deemed to hold only for an utterer at a time. Another might be a Lewisian treatment in which different standards of similarity were held to be mobilized by Zack and Jack respectively. Still another might be a Chisholmian one, in which Zack's and Jack's antecedents were held to be (divergingly) elliptical; Chisholm's ellipticality theory, implausible as it is on its own, works rather well on the present problem. But one further option open to us, which no one has yet explored, is to deny Conditional Noncontradiction in the first place. Such a denial may seem absurd; certainly it is counterintuitive. So far as I can see, the only support for it comes from the fact that the material conditional, at least, is known not to obey Conditional Noncontradiction. If our straight conditional is to invalidate Conditional Noncontradiction also, it must share the horseshoe's habit of merely making its antecedent false when contradictory consequents are true. One suspects that any straight conditional that has this property would be a material conditional, but offhand I see no proof to that effect. Perhaps some logician could devise a conditional that has the properties in question (logicians are, I admit, good for something).

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choose to respect the Reality Requirement here and stipulate that all actual relevant events must be included in one's restriction-class, we get the right non-irenic result. Suppose that a freakish burst of Qradiation from the sky rearranges Pete's brain in such away as to make him call, irrationally, in the full knowledge that he had a losing hand. (We can add this supposition to our description of the case without contradicting anything in that description.) Then, if all actual relevant events are necessarily included in both Zack's and Jack's restrictionclasses, this event is included too, and that falsifies Zack's conditional, while Jack's still comes out true. That is the result we want, and it would also explain the sense in which Jack is objectively right at Zack's expense. Perhaps, though, the Reality Requirement need not be invoked, for the purely epistemic change wrought by a Zack-Jack confrontation is enough to explain Zack's recantation. In the confrontation, Jack reveals to Zack the contents of Pete's hand. A fortiori, Zack's epistemic situation changes, becoming in fact relevantly identical to Jack's. So even on our predominantly epistemic theory without the Reality Requirement, and despite its rejection of NTV, Jack's 'correcting' of Zack's original conditional is no surprise; for a range of circumstances that were envisageable by Zack despite their unlikelihood (ones in which Pete had a winning hand) are no longer so, and that is enough to switch truth value. Neither conspirator can comfortably utter 'If Pete called,... [anything]', since for conversational purposes both now know Pete did not call, but if they force themselves to envisage Pete's calling for whatever aberrant reason, they agree he had the losing hand and there is no circumstance in which he escapes losing—an even more wildly aberrant scenario would be needed to produce a win consistently with everything contextually permissible so far. But would Zack be right to express his recantation as the correction of what had been an error? On my view, no. His original assertion was not only assertible but true in the context. I am happy with this understanding of the case. I do not hear the recantation as a confession of error ('I was mistaken; I trusted he had a losing hand but he didn't'). Zack made his claim without relying on any presumption about the contents of Pete's hand, and (as Gibbard originally insisted) Zack had no relevant false atomic or other non-conditional beliefs. When he recants, it is only because his hidden parameter has shifted, and shifted in an irrevocable way; once he knows that Pete had the losing hand, he can no longer count Pete's winning as a real possibility.

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I would offer one further comment on the nature of the Zack/Jack pair, which observation will help to vindicate my claim that Zack's recantation would be no confession of error. Zack's conditional strikes me, and has struck several colleagues with whom I have discussed the Riverboat Puzzle, as having the ring of a backtracker in the sense of Lewis (1979).5 Lewis argues convincingly that backtrackers require a different similarity relation on worlds from that mobilized by ordinary subjunctives. Consider the difference between (14a) and (14b): (14) a. If I were to jump out this sixth-story window, I would be badly hurt. b. If I were to jump out this sixth-story window, I would be perfectly OK [because I would never have done such a thing without having previously taken precautions in the form of a luxurious safety net]. (14a) is true as it stands. (14b) is true also, even though the intended interpretation is harder to process. The hearer mentally fills in something like 'If I were to j u m p . . . , that could only be because I had already taken precautions ....' Lewis offers no particular semantics for backtrackers; he distinguishes them from ordinary conditionals only to dismiss them from official consideration. But Lycan (1988) formulates one on his behalf. As Lewis noted (following Bennett (1974), Slote (1978), and Davis (1979)), the standard closeness relation favors the past over the future, in that past similarities are taken for granted or at least weighted very heavily in the overall comparison of worlds while similarities of futures are traded off.5 On this understanding, (14a) is true, because in evaluating it we hold past and present conditions fixed, including the absence of a safety net, and compare only futures (some world in which things are as they are now and I jump and I get hurt is more similar to this world than is any world in which things are as they have been up till now and I now jump and do not get hurt). But what understanding of closeness makes (I4b) true? We must ask what is held fixed. My jumping, of course, since that is the conditional antecedent. But there must also be my present frame of mind and its retraceable background. Worlds will be counted as 5 Lewis obtained the idea of a backtracker from Downing (1958-9), Bennett (1974), and Slote (1978). My safety-net example is Slote's. 6 Hence an asymmetry of counterfactual dependence, hence a number of other asymmetries that need explaining.

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reasonably similar only if they contain my present standing desire not to get hurt (along with my having the means or resources to avoid getting hurt) and as much historical background as is consonant with that. (14b) is true iff some world in which I jump and am OK is closer to our world than is any other world in which I jump and get hurt. On the standard, past-hugging understanding of closeness, the latter truth condition does not obtain. But if we start with my desire not to get hurt and make whatever adjustments in the past are needed to produce my jumping consistently with that desire, worlds in which I jump and get hurt are further away; the safety-oriented adjustments needed to sustain my jumping consistently with my not getting hurt keep the Jump-and-Get-Hurt worlds at bay. To evaluate a backtracker, then: find the present actual fact that is most jarring relative to the counterfactual antecedent (in the sense of making the antecedent noteworthy or unlikely), hold that fact fixed, and adjust the antecedent's etiology backward but only as far as is needed. Can we translate this Lewisian backtracker procedure into our own semantics for straights? First let us construct a sample pair of an ordinary straight and its corresponding backtracker, using our appointed sixth-story window: (15) a. If Lloyd jumped, he got hurt. b. If Lloyd jumped, he didn't get hurt [because he would never have been such a dweeb as to jump before carefully arranging for a safety net]. What makes (15b) come out true? First, find the jarring fact. Note that the 'jarring fact'in question here, that distinguishes (I5b) from (15a), may well not be the same 'salient' fact that is held fixed for straights but let rip for the corresponding boxarrows; neither (15a) nor (I5b) figures in an Adams-pair. As with ( I 4 b ) , what makes the difference is Lloyd's present standing desire not to get hurt (along with his having the means to avoid it). In Lewisian semantics one juggles similarity relations. In mine one trades in 'real and relevant' possibilities. For me, (15a) is true because any event that is a real and relevant possibility and in which Lloyd jumped is one in which he got hurt; neither any safety net nor Superman nor intervening Venusians, etc., are real possibilities for speaker and hearer in the context. To get (I5b), we must instead rule out the possibilities of (i) Lloyd's failing to know that jumping from

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sixth-story windows is dangerous and (ii) Lloyd's knowingly risking life and limb, (i) is ruled out anyway; we did not envisage it in evaluating (15a) either, (ii) takes a bit more effort, for in tokening the antecedent common to (15a) and (I5b) we would ordinarily envisage Lloyd's suspending his normal caution; a cautious person does not jump out of sixth-story windows. Yet there are remote circumstances in which even a cautious person might do such a thing, and in acknowledgement of those circumstances someone might utter (I5b): Lloyd's desire not to be hurt is the fact amongst the common ground that makes (15fe)'s antecedent as unlikely as it is, and in virtue of that desire Lloyd would of course not jump, but we force ourselves to envisage his doing so within the range of real possibility, which now does not include his going mad; any such event is one in which he has previously arranged for a safety net (or whatever) and so prevented himself from getting hurt. This reading of (I5b) is hard to hear, but it seems to exist, if only for use by smart alecks. Thus we have a secondary way of marking off'real' possibilities within the Event theory, corresponding to our secondary Lewisian way of measuring 'similarity'. Let us return to the Riverboat Puzzle. Right at the outset, (15) bears a strong intuitive resemblance to the Riverboat example. We have superficially but not genuinely conflicting conditionals, driven by different standards of what is counted as a 'real' possibility, one of them in particular being a backtracker. There is no threat to Conditional Noncontradiction, and so no threat of NTV. Can we then go ahead and assimilate the Riverboat Puzzle to (15), taking Zack's conditional, 'If Pete called, he won', to be the backtracker? There are two glaring differences between the two examples. First, as we have seen, the backtracker (I5b) is unusual to the point of smartaleckiness; but Zack's conditional is a sensible thing for him to say—perhaps the only sensible thing, if he is forced to issue a conditional opinion at all. Second, unlike the Riverboat case, (15) involves no particular difference in the epistemic situations of the speakers—it is not that an utterer of (15 b) knows something the other speaker does not. By contrast, the Riverboat Puzzle arises because of the difference between the observers' respective bodies of evidence. And the reason Zack affirms his backtracker is that he lacks the evidence to do anything but backtrack in following up his conditional antecedent; Jack, knowing both hands, has no need of such indirect reasoning backward, but goes straight ahead.

