THOUGHT-CONTENTS: ON THE ONTOLOGY OF BELIEF AND THE SEMANTICS OF BELIEF ATTRIBUTION
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THOUGHT-CONTENTS: ON THE ONTOLOGY OF BELIEF AND THE SEMANTICS OF BELIEF ATTRIBUTION
Philosophical Studies Series VOLUME 104
Founded by Wilfrid S. Sellars and Keith Lehrer Editor Keith Lehrer, University of Arizona, Tucson Associate Editor Stewart Cohen, Arizona State University, Tempe Board of Consulting Editors Lynne Rudder Baker, University of Massachusetts at Amherst Radu Bogdan, Tulane Universtiy, New Orleans Marian David, University of Notre Dame Allan Gibbard, University of Michigan Denise Meyerson, Macquarie University François Recanati, Institut Jean-Nicod, EHESS, Paris Stuart Silvers, Clemson University Barry Smith, State University of New York at Buffalo Nicholas D. Smith, Lewis & Clark College
The titles published in this series are listed at the end of this volume.
Thought-Contents On the Ontology of Belief and the Semantics of Belief Attribution
STEVEN E. BOËR Department of Philosophy The Ohio State University Columbus, Ohio, USA
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-5084-4 (HB) ISBN-13 978-1-4020-5084-8 (HB) ISBN-10 1-4020-5085-2 (e-book) ISBN-13 978-1-4020-5085-5 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com
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For Ann and Leah
CONTENTS
Preface and Acknowledgements Introduction
xi xiii
PART I: PRELIMINARIES 1.
2.
Terms of the Art 1.1. Some types of intentionality 1.2. The substitutional approach and its problems 1.3. Non-Actualism 1.3.1. The being-existence distinction: a proposal 1.3.2. The non-actualist approach to existence-independence and concept-dependence 1.4. Intensionality and extensionality 1.5. Hyper-intensionality 1.6. Opacity and transparency 1.7. De re / de dicto / de se
3 3 9 12 12 15 21 27 32 34
Adequacy Conditions and Failed Theories 2.1. Some general adequacy conditions 2.2. Frege’s theory of thoughts 2.3. Russell’s propositional and multiple-relation theories 2.4. Chisholm’s property-attribution theory
39 39 45 54 65
PART II: ONTOLOGY 3.
Logical Forms and Mental Representations: The Lesson of Russell’s Multiple Relation Theory of Judgment 3.1. Adequacy conditions on the reduction 3.2. The formalities of MRTJ 3.2.1. The base language and underlying logic 3.2.2. Some primitive vocabulary and axioms of MRTJ 3.2.3. Truth in MRTJ
vii
81 82 83 83 84 89
viii
Contents
3.3. 3.4. 3.5. 3.6. 3.7. 4.
5.
The theory The bridge principles and reduction of MRTJ to + Vindication and the adequacy conditions Implications of the reduction of MRTJ for our wider project The shape of things to come
Thought-Contents, Senses, and the Belief Relation: The Proto-Theory 4.1. Overview 4.2. The underlying theory of abstract objects 4.2.1. Zalta’s System ILAO 4.2.2. Departures from ILAO 4.3. TC: The proto-theory 4.3.1. Senses as A-objects; thought-contents as senses 4.3.2. Valuation relations and canonical λ-profiles 4.3.3. Thought-contents with specified objects as constituents 4.3.4. Interpreting canonical names of atomic thought-contents 4.3.5. Mentalese denotation; the constituents and canonical objects of n-ary atomic thought-contents 4.3.6. Entertaining and believing thought-contents 4.3.7. Application to belief de re 4.3.8. Senses as constituents of thought-contents: translucent and opaque senses 4.3.9. Belief de dicto, belief de se, and substitutional opacity 4.3.10. Transparent senses and Soames’s problem Thought-Contents, Senses, and the Belief Relation: The Full Theory 5.1. Revisions to the proto-theory 5.2. Application to higher-order belief 5.3. Generalizing key definitions, principles, and theorems 5.4. Doing without empty senses Appendix to Chapter 5: The formal theory TC A.1. Metalinguistic conventions A.2. Special vocabulary of TC A.3. Formation rules for special terms of TC A.4. Definitions in TC A.5. Axioms of TC
92 96 104 109 111 121 121 124 124 125 127 127 129 133 135 138 141 144 145 154 157 169 169 179 183 188 190 190 191 192 192 197
PART III: SEMANTICS 6.