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I believe that the differences are harmless and that the first is explained by the second. By hypothesis, Zack is deprived of a key piece of information, the contents of Pete's hand, but is called upon for a conditional opinion regardless. Under shortage of information, all he can do is backtrack, and fortunately he has enough information to complete that computation reliably, the result being 'If Pete called, he won'. That conditional unlike (I5b) is not frivolous, precisely because the missing information is not common ground for Zack. Lloyd's desire not to get hurt is presumably common ground for utterers of (15a) and ( I 5 b ) , and that is why special effort must be made to support (I5b). I conclude that Zack's conditional is compatible with Jack's in the way, or in much the way, that backtrackers are compatible with ordinary forwardly evaluated conditionals. Stalnaker (1984:108) offers a case similar to Gibbard's, but offering a point or two of interesting difference. Suppose Paul does not know whether the British will be coming by land or by sea, but he is reliably told (16): (16) If they are coming by sea there will be two lanterns in the church tower, and he accepts that conditional. Upon checking later, Paul sees clearly that there is only one lantern. Since he now knows there to be only one lantern, he accepts (17): (17) (Even) if the British are coming by sea [or by pogo-stick or by wheelbarrow for that matter], there is only one lantern in the church tower. Yet, Stalnaker points out, in a sense Paul does not give up (16), the contrary conditional he was originally vouchsafed, for he still uses it reliably to infer by Modus Tollens that the British are not in fact coming by sea: apparent violation of Conditional Noncontradiction. Here neither conditional feels like a backtracker. Moreover, there seems to be no confrontation-recantation phenomenon. What has my account to say?7 I represent Stalnaker's two conditionals as 7 Stalnaker himself uses his own example and Gibbard's to motivate a distinction between accepting a conditional sentence and affirming a conditional proposition which may or may not be expressed by the corresponding sentence depending on context. Stalnaker's subtle view is set within a broader theory of belief and doxastic action.

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The Riverboat Puzzle (18) a. (eER) (In (e, The British are coming) D In (e, There are two lanterns [not one]). b. (e E R)(In(e, The British are coming) D ln(e, There is one lantern [not two]).

As usual, we may expect parameter shift here, and we get it. What Paul's informant says is that any real and relevant event in which the British are coming is a Two-lantern event. Thus (18a) is true, and supports Modus Tollens so long as either the Reality Requirement is in force or at least things do not get seriously out of hand. But when Paul himself sees it settled that there is only one lantern and not two, he can no longer envisage Two-lantern events, since after that point any relevant envisaged event will be a One-lantern event, (I8b) is redundantly true as (17) feels to be. Now, knowing there to be only one lantern, how can Paul continue to affirm (18a) and (16)? For as we have just said, he can no longer (realistically) envisage events in which there are two lanterns. In the Riverboat case, we counted this 'irrevocable' loss of envisageability as a reason for Zack's recantation, even though we argued that the recantation did not amount to outright confession of error. Therefore, should we not expect Paul to give up (the now present-tense version of) (16)? For by his present epistemic, no Sea event is a Twolantern event. One reason Zack's conditional was true when he originally tokened it (and remains true as uttered even though Zack can no longer use the same sentence to express the same proposition) is that it was a backtracker, and we already know backtrackers mobilize a special 'working backward' epistemic even relative to the same body of evidence (cf. (15)). But (16) is not a backtracker; (16) was originally affirmed on the basis of a forward-looking causal connection between the British strategy and the colonists' communication system. Its evaluation should be computed in the way normal to ordinary forward-looking causal conditionals, albeit in light of Paul's epistemic situation. This point reveals an anomaly in Stalnaker's presentation of the example. According to Stalnaker, (16) allows us to consider it settled that the British are not coming by sea. But then we must regard (16)'s own antecedent afresh, as straying outside what is now the common ground. But then by Stalnaker's pragmatic constraints (16) is anomalous and should have been lexicalized as a boxarrow. Yet if (16) is

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anomalous, how can (16) participate in licensing the denial of its own antecedent, or in licensing anything at all? I think the answer is that (16) does not any longer participate in Paul's Modus Tollens, for Paul cannot assert (16). If Paul were artificially forced to envisage a Sea event despite his knowledge that only one lantern is displayed, he would not start envisaging present events in which there are actually two lanterns of which one is for some reason invisible to him; rather he would envisage some breakdown of the signalling system. I reject Stalnaker's suggestion that (16) is still in some sense true or assertible for Paul. But whence, then, Paul's Modus Tollens? It has two compossible sources. First, Paul would naturally affirm (16)'s corresponding boxarrow, (19): (19) If the British were coming by sea, there would be two lanterns in the church tower, for our evaluation procedure for boxarrows allows the envisaging of possibilities one well knows to be non-actual, as Stalnaker's allows his selection-function to roam outside the context set. And (19) gives Paul Modus Tollens. Secondly, though less likely, Paul is still justified in affirming the corresponding material conditional, which supports Modus Tollens also.

APPENDIX

Nonconditional Conditionals M I C H A E L L. GEIS Linguistics, Ohio State University

W I L L I A M G. LYCAN Philosophy, University of North Carolina, Chapel Hill

Certain superficially conditional sentences are not conditional in meaning. E.g., J. L. Austin's (1) There are biscuits on the sideboard if you want them.1 The hearer's wanting biscuits is in no way a condition of the biscuits' being on the sideboard; they are on it already, if (1) has been uttered truly. Or consider the following bit of dialogue from the movie From Here To Eternity: (2) D E B O R A H K E R R : If you're looking for the captain, he isn't here. B U R T L A N C A S T E R : And if I'm not looking for the captain? D K: He still isn't here. Philosophers since Austin have referred to such sentences as '"biscuit" conditionals'; and both philosophers and semanticists have joined in ignoring them once they have been labeled. In this paper we shall consider some further examples of intuitively nonconditional conditionals (NCCs), botanize them a bit, and try to establish what semantically distinguishes them from genuine conditionals. Then we shall raise several questions about them and float some possible answers. No more; this is only the beginning of a work in progress.

Reprinted from Philosophical Topics, 21, 2 (Sprint 1993). 1 J. L. Austin, 'Ifs and Cans," in his Philosophical Papers (Oxford: Oxford University Press, 1961), p. 158. The example would have been clearer had Austin included a comma: 'There are biscuits on the sideboard, if you want them."

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I

First we must form some notion of what makes for 'genuine' conditionality or conditionalhood. Here is a list of what we take to be some paradigm features of conditionals (we shall use the notation 'A > C' to reflect the conditional surface form, irrespective of 'genuineness'). Genuine conditionals have other obvious distinctive features as well, those that they share with NCCs (such as, obviously, containing adverbial if-clauses); the ones we shall list are those not shared by NCCs.

SYNTACTIC FEATURES A. Taking the resumptive pronoun 'then' (without change of

meaning) .2 (3) a. If she goes, I go. b. If she goes, then I go. B. Modification by 'only.' c. Only if she goes (do) I go.

S E M A N T I C FEATURES C. Evaluation by Ramsey Test.3 To check the truth or assertibility of A > C, one adds A hypothetically to one's present stock of beliefs, and then sees whether minimal coherence-preserving revision results in a revised stock containing C. (And epistemically, when A > C is a genuine conditional, C is inferable from A plus contextual assumptions of some sort.)

2 This was noted by Alice Davison, in 'On the Semantics of Speech Acts," Journal of Pragmatics 3 (1979): 413-29. Davison distinguishes genuinely conditional 'if clauses from 'if clauses that 'are not as much part of the contents of the statement made as they are justifications for making the statement" (416-17). 3 Or something like it. See R. Stalnaker, 'A Theory of Conditionals," and other papers in W. Harper, R. Stalnaker, and G. Pearce (eds.), Ifs (Dordrecht: D. Reidel, 1981). But for some qualifications, see also Lycan's 'MPP, RIP," in J. E. Tomberlin ed., Philosophical Perspectives, Vol. 7: Philosophy of Language and Logic (Atascadero, Calif: Ridgeview Publishing, 1993).

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D. Usual validity of Contraposition and Modus Tollens.4

A> C

A>C Not-C

.'. Not-C> Not-A

.'. Not-A

E. Equivalence to disjunction. A C is equivalent to Not-A v C. d. Either she doesn't go or I go. F. Relation to corresponding subjunctive (close if not identical in meaning). e. If she were to go, I would go. G. Being conditional in intuitive meaning. (A is in some sense a condition of C.)5

PRAGMATIC FEATURE H. Assertion pattern: An utterer of A > C asserts neither A nor C, but does make an actual and not merely conditional assertion. More generally, illocutionary force attaches to the conditional sentence as a whole. Notice that Austin's sentence (1) has none of the eight features we have codified: A. (4) *If you want them, then there are biscuits on the sideboard. (OK in itself, but differs in meaning from (1).) B. (5) ??There are biscuits on the sideboard only if you want them. (Ditto.) 4 It is generally agreed that Contraposition does not hold for subjunctive conditionals (see Stalnaker, op. cit, and D. Lewis, Counter/actuals [Cambridge, Mass.: Harvard University Press, 1973]), but the majority view is that Contraposition does hold for indicatives. Lycan (op. cit.) argues against Contraposition for indicatives, but the counterexamples adduced are, though genuine, neither common nor universally heard as such, and almost any real-world instance of Contraposition is a valid argument; by contrast, as we shall see, NCCs do not even begin to look like contraposing. 5 Along with this goes, normally, a fairly clear indication of tense and time relationships, but we cannot go into this feature for now.

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C. Add 'You want biscuits' to your present stock of beliefs and see whether minimal revision results in a revised stock containing 'There are biscuits on the sideboard.' No minimal revision results, unless the corresponding genuine conditional (4) is there to begin with. By the same token, the consequent cannot justifiably be inferred from the antecedent plus background information. In offering that judgment we are taking the hearer's point of view. From the speaker's point of view, of course, the Ramsey Test comes out differently since the speaker already believes the consequent and that belief would remain following conservative revision. This will be degenerately true for any NCC, because every NCC asserts its consequent. So far as NCCs are evaluated by the Ramsey Test from the speaker's point of view, it is not functioning as a test. D. (1) does not entail (6) If there are no biscuits on the sideboard, you do not want biscuits. Nor do (1) and

(7) There are no biscuits on the sideboard, jointly entail (8) You do not want biscuits. —except possibly by contradiction explosion ((1) and (7) are felt to contradict each other). E. (1) is not equivalent to (9) Either you do not want biscuits or there are biscuits on the sideboard, though (1) is felt to entail (9). F. (1) is quite different in meaning from (10) If you were to want biscuits, there would be biscuits on the sideboard. G. Your wanting biscuits is not in any sense a condition of there being biscuits on the sideboard. H. An utterer of (1) asserts (1) 's consequent, that there are biscuits on the sideboard. Moreover, it is unclear what (l)'s 'antecedent' is doing in the sentence. The lack of A, C, D, G, and H in particular make (1) intuitively nonconditional and (l)'s 'antecedent' a mere appendage. All the same observations are true of Deborah Kerr's sentence (2).