Belief Reports and Compositional Semantics 6.1. The theory TC as a semantical metalanguage 6.2. The target language L1
205 206 213
Contents
ix
6.3. STC : A TC-based sense-reference semantics for L0 and L1 6.4. Semantics for mentalese—or: speak for yourself! 6.5. Prospects for naturalization
216 224 229
7.
Meeting the Semantical Adequacy Conditions 7.1. De dicto / de re / de se 7.2. Iterated belief reports 7.3. A problem about reflexivity 7.4. Saul Kripke’s original puzzle 7.5. Kripke’s puzzle and iterated belief reports 7.6. David Austin’s ‘Two Tubes’ puzzle 7.7. Pragmatics versus semantics 7.8. Mark Richard’s puzzle
235 235 242 244 246 250 253 255 258
8.
Objections and Replies 8.1. Specific objections to our semantical theory 8.1.1. Belief reports and valid arguments 8.1.2. The problem of translating our semantical metalanguage 8.1.3. Twin Earth semantics 8.2. Generic objections to ‘Fregean’ semantics 8.2.1. Stephen Schiffer’s critique 8.2.2. The problem of negative existential generalization 8.2.3. Saying, meaning, and believing
265 265 265 269 272 276 276 284 288
PART IV: REAR-GUARD ACTION 9.
The Case for Object-Dependent Thoughts 9.1. The central theses 9.2. Gareth Evans’ first argument for (ODT-1) 9.3. Critique and defense of Evans’ first argument 9.4. Evans’ second argument for (ODT-1) 9.5. Critique and defense of Evans’ second argument 9.6. The problem of negative existentials involving empty singular terms 9.7. The problem of attitude-ascriptions with ‘that’-clauses containing empty terms 9.8. A problem about certain conditionals 9.9. An argument for (ODT-2) yielding (ODT-1) as a corollary
10. A Critique of Rival Accounts of Singular Thoughts 10.1. Kent Bach’s theory of ‘de re beliefs’
297 297 300 303 308 309 313 317 320 322 329 329
x
Contents
10.2. Harold Noonan’s theory of demonstrative thoughts 10.3. The narrow content objection 10.4. Object-dependence and the senses of general terms
339 346 352
References Index
357 363
PREFACE AND ACKNOWLEDGEMENTS
This book has three primary aims. The first is to articulate the theory TC, a formal ontology of belief as a dyadic relation to a special kind of property (a ‘thoughtcontent’). The second is to wield TC in the construction of STC , a semantics for attributions of belief which treats substitutional opacity in belief reports as a genuine semantic datum. And the third is to defend the resulting account at length by showing how it solves standard puzzles, avoids a variety of objections that have been raised against rival views, and satisfies an array of ontological and semantical adequacy conditions not fulfilled by traditional theories. Along the way, two secondary tasks are undertaken: one is to clarify and defend the Neo-Fregean conception of ‘object-dependent senses’ that TC incorporates in its account of thought-contents; and the other is to show how adoption of the language of thought hypothesis aids in understanding the obscure doctrine of ‘logical forms’ in Bertrand Russell’s infamous Multiple Relation theory of belief in a way that not only vindicates it as an account of de re belief but also reveals these logical forms as precursors of the thought-contents that figure in TC’s account of belief in general. The