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Thus two immediate general problems about NCCs: Our F I R S T main question is, since NCCs' 'antecedents' are not genuinely conditional antecedents, what is their function? Our S E C O N D is, since superficially NCCs have the forms of conditionals and often have genuinely conditional readings (however unlikely or contrived), how do hearers immediately perceive and compute them as NCCs without pausing even for half a second to disambiguate them? ('If you want them' in (1) might be thought to be an elliptical conjunct, short for 'and you may have some if you want them.' But that would be incorrect, since (1) certainly does not entail that you may have some, nor is there any syntactic evidence of ellipsis.6 Moreover, Kerr's 'if you're looking for the captain' is not elliptical for anything of the form, 'and if you're looking for the captain,' unless possibly but again implausibly the blank is filled with 'you're out of luck.') We suspect the reason philosophers and semanticists have written 'biscuit' conditionals off as don't-cares is precisely that such sentences are intuitively so nonconditional. But (1) and (2) are members of a considerably wider class, worth attention in its own right. Moreover, as we shall see in section VIII below, there is a further problem: Piquantly but frustratingly, further data seem to show that the distinction between 'biscuit' and genuine conditionals is one of degree, or at least that a fairly smooth spectrum of cases connects the two. Let us take these points in order. Here are some more NCCs, each of which seems to display the same pattern of (non-)features as do (1) and (2).

didn't >, know, she and I never got along. want to If you'll take my word for it, she is better at karate than Ted is. I've been out buying David's present, if you care. If you have time to talk about the meeting, Geoff really made an ass of himself. If I may remind you, I've been working here for seventeen years. If you don't mind, I'm trying to read. If you're listening, I'd like to be picked up now. (Said to a telephone answering machine in the hope that its owner is home and listening in.) If you're reading this, it's a Carolina-blue day here in Chapel Hill. (Uttered, say, over e-mail, when the speaker doubts whether the

(11) If you < (12) (13) (14) (15) (16) (17)

(18) 6

Though perhaps (1) conversationally implicates that you may have some, and (1) may also count as having the illocutionary force of an offer; more on these points below.

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message is going through. Contrast the bumper sticker, 'If you're reading this, you're too close'—a genuine conditional.) Note that NCCs can also be expressed using 'unless': (19) I want some pad thai, unless there isn't enough time to fix it.

Ill

Once we have proliferated such examples for awhile, a generalization suggests itself in answer to the F I R S T of our main problems, though it is one that solves little else: that an NCC's 'consequent' is itself alone used to perform the main speech act7—plain assertion, or admission, or concession, or request, or whatever—while the 'antecedent' for some reason picks out and articulates an illocutionary felicity condition on the performance of the main speech act. Call this generalization '(Gl).' (Hereafter we shall drop the cumbersome scarequotes and use the words 'antecedent' and 'consequent' without remark, leaving the reader to understand that the clauses in question are not genuinely conditional antecedents and consequents. Also, throughout the rest of this paper, hearers or addressees will be called 'Ad' and speakers 'Sp.') For example: (11) and (12) allude to standard felicity conditions on asserting: that Ad does not know and wants to, and that s/he accepts Sp's epistemic authority. (13)—(16) allude to felicity conditions less specifically tied to asserting in particular. (17) and (18) allude to what Searle calls 'normal input and output conditions.'9 7

Geis (Speech Acts and Social Action: Toward a Theory of Conversational Competence [Cambridge: Cambridge University Press, 1995] ) offers a new theory of speech acts designed to account for how we do such things as requesting, inviting, proposing, etc. in multiturn conversational sequences. He argues that individual utterances do not, in fact, have illocutionary force in themselves, but, rather, have illocutionary significance that reflects what they contribute to satisfaction of conditions on the act being negotiated in the sequence in which it occurs. But since we are treating here only cases in which something gets done in uttering a single sentence, we will take the more standard line that individual utterances do have illocutionary force. 8 Davison (op. cit.) defends a version of (Gl): Regarding her original declarative examples, she characterizes NCCs' 'antecedents' as offering 'justifications for making the statement[s effected by the "consequents"]' (417). Then, after considering nondeclarative examples, she says, The contents of the conditional clauses [= 'antecedents'] correspond fairly closely with the conditions associated with the felicitous performance of various kinds of speech acts (for instance the preparatory, sincerity and essential conditions described by Searle...), with some modifications to factor out what would follow from general principles of cooperative conversation.... Not all surrounding circumstances can be mentioned in if clauses of this type. (418-19) 9

J. R. Searle, Speech Acts (Cambridge: Cambridge University Press, 1969), 57.

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(Gl) is supported further by the examples of certain nondeclarative conditionals (a class of sentences almost entirely ignored by philosophers and semanticists everywhere):10 (20) If you don't mind, please pick up some Molson's. (21) If you can hear me, come over here and pull us up! (22) If it's not too much trouble, could you give me a ride home? (23) If you know, could you tell me who's won the prize? (24) If you have the time, why is Johnson going to quit the firm? The antecedents in (20)—(24) seem perfunctory in much the way those of declarative NCCs do; the relevant speech acts get performed regardless of the antecedents' truth. ((20)—(22) also have genuinely hard to hear readings in which they are genuine conditional requests or questions. And, N.B., plenty of other nondeclarative conditionals are genuine rather than NCCs, in the sense of being used to perform what are genuinely only conditional speech acts rather than actual, categorical acts with fake antecedents tacked on.)11 The term 'illocutionary' occurring in (Gl) needs to be understood a bit more broadly than it would be in classical Austinian speech-act theory, for NCCs' antecedents sometimes focus on politeness, or on matters of Gricean conversational felicity, rather than on traditional constitutive or regulative conditions on speech acts. (25) and (26) concern politeness or civility: (25) I think you could get more work done than you do, if that's not being offensive. presumptuous. (26) You need a haircut, unless I m beingD rude The antecedents of (27)—(30) are conversational in function: (27) John is having0 a little rest, if you

follow me know what I mean

(27) signals a significant implicature, by treating Ad's 'following' Sp as being nonautomatic. The antecedents of (28)—(31), like those of (1) and (2), apparently serve to secure conversational relevance. 10

But see again Davison, op. cit. A mixed or possibly ambiguous type of example might be the 'challenge' question: 'If you're so smart, why ain't you rich?'; 'Why didn't McClellan attack, then, if you know so much?'; 'If you're such a hotshot linguist, what's the difference between a gerund and a gerundive?' But we are inclined to think these are genuinely conditional questions; were an addressee to deny the relevant antecedent, the attempted question would be moot or void. (Granted, the case is not straightforward: Sp presumes that Ad accepts the antecedent, and is herself or himself challenging the antecedent by posing the ensuing question. But Sp is not presuming the antecedent's falsity.) 11

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(28) If Peter asks you, I did receive his letter. (29) If you're hungry, there's a Taco Bell. (Note that genuine conditionals cannot have such 'presentational' consequents.) (30) That Adverbs book came, if you ever need to look at it. (31) Ken knows about that kind of stuff, if he's still in College Park.

IV

Even though 'illocutionary' is now to be understood as including politeness and conversational phenomena, it is important to notice that the 'felicity conditions' invoked by NCCs' antecedents need not be illocutionary even in that broader sense; their natures can vary quite widely: (32) It was a great article, if I do say so myself. (Modesty.) (33) If I don't see you, have a good trip and best of luck with your project. (Guarding against potential charge of repetitiousness.) (34) a. How about inviting Fritjof Boeger, if I've spelled his name correctly? (Orthography.) b. How about inviting Fritjof Boeger, if I'm pronouncing his name correctly? (Phonology.) (35) If I'm not talking too loudly, can you tell me why you didn't want to come to this concert? And there are exotica: (36) For me, I think, there began that sad rift between British and American literature which has done so much to impede our common cultural understanding, unless that sounds too horribly solemn. [Kingsley Amis, Memoirs] (37) Do you know, Clare, if this doesn't sound too much like somebody's auntie talking, I can remember holding out some toy to him when he was really small... [Kingsley Amis, The Folks That Live on the Hill ] (38) Anthea, if this doesn't remind you too vividly of the way Wally used to go on, have you looked at the 1973 records lately? Notice further that NCC consequents do not actually have to be clauses. (39) Dear Pinky (if you don't mind my calling you that),... [Salutation.] Indeed, they do not have to have grammatical structure at all.

192

Appendix (with Michael L. Geis) (40) @&% &*#!!!—if you'll pardon my Serbo-Croatian.