proffered ontology incorporates three key theses: (i) belief is a relation of self-ascription obtaining between an agent and a property (not a proposition); (ii) this property is not the belief’s truth condition—i.e., the intuitively self-ascribed property which the agent must exemplify for the belief to be true—but is instead a certain non-actual ‘abstract’ property (a thought-content) which contains a way of thinking of that truth condition; (iii) to have a belief about such-and-such items one must possess a language of thought (one’s ‘Mentalese’) and be disposed as one who inwardly affirms therein a sentence containing terms that denote those items. Thesis (i), of course, derives from the work of Roderick Chisholm and David Lewis, and Thesis (iii) is familiar from the work of Jerry Fodor and others. A distinctive feature of this book is Thesis (ii) and the way in which TC explains it and integrates it with the others, using a modified and extended version of Edward Zalta’s system of intensional logic for abstract objects to locate thought-contents within a typed hierarchy of ‘senses’ and the ‘modes of presentation’ they contain. Another distinctive feature of this book is the way in which the resulting apparatus is used to provide a quasi-Fregean sense-reference semantics STC for belief attributions xi
xii
Preface and Acknowledgements
which (a) is finitely axiomatizable, (b) accommodates context-dependent terms, (c) respects compositionality, (d) smoothly handles belief ascriptions with arbitrarily complex ‘that’-clauses (in particular those embedding further belief attributions), (e) sensibly adjudicates various controversies while solving alleged puzzles regarding such attributions, and (f) avoids the difficulties encountered by most if not all extant accounts that take opacity as a semantic datum. I am grateful to my colleagues at OSU for helpful discussion, to Edward Zalta for his comments on ancestral fragments of the present work, and to my wife and daughter for tolerating my retreat into the Cave of Solitude while completing the manuscript. Some material from earlier publications of mine has found its way into the Chapters indicated below. Chapter 2: [1] Chisholm on Intentionality, Thought, and Reference. In: Bogdan R (ed) Profiles: Roderick Chisholm. D. Reidel, Dordrecht (1986), pp. 81-111. Chapter 3: [2] On the Multiple Relation Theory of Judgment. Erkenntnis 56 (2002): 181-214. Chapters 4-5: [3] Thought-Contents and the Formal Ontology of Sense. Journal of Philosophical Logic 32 (2003): 1-79. Chapters 6-8: [4] Propositional Attitudes and Compositional Semantics. In: Tomberlin J E (ed) Philosophical Perspectives, 9: AI, Connectionism, and Philosophical Psychology. Ridgeview Publishing Co., Atascadero (1995), pp. 341-80. Chapters 9-10: [5] Object-Dependent Thoughts. Philosophical Studies 58 (1990): 51-85. [6] Neo-Fregean Thoughts. In: Tomberlin J E (ed) Philosophical Perspectives, 3: Philosophy of Mind and Action Theory. Ridgeview Publishing Co., Atascadero (1989), pp. 187-224. The extracts from items [4] and [6] appear by kind permission of Blackwell Publishers Ltd., and those from items [1], [2], [3], and [5] by kind permission of Springer Science and Business Media.