Possibly they need not even be linguistic utterances. (41) [Belches explosively]... if you'll excuse me. (42) [Holds out lighter]... if I may. (Though no doubt other accounts could be given of (41) and (42).) So it seems NCC antecedents are not tied to the traditional notion of a speech act; (Gl) needs to be liberalized in this regard. We believe the appropriate liberalizations are two. First, the infelicities that figure in NCC antecedents need not be specifically illocutionary even in our inclusive sense. The performance of any illocutionary act is subject to infelicity at every level of action identified by Austin, and more, not just at the illocutionary level. There might be a failure of pronunciation (a phonetic act failure), of word choice (a phatic act failure) or a failure to make sense (a rhetic act failure). Thus, (Gl) should be replaced by (G2): An NCC's consequent is itself alone used to perform the main speech act, while the antecedent picks out and articulates some illocutionary or linguistic felicity condition on the performance of the main speech act. But (G2) is not enough either, for a number of our examples' antecedents key on 'infelicities' that are neither illocutionary nor, arguably, even linguistic at all:13 (15)'s antecedent 'If I may remind you,.. .'was pointedly polite, but not in any specifically linguistic way; reminding is not per se a linguistic act. (16)'s antecedent, alluding to Ad's possibly minding what Sp is about to do, is hardly specific to linguistic acts at all. (32) is questionable, since modesty is not a linguistic virtue. The exotica (36)-(38) do not focus on particularly linguistic properties, though someone's sounding 'too horribly solemn' or 'too much like somebody's auntie talking' is at least language-bound. (41) and (42), taken at face value, are simply not linguistic, in any sense. Thus, (G2) is still too restrictive. Our second and more interesting liberalization is afforded by a pragmatic concept from well outside classical speech-act theory: the linguists Brown and Levinson's14 notion of a 'face-threatening act' (FTA). This will take a bit of explaining. 12 J. L. Austin, How to Do Things with Words (Oxford: Oxford University Press, 1962), 94-102. 13 It should vigorously be noted that Geis (op. cit.) argues that speech acts are better viewed as communicative social actions than as acts of a peculiarly linguistic character. However, we shall continue to employ the traditional term 'illocutionary' here, for the distinction is not critical to issues we shall be discussing. In fact, the existence of NCCs provides particularly good evidence that the speech acts in which they figure have a critical social dimension, for as we shall see, they are more concerned with the interactional social effects of acts than with the acts' Searlean essential conditions. 14 P. Brown and S. Levinson, 'Universals in Language Use: Politeness Phenomena,' in E. N. Goody, ed., Questions and Politeness: Strategies in Social Interaction (Cambridge: Cambridge University Press, 1978).

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V

Brown and Levinson argue that the performance of an illocutionary act may carry with it a threat to some person's face (in the social rather than the anatomical sense), specifically either a threat to Ad's 'negative face-want' to have her/his freedom of action not restricted, or a threat to Sp's or Ad's 'positive face-want' to be valued and to have valued what she or he values. Normally, for instance, if Sp requests Ad to do this or that, Sp threatens Ad's negative face-want not to have her or his freedom of action restricted (which it would be during the time required to carry out the act, should Ad agree to it), and Sp also threatens herself or himself through the potential loss of face attendant on a refusal of the request. On such an occasion, Brown and Levinson argue, Sp may choose to redress or mitigate such an FTAs by engaging in a display of politeness. Let us consider our recalcitrant examples in this light. (15) is a politeness conditional, in that reminding someone of something is a face-threat, and Sp seems to be trying to mitigate that threat. In tokening (16), Sp is engaging in the FTA of telling Ad to shut up, but is mitigating the face-threat by performing the act indirectly in the antecedent itself and through specifying the willingness condition of requests. (32) saves face for both Sp and Ad by explicitly acknowledging Sp's possible immodesty. The antecedent of (37) or (38) tries to preempt a threat to Sp's positive face-want, by distancing Sp from the (allegedly) problematic behavior of 'auntie'/Wally. (41) and (42) save face for Sp by asking Ad's permission to do (actually, to have done) something that might offend. Thus (G3): An NCC's consequent is itself alone used to perform the main speech act, while the antecedent either picks out and articulates some illocutionary or linguistic felicity condition on the performance of the main speech act, or helps to redress or mitigate a face-threat associated with the main speech act. Let us test (G3) against some further examples, all NCCs whose antecedents do not, at least directly, allude to felicity conditions of any sort. (43) If you'll forgive my asking, why does your brother walk that way? Ad's (actually) forgiving Sp is not strictly a felicity condition on the question. At best, the antecedent alludes indirectly to politeness or decency, by acknowledging that the question is one the asking of which might call for apology and repentance. Here we would say that Sp is redressing the threat to Ad's positive face-want that would derive from the implicature that something is wrong with someone whom she or he can be expected to value, by apologizing in advance. (44) If you must know, {yes,} I do make over $75,000 a year. (Inclusion of'yes' seems to force the NCC reading.)

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Ad's having to know or insisting on knowing is not a felicity condition on the assertion; it is merely what wrings the assertion from Sp. Sp is willing to divulge her or his salary only because Ad has importuned. (44)'s antecedent saves Sp's own face by signaling that as a well-bred person, Sp would not be revealing details of her or his financial standing, but is doing so only under pressure from Ad. (Here there is an unmitigated face-threat to Ad; Ad deserves it, for having been extremely rude.) (45) If you've been going to the Health Center at 6:45 every morning, what have they been doing for you? [Both Sp and Ad are painfully conscious of the fact that Ad has been keeping those appointments.] (45) could be heard as an implied criticism of Ad, where the antecedent establishes relevance and the consequent is a semi-rhetorical question. But there is also a sympathetic understanding of (45): The idea would be to mitigate the face-threat potentially carried by the consequent by indicating Sp's awareness that Ad has, so to speak, kept her or his part of the bargain with the Health Center. (46) If you recall, I'm booked to work in the Bloodmobile all Saturday afternoon. Ad's (already) recalling what she or he is being told by Sp is hardly a felicity condition on Sp's assertion. Rather, 'If you recall' forestalls a potential slighting of Ad's cognitive powers by explicitly treating her or his having forgotten as a real and normal possibility. (47) D E B O R A H K E R R : Did you know that the captain sniffs bird droppings? B U R T L A N C A S T E R : If you say so.15 'If you say so' can be a conventional way of saying 'I am not going to argue with you, though I think you are wrong.' But it can also mean simply that although Sp neither has direct evidence supporting Ad's claim nor awards that claim much a priori plausibility, Sp is willing to take Ad's word for it and does take Ad's word; thus, Sp at one and the same time expresses doubt and redresses the face-threat attending that action. Notice that NCC antecedents can be used ironically, as when 'If you say so' does have its conventional meaning and so becomes only a blatant pseudomitigation of the face-threat associated with disagreement. Or consider the sarcastic (48) I'm glad you enjoyed the party; if you recall, we were all watching when you threw up so carefully down the rain guage. 15

Fictional example, sorry.

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Here 'If you recall' parodies its normal face-saving use as in (46), but intensifies the face threat of implied criticism by alluding to Ad's reason for having filled up the rain guage (being very drunk), indirectly in terms of a likely result of that reason. Someone might argue that (G3) is redundant, in that every illocutionary or linguistic felicity condition is associated with some FTA. It is possible that every illocutionary act-type has an associated set of socially configured potential face-threats that a speaker might choose to redress by means of an NCC antecedent. Even if not, it may be trivially true that any illocutionary or linguistic infelicity, even speaking too softly or mispronouncing a word, would threaten the speaker's positive face by being a potential source of embarrassment. (In speaking at all we take up other people's time and put ourselves on the line). That claim maybe true, and perhaps (G3)'s felicitycondition disjunct could just be dropped in the interest of simplicity, but we shall not decide that question here.

VI

Here is a further, quite different (apparent) problem for our original (Gl), which would afflict (G2) and (G3) as well: (Gl) entails or at least strongly suggests that, given a particular speech act, any felicity condition on that speech act could reasonably be codified in the pseudo-antecedent of a corresponding NCC. But some of the most central and fundamental illocutionary felicity conditions on paradigmatic speech acts such as asserting, requesting, and promising fail that test: (49) (50) (51) (52)

??If I mean what I am saying, your cat is chasing my dog. *If I sincerely believe this, I don't like turnips. ??If I have adequate evidence for saying this, my feet hurt. *If I want you to bring me that siphon, please bring me that siphon. (53) *If I am hereby undertaking an obligation to pay you tomorrow for a hamburger today, I promise to pay you tomorrow for a hamburger today.

But cases like these prove not to be a problem. The reason is that to call into question a speaker-oriented felicity condition of the sort illustrated by (49)— (53)'s antecedents would actually void the act. One cannot simultaneously make a good faith assertion ('Your cat is chasing my dog') and question one's 16

This predicts, we think correctly, that any speech act could involve an NCC antecedent of the fully general 'If you've got a moment" type.

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own sincerity in making it. Compare (49), for instance, with (54), in which the speaker specifically recants meaning what s/he says, or (50) with (55), in which the speaker recants a belief. (54) *I'm telling you that your cat is chasing my dog, but I don't mean it. (55) *I don't like turnips, but I don't believe I don't. In contrast, there are genuine conditionals whose antecedents codify speakerbased conditions. (56) If I were to want you to give me a ride tonight, would you do so? (57) If I were to believe this, would you? (58) If I had evidence of his criminality, would you prosecute? In general, as these examples illustrate, such utterances are heard counterfactually. There is a straightforward symmetry between NCCs and genuine conditionals in this respect. When antecedents of NCCs codify sincerity conditions, since they are not being heard conditionally, the act is voided; when antecedents of genuine conditionals codify such conditions, they must be heard counterfactually. Thus, (G3) is fine, so long as we do not understand (G3) as predicting that such self-undermining acts would be illocutionarily well-formed. But now it is time to expound some further general difficulties presented by NCCs.

VII

Here is a T H i R D puzzle: why would a contextually appropriate allusion to a felicity condition on one's main speech act be expressed in the form of a phony antecedent adverbial tacked onto one's main clause, resulting in what is no genuine conditional at all? Possibly just (somehow) to acknowledge the speaker's uncertainty—real or presumed or postured—as to whether the felicity condition in question does obtain. 'If is normally a (somehow) conventional expressor of uncertainty and open questions, and perhaps this feature is exploited and carried over to the actually unconditional speech acts that would be performed by utterers of (1), (2), and (ll)-(38). Possibly NCC antecedents and genuinely conditional antecedents are co-species of a more general genus that consists of devices for articulating possibilities and treating those possibilities as 'live' or non-idle.17 17 In conversation, Robert Stalnaker has embraced a version of the latter idea, but has taken it in just the opposite direction from ours: He does not buy our distinction of kind between 'NCCs' and 'genuine' conditionals, but maintains that our alleged NCCs are

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Even if that crude conjecture is right, it does not help much with our S E C O N D problem, that of how hearers so readily detect NCCs as such. Perhaps the process is a matter of conversational or conventional implicature, but we do not offhand see any very plausible story of that Gricean sort. It is a great mystery.

VIII The conjecture also still leaves us with the additional problem we mentioned in section II above; it will be our F O U R T H main issue. Consider the following types of surface conditional, each less intractably nonconditional than our plain surly NCCs.

Factive concessives (59) [I] f some of the paid professionals made fun of him, regarding him as a pedestrian, hard worker with not much insight, he was universally liked for his modesty and good nature. (John Toland, The Last 100 Days) (60) a. James' theory was plausible, if elaborate. b. James offered a plausible, if elaborate, theory. As well as asserting their consequents, these sentences explicitly concede their antecedents. Indeed, in one sense they assert their antecedents as well. Though linguists would insist on a distinction between asserting and presupposing, the point is that by uttering such a sentence, the speaker commits herself or himself to the antecedent's truth. Moreover, strikingly, the commitment can be brand new, in that the antecedent need not already have been presumed in the context; the antecedent possibility need not even have been hinted at in the slightest. So far as the antecedent is concessive, it is a preemptive strike. genuine conditionals which only implicate their consequents; in context, Ad knows that Sp would not be asserting the conditional in question unless Sp had the truth of its consequent as a ground. We are unsure how the relevant Gricean reasoning would go, and/but we shall not try to criticize Stalnaker's view until he has spelled it out in writing. We do have a direct objection to the claim that an NCCs consequent is not flatly asserted: As Jamie Tappenden noted in the same conversation, one can pronominalize freely into NCC consequents, making further, indisputably flat assertions, as in 'There are biscuits on the sideboard if you want them; they're made with your special oat flour and they're still warm." But Stalnaker replied that conditional antecedents always create contexts that can subsequently be referred into, as in 'If I marry a post-structuralist, she'll be rich."

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(59) and (60) have barely any of the paradigm features of genuine conditionals. Not A (taking the pronoun 'then'); nor B—interpolation of 'only' produces unintended sense. Not C, because although Sp is convinced of both antecedent and consequent, Ad cannot verify such a conditional using the Ramsey Test. The sentences have D and E, but only degenerately, owing to the presumed truth of their antecedents. They entirely lack F (closeness in meaning to the corresponding subjunctive) and G (being conditional in meaning). They lack H, because they assert their consequents, but they deviate even further from the standard assertion pattern in that they assert (or presuppose) their antecedents as well. In that respect they are even less genuinely conditional than are our standard NCCs. Nonetheless, we hear (59) and (60) as on the whole being slightly more genuinely conditional than the standard NCCs, and so we suppose that even the degenerate possession of the logical properties D and E is a more than offsetting qualification.

Qualified denial: (61) If Ronald Reagan stole money, I've never heard of it. (61) seems to have feature A; at least, adding 'then' does not sound awful. But 'only' is still bad (feature B). (61) has C nondegenerately; if one disbelieves that Reagan stole money and adds (61)'s antecedent to one's belief store, revision will be required, but any conservative revision will preserve (61)'s consequent. (61) has feature E, equivalence to disjunction ('Either Ronald Reagan stole no money or I've never heard of it'), but lacks D (Contraposition and Modus Tollens) and has none of the remaining features F, GorH.

Pseudo-Factive concessives: (62) If I survived the summer, it was no thanks to you. (63) If I'm still here, it's because medical science has made great strides in the last twenty years. (64) If she did badly, she paid the price for it. (65) If I have seen further, it is by standing upon the shoulders of Giants. (Sir Isaac Newton, letter to Hooke, February 5, 1675 or 1676) These sentences display three features of interest. First, their antecedents are presupposed to be true; they are discourse givens. Obviously, the utterer of

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(62) has survived the summer and the utterer of (63) was still at the place in question at the time of utterance. We may imagine that in the other cases, the speaker is assuming the truth of the antecedent for the purposes of making the claim of the consequent. Second, the consequents of (62)—(65) each have pronouns that refer back to the antecedent clause. Thus 'it' in (62) refers back to 'I survived the summer' (and therefore means, 'If I survived the summer, my surviving the summer was no thanks to you.' 'It' in (63) refers back to 'I'm still here,' and the sentence therefore means 'If I'm still here, my still being here is because medical science has made great strides in the last twenty years.' And so forth. Thus grammatically, and therefore semantically, the consequent depends on the antecedent for its interpretation. Third, the antecedents are seen by speakers as effects of, not conditions on, the consequent clause. (62)—(65) have more of the paradigm features of genuine conditionals than did our factive concessives or qualified denials. Though they lack A, B and H, they have C, D, E and F—but only degenerately, because their antecedents are already presumed to be true. They do not have G; notice that a sentence having G could not be used to convince a hearer of the truth of its consequent via Modus Ponens, because given the established truth of its antecedent, the conditional assertion would itself beg the question.

Qualified assertion: (66) If I'm not mistaken, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night. (67) If memory serves, the capital of Honduras is Tegucigalpa. Arguably, (66) and (67) have feature A (taking the pronoun 'then'), though to our ears the resulting sentences sound more genuinely conditional than do (66) and (67) themselves. (66) and (67) also have E, and G (being conditional in meaning), since there is at least dependency between their respective antecedents and consequents. Feature H (assertion pattern) is equivocal at best: if one tries, one could hear (66) and (67) as genuinely conditional and not as asserting their consequents, but more commonly the consequents would be heard as asserted but marked for suboptimal confidence; their antecedents seem illocutionarily superfluous in some sense weaker than that in which a full-bore NCC's antecedent is superfluous. What of C and D (Ramsey Test, Contraposition and Modus Tollens)? Those questions pose a special problem about assertions qualified in the manner of (66) and (67). Viz.: It is none too easy a task to spell out exactly what such sentences mean, for although it is obvious that their antecedents are elliptical, it is anything but obvious what has been suppressed. In uttering

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(66), Sp is not hypothesizing her or his own omniscience; there is something more specific that Sp is or is not mistaken about: 'If I'm not mistaken about W, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night.' What is W? Surely W does not concern whether there is life on Saturn or whether Clinton is a good president or the like. Instead (at least by Grice's Maxim of Relation), W must be something that bears directly on the truth or falsity of the proposition that the Bobby Floyd Ensemble will be playing at Max and Erma's on Sunday night. W might be something more general, such as the plans of the Bobby Floyd Ensemble or Max and Erma's calendar, or even just that the Bobby Floyd Ensemble will be playing at Max and Erma's on Sunday night. Indeed (66) might be equivalent to any of (68): (68) a. If I'm not mistaken about their plans, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night. b. If I'm not mistaken about Max and Erma's calendar, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night. c. If I'm not mistaken as to whether the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night. d. If I'm not mistaken in thinking that the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night, the Bobby Floyd Ensemble will be playing at Max and Erma's Sunday night. Such sentences do support the Ramsey Test, Contraposition and Modus Tollens. One reason the presence or absence of H is unobvious is that such sentences at least implicate their consequents. Since the sincerity requirement forbids the assertion of something one does not believe to be true and the Maxim of Relevance requires that the speaker in fact have a belief about W, a sentence like (66) cannot felicitously be uttered unless the speaker believes its consequent.18 In contrast, a genuine conditional will normally not implicate a speaker's belief in the truth of the proposition expressed by the consequent clause. 'Weak' conditionals in Wayne Davis' sense:19 (69) If you open it, the refrigerator won't explode. 18 Actually, the details of the Gricean inference here are vexed, but there is no doubt of the implicature itself. 19 Wayne Davis, 'Weak and Strong Indicative Conditionals," Pacific Philosophical Quarterfy64, (1983): 57-71.

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(70) If it's humid out, the TV will work. What Davis finds distinctive about these conditionals is their lacking feature A, at least on one reading; adding 'then' changes their meanings or at least their contextual understandings. [E.g., (69) is true because, as is normal, opening the refrigerator will not cause it to explode. If one adds 'then' (or perhaps reads (69) more strongly), the resulting sentence seems to mean that opening the refrigerator will prevent the refrigerator from exploding.] 'Weak conditionals' do have B (modification by 'only'), and C; also E, though slightly degenerately due to the 'normal' truth of their consequents. They have F. They have G, but only loosely, in that the conditionality or dependence is negative rather than positive. Unlike their predecessors in our rogues' gallery of would-be conditionals, they have H; their assertion pattern is normal. (For this reason, we think, it is now less strained to call our sample sentences 'conditionals,' as we did in the opening sentence of this paragraph; in fact, it is not strained at all.) But they do not contrapose (feature D).

Hedging. (71) Jay drank few Margaritas, if any at all. (72) She recanted too late, if she ever recanted. (71) and (72) are almost genuine conditionals. They have features B, C, D, E, F, and G. Arguably they have H, though some hearers may understand them as qualified assertions; they do not obviously lack even A, though 'then' is the less interpolable, the more their antecedents are given afterthought intonation. How should we accommodate this apparently nearly continuous spectrum connecting flagrant NCCs to bonafide conditionals?

IX

Perhaps we should say just that—i.e.: There is such a spectrum, and that is the way English is, so sue us. Certainly it is possible that the notion of 'genuine conditional' constitutes what J. R. Ross used to call a 'squish,'20 and superficially conditional sentences are just more fully or less fully conditional, not divided between 'genuine' and 'nonconditional' conditionals. (If correct, this outcome would at least slightly embarrass the F I R S T main question posed in section II above, for that question as stated assumes a 20

J. R. Ross, 'Nouniness,' in O. Fujimura, ed., Three Dimensions of Linguistic Theory (Tokyo: Eichosha Shinsha, 1973), 137-257.