INTRODUCTION
According to our commonsense view of the matter, beliefs, desires, intentions and the like are special kinds of internal states the possession of which by a given creature potentially explains its behavior and otherwise renders the creature intelligible to us. So-called folk psychology provides us with a rough-and-ready network of counterfactuals delimiting the role supposedly played by these internal states visà-vis perceptual input, inference, and behavioral output in a normal member of our species. The exact empirical details of this network do not matter here, for we are not undertaking further refinement or systematization of the relevant counterfactuals. Instead, our topic is the ontological analysis of the internal states that occupy the nodes of this complex network and the bearing of that analysis on the truth conditions of the sentences we use to ascribe beliefs and related states. The relevant counterfactuals canonically describe particular belief-, desire-, and intention-states as states of believing, desiring, and intending that such-andsuch. The use of infinitival clauses to describe desires and intentions is not really an exception, for desiring or intending to do A (or to be F) is just having a self-regarding desire or intention that oneself does A (or that oneself is F). By the lights of our commonsense psychology, then, to be in a particular belief-, desire-, or intention-state is to bear the corresponding attitudinal relation— believing, desiring, or intending—to a certain content. Since these contents are potentially common to many different thought-states, we shall call them thoughtcontents. So understood, beliefs, desires and intentions are examples of what philosophers have come to call ‘propositional attitudes’—psychological states of a subject A that one can report (in English) by means of a sentence of the form ‘A Vs that P’ in which ‘V’ is replaced by suitable attitudinal verb (e.g., ‘believe’, ‘hope’, ‘doubt’, ‘wish’, etc.) and ‘P’ is replaced by a sentence conveying a thought-content. Propositional attitudes involving the same attitudinal relation are thus individuated by their thought-contents. (In light of the etymology of ‘propositional attitude’, it is obviously tempting to call these thought-contents ‘propositions’, but this term has come to carry so much philosophical baggage that it is best, at least at the outset, to use a more neutral expression.) For the most part, our discussion will follow the traditional practice of focusing on belief as the paradigm of a propositional attitude. xiii
xiv
Introduction
The propositional attitudes contrast with those ‘direct-object’ attitudes reported by means of so-called intensional transitive verbs like ‘worship’, ‘seek’, ‘depict’, etc., which take as grammatical complements not ‘that’-clauses but noun phrases of various sorts.1 It is a matter of controversy whether such direct-object attitudes can be adequately analyzed in terms of propositional attitudes. Some, like seeking, intuitively invite such analysis; others, like worshipping, seem to resist it. But settling this question is impossible without an adequate prior account of the propositional attitudes themselves. Since our concern here is with latter, we may put the analyzability issue aside and return to the case of the propositional attitudes. By virtue of their distinctive thought-contents, beliefs and other attitudes will possess various quasi-semantical features. Corresponding to particular thoughts in the various modes (belief, desire, intention, etc.) are what might naturally be called their conditions of satisfaction—the conditions which, in light of thought-content, are necessary and sufficient for a given belief to be true, for a given desire to be fulfilled, for a given intention to be realized, etc. However, a propositional attitude’s condition of satisfaction, unlike its thought-content, does not seem sufficient to individuate it. Thus, e.g., the belief that woodchucks are mammals is intuitively distinct from the belief that groundhogs are mammals—some people, being ignorant of matters zoölogical, have the one belief but lack the other—yet these two different beliefs possess the very same truth condition in light of the fact that being a woodchuck is the same property as being a groundhog. (The proper criterion of identity for satisfaction conditions may not be self-evident, but surely any plausible criterion would have to entail that if F and G are the very same kind, then the satisfaction condition being an F is identical to the satisfaction condition being a G!) In sharp contrast to the semantical features of natural languages which they parallel, the conditions of satisfaction that propositional attitudes inherit from their thought-contents are not, at least in the first instance, matters of human convention. Indeed, as David Lewis (1969) has convincingly argued, the very existence of conventions in a human community presupposes the capacity of its members