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dichotomy between NCCs and 'genuine' conditionals. But the question can be reformulated. For the puzzle is created essentially by feature H, the assertion pattern; if an NCC's consequent were not heard as itself making the focal assertion and the antecedent were not heard as merely incidental, the question of the antecedent would not arise so starkly. Thus, we can understand that question as directed upon any superficially conditional sentence having a reading on which the sentence lacks H, though it may not admit an answer that is uniform across NCCs, concessives, qualified denials, and qualified assertions. Similar remarks apply to the S E C O N D main question.) There is a more vigorous response to our F O U R T H main question and to the threat of the squish. It is to see a natural break in the alleged continuum, specifically, between qualified-assertion sentences and Davis' 'weak' conditionals. Again, the break would depend on feature H. Weak conditionals have H, and hedged conditionals either have H or are in some wise ambiguous as between H and non-H readings. Qualified denials and assertions can similarly be called ambiguous as between NCC and genuinely conditional readings. The ambiguities posited here are not gratuitous or particularly ad hoc, for we already know that paradigmatic NCCs usually have genuinely conditional readings also. This vigorous response has the virtue of apparently restoring NCCs to the status of a natural kind. But that kind, if it is one, is pretty feeble, for its distinguishing feature (non-H) is a pragmatic feature, not a crisply syntactic or semantic one. And, more particularly, that feature is at least slightly elusive and contentious. What a sentence 'asserts,' especially when the sentence is considered as a disembodied display upon a blackboard, can be disputed; even when the object of consideration is an utterance-token produced within an actual 'total speech situation,' theorists can disagree over exactly what the utterer 'asserted.' Though it seems entirely clear to us that the utterer of a fullbore NCC asserts the NCCs consequent and makes no conditional assertion at all, we can imagine someone's urging a rival theory according to which the utterer has really asserted a literal conditional, and hearers are left to infer the truth of the consequent by some nearly instantaneous pragmatic means.21 If NCCs are to be marked off as a natural kind, then, it would be nice to find a clear semantic difference underlying their lack of H. This raises, albeit belatedly, our F I F T H main question: What is the logical form of an NCC? Space limitations afford us only a few concluding remarks. X

If we take our cue from the non-H assertion pattern, we might suppose an NCC's semantic representation to be some variation on that of the NCC's 21

Stalnaker's view, mentioned in n. 17 above, maybe such a rival.

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consequent. Perhaps it is some more complex formula, redundantly equivalent to the consequent's semantic representation. But in view of the arbitrarily complex amount of conceptual structure that can be packed into an NCC antecedent, the logical equivalence idea seems unlikely to prove correct: (73) If nobody had time to tell you because they were all too busy packing and closing up the house and getting drunk, the new owner arrives tomorrow morning. Some NCCs bear very strong resemblances to the odd sentences that originally encouraged the 'Performative Hypothesis' posited by J. R. Ross and other Generative Semanticists of the 1960s.23 (Boer and Lycan called those sentences 'performadoxical.') Two examples: (74) Frankly, the boss here is an idiot. (75) Just because my mother may want to know, what is this stuff we're smoking? (The sentence adverbials in such sentences were taken by proponents of the Performative Hypothesis to modify hidden underlying performative verbs— thus, 'Frankly I state that the boss..." and 'Just because..., I ask what this stuff is...') Some of our NCCs, such as (11), (14), (28) and (20), have factive versions containing 'since' or 'because': (76) Since you want to know, she and I never got along. (77) Since you have time to talk about the meeting, Geoff really made an ass of himself. (78) Because Peter will ask you, I did receive his letter. (79) Since you don't mind, please pick up some Molson's. These have the performadoxical ring. So it may seem attractive to suggest that whatever semantics is true of performadoxical sentences can easily be extended to cover NCCs. The semantic analysis of performadoxicals is extremely problematic, whether or not one accepts any version of the Per22 We assume here that semantic representations are logical formulas depicting the truth-conditions of their target sentences. If some Adamsite or some general assertibility semanticist should insist that indicative conditionals do not have truth-conditions, we think our remarks here would still stand when reinterpreted in terms of assertibility conditions. 23 J. R. Ross, 'On Declarative Sentences," in R. Jacobs and Rosenbaum, eds., Readings in English Transformational Grammar (Waltham, Mass.: Ginn & Co., 1970). See also (especially) J. Sadock, Toward a Linguistic Theory of Speech Acts (New York: Academic Press, 1974). 24 Boer and Lycan, 'A Performadox in Truth-Conditional Semantics," Linguistics and Philosophy 4 (1980): 71-100; see also Alice Davison, 'Linguistic or Pragmatic Description in the Context of the Performadox,' Linguistics and Philosophy 6 (1983): 499-526.

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formative Hypothesis, 5 but that is no embarrassment to the idea of extending that analysis, whatever it may turn out to be, to a wider range of phenomena. However, the present suggestion is not very promising even taken on its own. For one reason, although factive adverbials headed by 'since' and 'because' do seem to modify the allegedly underlying performative verbs, serving as reason-adverbials describing the corresponding illocutionary acts, 'if itself does not go well with such verbs: (80) ??If I may speak frankly, I state that the boss here is an idiot. (81) ??If my mother should want to know, what is this stuff we're smoking? Though (80) and (81) are grammatically fine as they stand, they are themselves NCCs; their antecedents do not particularly modify the subsequent illocutionary verbs. A second reason for doubting that performadoxical semantics will help is that most NCCs do not have factive equivalents of the performadoxical sort. E.g, (82) (83) (84) (85)

??Since you don't mind, I'm trying to read. *John is having a little rest, because you follow me. *It was a great article, because I do say so myself. *How about inviting Fritjof Boeger, because I've spelled his name correctly?

A separate semantics would have to be provided for those NCCs in any case, and it is more likely that that separate semantics would extend to cover the NCCs that do have performadoxical factive equivalents than that the performadoxical semantics would. It is quite possible that a semantics for NCCs might fall degenerately out of a general semantics for conditionals, though for this to happen, some of the theory's parameters would have to be set to extreme or anomalous values, at least if NCCs are understood to entail their own consequents.26 All this 25 For exposition of the main problems, see Boer and Lycan, op. cit. For an alternative explanation of the performadoxical data, see ch. 6 of Lycan, Logical Form in Natural Language (Cambridge, Mass.: Bradford Books/MIT Press, 1984). 26 In conversation, David Lewis once offered a suggestion for extracting an NCC semantics from Lycan's semantics for conditionals. (See Lycan's 'A Syntactically Motivated Theory of Conditionals," in T. E. Uehling, P. French and H. Wettstein eds., Midwest Studies in Philosophy, Vol. IX: Causation and Causal Theories [Minneapolis: University of Minnesota Press, 1984], 437-55; see also his 'MPP, RIP," loc. cit.) But we have yet to pursue that suggestion in any detail. [See the Revisionary Postscript. W G L ] If one does not suppose that NCCs semantically entail their consequents, but instead offers some pragmatic explanation of why they are heard as asserting those consequents, one

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continues to assume from the previous section that NCCs are dichotomously distinguished from 'genuine' conditionals. The semantic task will be all the tougher if we drop that tendentious assumption and admit that 'genuineness' comes in degrees. As if that were not trouble enough, there are two further complications that will obstruct semantics for NCCs. One is that NCCs can nest; one NCC antecedent may contain another as a part: (86) If you're finished 'rehearsing' and being incredibly noisy and, if you ask me, making total fools of yourselves, what are those socalled instruments you were playing? The second complication is that asserted conjuncts can be interpolated between an NCCs antecedent and consequent: (87) If you want to know, and I'm sure you do because this is a really juicy piece of gossip about that world- class turkey you got married to time before last—the whole Personnel Department was arrested last week and he in particular was charged with molesting marsupials. And that seems a good place to stop. might much more easily start from a general conditional semantics; we believe this would be Stalnaker's strategy (see again n. 17 above). But of course then the pragmatics will have an heroic job to do. And between them, semantics and pragmatics will still have to explain the utter failures of Contraposition and Modus Tollens. It is possible that the 'if of NCCs is related to the complementizer that occurs with some attitude verbs, as in 'S wonders if..." and 'S does not know if..." The latter, indirectquestion 'if is well paraphrased by 'whether' and by 'whether or not": and indeed, our original (1) is not badly paraphrased by 'There are biscuits on the sideboard whether or not you want them." This hypothesis would answer our T H I R D main question, explaining why NCCs contain 'if even though they are not genuine conditionals, as well as why their consequents seem to be used to perform acts independently of the antecedents. It also would address our S E C O N D question, revealing some of the basis of our quick recognition of NCCs as such; it makes that recognition a simple case of literal disambiguation.

Revisionary Postscript on NonConditional Conditionals I can now offer a proposal as to the semantics (the logical forms) of NCCs: that they do after all have a conditional semantics, as Stalnaker suggested, and more specifically they are akin to 'weak' conditionals as I construed those in Chapter 2. Recall that our representation of weak P > Q is: (C E R) (In(e,P) D In(e,Q)), but where R contains no ~Q events. Given the latter distinctive stipulation, that formula is equivalent to (C E R) (In(e,Q) & (In(e,P) D In(e,Q))), which in turn is redundant on (C E R) (In(e,Q)). If the Reality Requirement is imposed, this simply entails Q. If we dispense with the Requirement, still a sentence that reflects (C E R) (In(e,P) D In(e,Q)) where R includes no ~Q events will be used as an assertion or near-assertion that Q (as was argued in Chapter 6). That explains why an NCC is heard as asserting its consequent. (Though not why an NCC does so more definitely than does a weak; see below.) This semantic conjecture also answers two of Geis and Lycan's three remaining questions. The ' T H I R D ' question was that of why 'if occurs in NCCs at all; that 'if occurs is self-evident if NCCs are semantically conditional. The F O U R T H was why there is a 'squish' or spectrum of sentence types connecting NCCs with genuine, including robust, conditionals. That is (potentially) clear enough, if the logical forms are the same and the differences are only pragmatic. But Geis and Lycan gave quite a specific characterization of weak conditionals, focusing on Davis's examples ('If you open the refrigerator, it will not explode,' 'If it's humid out, the TV will work'; cf. 'If you ask him, he won't bite your head off,' 'I will finish the paper today (even) if Norway has an early autumn in 2010') and distinguishing them from our NCCs. We said that, unlike NCCs, weak conditionals have features B (modification by 'only'), C (Ramsey Test), degenerately E (equivalence to disjunction), F (closeness to subjunctive), G (intuitive conditionality, though only weakly), and H (normal assertion pattern). NCCs have none of those. G and H are particularly important: weak conditionals are heard as conditional, even though they are not what I have called robustly so, and they are heard as asserting their consequents, not as themselves being asserted. So it would not do to suggest that NCCs are a species of weak conditionals. Rather, Davis's conditionals and NCCs are both species of a wider genus, the genus defined by the semantic representation I have assigned to weaks. The difference must be pragmatic. 1

This elaborates the suggestion made to Geis and me by David Lewis, Appendix, n. 26.

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What primarily needs explaining is why an NCC is heard as not being conditional at all. Ordinary weaks not only are heard as conditional, but have more obvious robust alternate readings than are the perverse genuine-conditional readings of NCCs; absent 'then', an 'if conditional always has both a weak and a robust reading, while robust readings of NCCs must be very contrived. First, we must revisit the question of whether an NCC entails its consequent. And there is evidence that it does, for an NCC's implication of its consequent is not, or not easily, cancellable: (1) *There are biscuits on the sideboard if you want them—but don't get me wrong: there aren't any biscuits on the sideboard. (2) *If you're looking for the captain, he isn't here; but actually he is here. (3) *John is having a little rest, if you follow me, but he is not having any rest. (l)-(3) sound contradictory. That is an appearance that must be explained away, if NCCs differ from weaks only pragmatically, since weaks do not entail their consequents. (2) would be represented as (4) (C E R) (In(e, You are looking for the captain) D In(e, ~ (The captain is here))) & The captain is here, where R contains no Captain-Here events. But this is not semantically contradictory. Just as Chapter 2's (5) ('If you open the refrigerator, it will not explode, but actually the refrigerator is going to explode anyway') is not strictly a contradiction but only anomalous from an illocutionary or speechact point of view, I believe the same is true of (2), and (1) and (3). Anutterer of (2) does not envisage any Captain-Here events, but none the less asserts(!) that the captain is here. Yet there are two further unexplained differences between NCCs and weaks. First, remember that weaks characteristically admit 'even', which on my view also licenses the full semifactual 'still', and when 'even' or 'still' is inserted, a conjunct is added in logical form. Yet the insertion of 'even' or 'still' into (1), (2), or (3) seems to change those sentences' meanings from NCC to semifactual: (1 e) There are biscuits on the sideboard even if you want them. (2e) Even if you're looking for the captain, he isn't here. (3s) (Even) if you follow me, John is still having a little rest. If NCCs are semantically the same as weaks and weaks can without significant change in meaning be promoted to semifactuals by the insertion of 'even' or

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'still', then it seems to follow that NCCs can be so promoted without significant change in meaning; but we have just seen that that apparent consequence is false. Second, 'If you open the refrigerator, it will not explode, but actually the refrigerator is going to explode anyway' is odd and illocutionarily anomalous but still reinterpretable as something like, 'Opening the refrigerator won't make it explode, but it's going to explode anyway for some other reason.' (1 )— (3) have no such charitable interpretations—certainly not 'Your looking for the captain hasn't kept him away from here, but he isn't here anyway for some other reason.' (l)-(3) sound more intractably contradictory. You just cannot say them. In keeping with my usual method in this book, I should look for a parametric difference between NCCs and weaks. And there may be one. But I am now inclined to think that the difference is pragmatic in a different way: not in the contextual setting of a parameter that fixes prepositional content itself, but purely illocutionary. What is distinctive about NCCs is precisely that their antecedents are not plausibly taken as conditions, either necessary or sufficient, of their consequents. So their illocutionary force cannot be to assert a robust or even a weak conditional proposition. We have seen that, instead, the function of an NCC is as specified in (G3): to perform a speech act whose locutionary content is expressed by the NCC's consequent while either calling attention to a felicity condition on that speech act or mitigating a face-threat associated with it. Evidently our speech community needs a linguistic device of illocutionary performance so accompanied. I conjecture that that illocutionary function is itself primarily what distinguishes NCCs from weaks. It maybe that the logical form of an NCC does not differ from its corresponding weak; what differs is only the assertion pattern. But what, then, explains the two differences I have noted? The first difference was that the insertion of 'even' or 'still' seems to change an NCC's meaning: I suggest that, as discussed in Chapter 6, the function of 'even' and 'still' is to gesture toward a range of circumstances or conditions that contrast with respect to the strengths of their inhibitory bearing on the consequent. But if that is so, they can apply only to conditionals that do specify conditions and/or a relation of conditionship, which NCCs notoriously do not. If a sentence can have either an NCC or a weak understanding, as strictly speaking every NCC does, the insertion of 'even' would disambiguate it by turning it into a semifactual. Hence the sense of meaning change. Second, the intractable contradictoriness of (l)-(3). Here the explanation is unexpectedly easy: if an NCC cannot be used to assert a conditional proposition, but only to assert its consequent, then (l)-(3) should sound firmly contradictory. Because even if semantically they are not strictly contra-

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dictions, they cannot be used to assert anything but contradictions. The undeniable ring of contradiction actually confirms the present hypothesis. What about the F O U R T H issue, squish of 'genuineness' versus NCCs as a natural kind? I no longer see as firm a 'natural break' as Geis and Lycan did between qualified assertions and weak conditionals. That is largely because, as I revealed in Chapter 2,1 now think that conditionals differ in the degree to which their consequents maybe heard in context as being asserted; feature H is not all-or-nothing. I said that weaks are heard as asserting their consequents to some degree, but not to as great a degree as are semifactuals, and neither of those absolutely. NCCs absolutely assert their consequents. So do factive concessives, qualified denials, and pseudo-factive concessives. Qualified assertions are just that, only qualified assertions of their consequents. Weaks, as before, are heard as asserting their consequents to a lesser degree; hedge conditionals assert their consequents hardly at all. So we see something approaching a consequent-assertion squish. As Geis and Lycan should have noticed, there is an exactly parallel semisquish based on G, intuitive conditionality. NCCs, factive concessives, qualified denials, and pseudo-factive concessives are not intuitively conditional at all. Qualified assertions seem a bit more conditional, though my not being mistaken is only loosely a condition of the Bobby Floyd Ensemble playing. Weaks are conditional but, of course, only weakly so. Hedge conditionals are more so but not entirely, and arguably they have A: they do not firmly reject 'then'. But if NCCs share consequent-assertion and their intuitive non-conditionality with factive concessives, qualified denials, and pseudo-factive concessives, something else must account for the intuitive differences in genuineness between NCCs and the others. The others do differ from NCCs in details of their assertion patterns, specifically in regard to their antecedents. An NCC only suggests the truth of its antecedent. A factive concessive asserts its antecedent. A qualified denial denies or nearly denies its antecedent. A pseudo-factive concessive presupposes its antecedent. But I admit that I am not sure how those differences would account for the various types' perceived genuineness rankings. As for NCCs forming their own natural kind despite being only one end of a squish, I have already proposed that they do, but that the kind is illocutionary, not semantic or necessarily parametric. And I think NCCs have an additional non-semantic and non-parametric feature distinctively in common as well, one that affords us at least a gesture toward answering Geis and Lycan's S E C O N D question, that of how NCCs are so quickly recognized as such. (This idea is independent of my previous two hypotheses, that NCCs do have conditional logical form and that what

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distinguishes them as a class is illocutionary.) I think Geis and Lycan's idea of a connection between NCCs and performadoxical sentences, though ultimately misguided as they said, contained a nugget of truth. It is that NCC antecedents are uniformly metalinguistic in purport. They make reference, explicit or tacit, to the speaker's utterance of the consequent. This follows from (G3): they either call attention to a felicity condition on that utterance or mitigate a face-threat associated with it. No conditional antecedent of the other types on our squish (normally) does that. And that gives a welcome hint as to how hearers recognize NCCs so automatically. A metalinguistic circumstance is very unlikely to bear any genuinely conditional relation to the consequent circumstance in question; it is nearly categorially different. (Though of course such relations do occasionally occur; recall 'If you're reading this, you're too close.') It is attractive to think that what kicks off the interpretation of an uttered conditional as an NCC is this metalinguistic character, though of course one would have to say something about later processing as well. The present overall view of NCCs has its drawbacks, but I believe it leaves us in a better position overall than did Geis and Lycan's. Geis and Lycan answered their F I R S T question, that of the function of NCC antecedents, by proposing (G3). They did not answer, but merely posed, their S E C O N D (how NCCs are instantly perceived as such), T H I R D (why 'if' occurs in NCCs), F O U R T H (why there is a squish), and F I F T H (what is an NCC's logical form). By contrast, the present view has answered the S E C O N D (in part), T H I R D , F O U R T H (to some extent), and F I F T H , the T H I R D and F I F T H at one decisive stroke.