to have certain propositional attitudes (in particular, certain beliefs, preferences, and expectations) with specific satisfaction conditions. Beliefs with certain kinds of thought-content will also pertain to specific individuals, properties, and relations in a manner reminiscent of the direct-object attitudes alluded to above. To believe that London is pretty one must think about London (and perhaps also about the property being pretty). To believe that patience is a virtue one must have in mind patience (and perhaps also the property being a virtue). It is natural to construe this kind of ‘thinking about’ or ‘having in mind’ as a mental analogue of speaker’s reference—let us call it mental reference. Now in connection with overt speech, it is often pointed out that speaker’s reference is not an act performed in isolation but is rather a subsidiary aspect of a total speech act of saying something (in some illocutionary mode) in the course of an utterance. In the same way, the mental analogue of speaker’s reference involved
Introduction
xv
in thinking about specific items should be seen as a subsidiary aspect of the total mental act of thinking something (in the course of some interior performance), i.e., of taking up an attitude towards a thought-content involving the mental referents in question.2 For a thought-content to involve an item in the relevant sense is for that content to determine an appropriate satisfaction condition of which that item is a constituent. The thought-content of the belief that Socrates is wise thus involves Socrates in the sense that it determines a truth condition (roughly, the state-ofaffairs Socrates being wise) of which Socrates is a constituent. So, as we shall understand it, mentally referring to an item is a matter of being in a thought-state with a thought-content that determines a satisfaction condition of which that item is a constituent.3 In the traditional literature, the phrase ‘object of thought’ is sometimes applied both to the thought-content of a given propositional attitude and to any item involved in that thought-content. Unfortunately this usage carries with it the danger of conflating thinking-that with thinking-about (hence with mental reference). It is crucial to distinguish the thought-content of a propositional attitude from any item which that thought-content itself might involve, especially when that thought-content involves another thought-content (as, e.g., in beliefs about the contents of others’ beliefs). Accordingly, let us reserve the phrase ‘object(s) of propositional attitude ψ’ solely for the item(s), if any, to which one mentally refers by virtue of having ψ, and let us employ ‘thought-content of propositional attitude ψ’ for what one thinks by virtue of having ψ, as this would be identified by an appropriate ‘that’clause in a canonical ascription of ψ. Then, e.g., the thought-content of the belief that Chisholm admires Brentano is that Chisholm admires Brentano, whereas its objects are Chisholm, Brentano, and perhaps also the relation admires. In cases where a propositional attitude ψ seems to be about a thought-content C, to the effect that it is F, the thought-content of ψ itself must be distinguished from C. What one thinks by virtue of having ψ (i.e., ψ’s thought-content) is that C is F; what one thinks of or about by virtue of having ψ (i.e., its object, or one of its objects) is C itself. Although commonsense psychology regards beliefs as relations to contents of some sort that determine satisfaction conditions, it does not, qua folk theory, endorse any particular ontological view of thought-contents. Detached from an ontological account of thought-contents and the belief relation, the claim that beliefs are propositional attitudes is noncommittal enough to sound plausible but not substantial enough to bear the weight of answering philosophical questions about belief. For example: Why is the set of a person’s beliefs not closed under logical equivalence, let alone under entailment? What would it mean for two or more people to have the same belief (as opposed to merely similar beliefs)? How can rational people believe things that cannot possibly be true? If water is nothing but H2 O, why doesn’t knowing the triviality that water is water automatically confer the scientific knowledge that water is H2 O? Nothing we have said so far sheds any light on perplexing questions like these. Answering them requires a substantive theory
xvi
Introduction