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Index Across-the-Board 4-5 Adams, E. W. 32, 33, 48-9, 57, 73, 74, 76, 78, 79, 83, 84, 86, 87, 88, 89, 139, 141, 148-50, 154-7, 161, 162, 164-6, 167, 171 Adams' Generalization 87-90 Adams-pairs 139-40 Future-Adams-pairs 162-6 Adverb Preposing 5-6 Anderson, A. R. 26 Anomalous Version (of Riverboat Puzzle) 167-8 Antecedent Requirement 28, 32, 35, 36n.23, 44, 45, 117 Antecedent-Strengthening 27, 28, 29, 30, 31,40,42,61,62,65-6,68 Appiah, A. 73, 78, 79, 83, 88, 90 Aquinas, T. 37 assertibility 48, 57-8, 61, 74, 77, 78, 83, 87, 88, 89 n., 96, 97, 141,142, 161,167, 168 Atlas, J. 37 Austin, J. L. 184, 192 Ayer, A. J. 80 backtracker 163 n., 178-82 Barker, S. J. vii, 106, 108, 109, 115n., 128-30, 156, 163 Bar-On, D. 81 Barwise, J. 17 n. 2, 101 n. Bayesian probability 48 Belnap, N. vii Bennett, J. 25 n. 13, 73, 86, 93, 95, 96-108, 115-17, 120-1, 140, 142 n. 4, 163, 178 Berckmans, P. 115n., 122, 125 n. 9, 126, 132-7 Boer, S. 92 n., 143 n., 203, 204 n. 25 boxarrow conditionals 139-43,144,145-7, 149, 151-66, 171-2, 183 Brown, P. 192-3 Brugman, C. HOn. 18 Carlstrom, I. E 87 n. Chisholm, R. 176n. Clark, M. 82 n. Cohen, L. 90,92 comparative-intensifying use of 'even' 115-16 Comrie, B. 3 n. 3, 8 n. 8, 75 n. 4

Conditional Excluded Middle (CEM) 49, 160-2, 166 Conditional Noncontradiction 83, 168, 175-6, 180,181 Conditional Proof 27 n. 15 Conjunction Reduction 4-5, 59 Consequent Requirement 32-5 Consequent-Assertion 128-30 Consequent-Entailment problem 108,122, 125-7 see also Consequent-Assertion Contraposition 31-6, 186, 198, 199, 200 conventional implicature 39, 94-5, 197 conversational implicature 3, 43, 94, 197 Co-ordinating-Conjunction hypothesis 4-6 cotenability 157 Creary, L. G. 42n.28 Davis, W. 20-1, 34, 36, 140, 142, 146-7, 151-5, 157, 158, 162, 165-6, 172, 200-2, 206 Davison, A. 185 n. 2, 189 n. 8, 203 n. 24 Deflationism 80 Delgado Lavin, E. 95 n. 4, 135 DeRose, K. vii Downing, P. B. 178n. 5 Dretske, E 174n. Ducrot, O. 105 n. 11, 125 n. 10 Dudman, V. H. 25 n. 12, 77, 93 n., 122 n. 7, 140, 142 n. 4, 156 n. 13, 163, 166 Edgington, D. vii, 27 n. 15, 73, 83-6, 89 Ellis, B. 87 envisaging 28, 30, 46, 47, 65, 118, 126 face-threatening act (ETA), 192-3, 195 factive concessives 197, 199, 209 Fauconnier, G. 105 n. 11, 120 Fillmore, C. 2, 101 Fine, K. 42 n. 28, 51, 53, 55 n. 3 floaters 110-12 Eraser, B. 133 n. future indicatives 77 Gallimore, R. 70 Gallimore's Problem 69-72 Gapping 4-5

222

Index

Gauker, C. 142 n. 5 Geis, M. vii, 5 n. 7,8 n. 9, 10-11, 14-15, 16-17,31,41, HOn. 18, 189n. 7, 192 n. 13, 209-10 Gibbard, A. 63-5, 73, 74, 76, 81-3, 89 n., 118-20, 126-8, 140, 142, 150, 154-5, 157, 162, 166, 167-72, 176 n. Goodman, N. 20 Grandy, R. vii Haiman, J. 4, 127 n. 11 Hanson, W. H. 27 n. 15 Hard Line (on the Riverboat Puzzle) 168-9 Harman, G. H. 58 n. 7, 90, 174 n. Harper, W. 48, 89 n., 185 n. 3 Hazen, A. 93 Hedge conditionals 209 Hill, C. 42 n. 28, 87 n. Horn, L. 37n., 105n. 11, 106n., HOn. 18, 112n.21, 113n.23 Horseshoe theory 26 n. see also New Horseshoe Theory illocutionary force 186, 188, 189-93, 195, 208-10 impossible antecedents 46-7 indicative conditionals 25, 27, 29, 48, 58, 71-4,76-9,81,86-8,91, 139 'indicative'/'subjunctive' distinction 140-1 Jackson, E 19 n. 4, 27 n. 15, 63 n. 11, 83, 86, 88-91 jarring fact 179-80 Jeffrey, R. 87 Jeffrey's Hypothesis 87-8, 90 n. Karttunen, L. 95 n. 3,106 n. Kay, P. 96, 101, 105 n. 11, 113n.23, 119-26 Kratzer, A. 17 n. 1, 23 n. 10, 25 n. 12, 55 Kremer, M. 77, 82 n., 176 n. Kvart, I. 52 n., 55 n. 3 Lakoff, G. 5 n. 7 Larson, R. 10 Levinson, S. 192-3 Lewis, D. 18 n., 23-5, 29 n., 31, 34, 36, 39, 42, 46, 48-54, 58-9, 61, 62, 66, 67, 69, 70, 81, 86-8, 89n., 90, 91, 139n., 141-2, 151, 153, 155, 156, 157, 159, 161, 162, 165, 166, 171, 178, 186, 204 n. 26, 206 lexical presumption 94-5, 143 n.

Loewer, B. 43 Mackie, J. L. 102, 146-7, 148, 150-5 material implication 25, 142 n. 5 McCawley, J. D. 15 n., 37 n., 38 n., 110 n. 18 McDermott, M. 27 n. 16, 39 n., 78 n., 129 n. 14, 145 n., 148, 160 McGee, V. 57 n., 66-7, 69, 72 n. McKay, T. 43n.31 Mellor, D. H. 85 n. metaphysical-similarity analysis 50-2, 65 metaphysical-similarity model 59, 70 Milne, P. vii Moderate Relevance Restriction 22-3 Modus Ponens 24, 57-69, 72, 118, 176 Modus Tollens 182-3, 186, 198-200, 204 n. 26 mood 4-5, 140, 143 n., 163 Morgenbesser, S. 155 Morgenbesser's Anomaly 155-60,166 New Horseshoe Theory 86-92, 143 see also Horseshoe Theory Nisbett, R. 90 No-Truth-Value thesis (NTV) 48-9, 57-9, 71-2, 73-90, 143, 177, 180 Nozick, R. 23 n. 10 Nute, D. 42-4, 46 n. 35, 51 Onions, C. T. 6, 12 'onlyif 1, 7, 14-15, 16-18, 37-41, 184, 186 parameter shift 28, 29, 30, 40, 41, 68, 118, 121, 174, 182 parametric strictness 23 Pearce, G. 48, 185 n. 3 Pendlebury, M. 85 n., 142 n. 4 performadoxical sentences 203-4, 210 Performative Hypothesis 203-4 Perry, J. 17 n. 2, 101 n. Peters, S. 95 n. 8, 106 n. Plus theory of'even' 127-37 Pollock, J. L. 102, 104, 106-8, 121 possible-worlds semantics 31, 49-50, 74 Priest, G. 47 n., 58 n. 6 probability theory 90 Problem of Comparison 99-100,103 pseudo-factive concessives 209 qualified denials 199, 202, 209 Quine, W. V. 159, 160 Ramsey, E P. 48, 80

Index Ramsey Test 48-59, 65, 70-1, 86, 139, 141-2, 154, 167, 171, 185, 187, 198-200, 206 Read, S. 85 n. 'real' possibilities 19, 21, 28-30, 46, 104, 108, 128, 158, 173-4, 179-80 Reality Requirement 56-67, 71-2, 117-18, 126, 128, 176-7, 206 reference-class 18-24, 60, 65, 99-101, 105-6 parameter R 21, 28, 33, 67, 85, 103, 175 presumed by 'even' 106 reference-time (a conditional's) 142, 146, 153-4, 157-8, 166 Relative Clause analysis 10-15, 31 Right Node Raising 5 n. 6 Rivero, M. L. 109 n. 15 Room, M. HOn. 18, 111, 112 Ross, J. R. 201 n., 203 Ross, L. 90 'salient fact' (used in evaluating straight conditionals) 145-8, 158 Sanford, D. 38 n., 62 n. 10, 91 n. 16, 92, 131 n., 147 Schumm, G. 51 Searle, J. 189 semifactual 20-1, 34-6, 207-9 see also weak conditionals Shapiro, S. 46 n. 36 similarity relation 49, 51-2 similiarity theory 31, 49, 55 Simple Version (of the Riverboat Puzzle) 167 Simplification of Disjunctive Antecedents (SDA) 42-6 Sinnott-Armstrong, W. 62 n. 9, 66 n. Slote, M. 93, 140, 142 n. 4, 155, 157-8, 178 Smart, J J .C. 80 n. 9

223

Sobel, J. H. 58 Sobel sequences 58-60, 63, 65 Stalnaker, R. 23,25,26 n., 27-31,34, 36,46, 48-54, 62, 66-7, 70, 76 n., 79-83, 87, 89, 139-43, 151-3, 155-7, 159, 161, 165-6, 171-2, 181-3, 185 n. 3, 196 n., 206

Stevenson, C. L. 26 n. straight conditionals 140-50, 153-68, 172, 176n., 179 Strict Relevance Condition 173 Strict Relevance Restrictions 22-3, 26-7, 32 subjunctive conditionals 12, 37, 39-40, 59, 76-7, 91, 139, 186, 198, 206 Subjunctive semifactuals 36 Sweet, H. 6, 12 Tappenden, J. 196 n. Taylor, J. R. 3 n. 3 Thomason, R. H. 27 n. 15, 37 n. Thomson, J. E 86 Transitivity 29, 40-1, 44 n. 34, 49, 68, 142 n. 5 Traugott, E. C. 75 n. 4 vagueness 39, 103-4 van Fraassen, B. 161 van Inwagen, R 43 variably strict conditionals 23 Weak conditionals 20-1, 31-6, 200-2, 206, 208

William of Sherwood 37 n. Within-Reason theory of 'even if 123-6, 131, 137 Woods, M. vii, 82, 89 n. Zwicky, 3 n. 2