of the ontology of beliefs qua propositional attitudes. One of the main objectives of this book will be to provide such a theory. Parallel to the foregoing questions about beliefs are equally perplexing questions about the ‘believes that’ constructions that we use in English to ascribe them. Logical operations which are equivalence-preserving in other environments apparently fail to preserve logical equivalence when applied within the ‘that’-clauses of belief reports. The truth condition of ‘A believes that P’ seems curiously detached from the truth condition of ‘P’ in a way that threatens the very possibility of providing a compositional denotational semantics for English within which all instances of the scheme (B) could be secured as theorems: (B) TrueEnglish (‘A believes that P’) ≡ Bel(A, p) (where ‘≡’ is the truth-functional analogue of ‘if and only if’, and ‘Bel’ and ‘p’ respectively name the posited denotata of ‘believes’ and ‘that P’). For there seems little hope of specifying the denotation of ‘that P’, for arbitrary sentential replacement of ‘P’, in terms of what the words in ‘P’ would normally be taken to denote (i.e., what they would be taken to denote if ‘P’ were uttered as a free-standing sentence). If, e.g., one attempts to regard p as some sort of set-theoretic construction from the ordinary denotations of the words in ‘P’, one quickly runs afoul of the fact that sets with the same members are identical, hence that the denotation of ‘that P’ should be unaffected by any replacement of terms within ‘P’ that preserves the ordinary denotation of those terms. Thus, e.g., if the complement clauses ‘that water is water’ and ‘that water is H2 O’ were taken to denote the sequences and respectively, we would have (i) and (ii) as theorems: (i) TrueEnglish (‘Socrates believes that water is water’) ≡ Bel(Socrates, ). (ii) TrueEnglish (‘Socrates believes that water is H2 O’) ≡ Bel(Socrates, ). And, in any event, we should expect to have (iii) as a theorem: (iii) TrueEnglish (‘water = H2 O’) ≡ water = H2 O. Since = if water = H2 O, theorems (i)-(iii) yield the further theorem (iv): (iv) [TrueEnglish (‘Socrates believes that water is water’) & TrueEnglish (‘water = H2 O’)] → TrueEnglish (‘Socrates believes that water is H2 O’). But (iv) appears to be false: most English-speakers (especially when they are reminded that Socrates knew no chemistry) have no trouble at all hearing readings of these sentences on which both ‘water = H2 O’ and ‘Socrates believed that
Introduction
xvii
water is water’ are true but ‘Socrates believed that water is H2 O’ is false. Indeed, the readings on which this is the case are arguably the most natural ones. What is needed is a systematic account of the values of ‘p’ and ‘Bel’ in the truth condition scheme (B) that not only accommodates but actually predicts these intuitions about the truth-values of ‘Socrates believed that water is water’, ‘Socrates believed that water is H2 O’, and correspondingly related belief reports. So the second main objective of this book will be to enlist its proffered ontology of belief and thoughtcontents in the cause of formulating, for a suitable fragment of English in which beliefs are ascribed, a compositional semantics that accepts and explains the logical oddity of belief reports (rather than trying, as is fashionable in some circles4 , to explain it away as a pragmatically induced illusion of some sort). The work that follows comprises four parts. Part I (Chapters 1-2) is devoted to background matters, attempting (in Chapter 1) to sort out the complicated terminology that attends discussion of the propositional attitudes and proceeding (in Chapter 2) to sketch, and to evaluate against certain proposed ontological and semantical adequacy conditions, the relevant proposals of three philosophers— Gottlob Frege, Bertrand Russell, and Roderick Chisholm—whose theories, though ultimately failing to meet various of those conditions, nonetheless provide important insights that our own account will incorporate. Part II (Chapters 3-5) presents the core of our ontological account, beginning (in Chapter 3) with an explanation of how Russell’s infamous ‘multiple relation’ theory of judgment (MRTJ) might be repaired with the aid of the language of thought hypothesis and a certain interpretation of Russell’s obscure notion of a ‘logical form’. Enlisting (in Chapter 4) a modified version of Edward Zalta’s intensional logic for abstract objects (Zalta 1988), the ingredients used to rescue MRTJ are employed in the construction of a simplified version an axiomatic theory TC of thought-contents and the belief relation, and TC is shown to meet most of the ontological adequacy conditions of Chapter 2. Chapter 5 then details the additions to TC needed for it to apply to beliefs of arbitrary complexity—in particular to beliefs about beliefs—and for it to satisfy the remaining ontological adequacy conditions. The Appendix to Chapter 5 presents the fully formalized version of TC thus supplemented. Part III (Chapters 6-8) addresses the semantics of belief reports. Chapter 6 begins with the construction of a finitely axiomatized TC-based compositional semantics STC for a fragment of regimented English containing the requisite vocabulary for belief reports and concludes with an indication of what a semantics for one’s own language of thought might look like from the vantage point of TC. Chapter 7 argues that STC meets all of the semantical adequacy conditions posed in Chapter 2. And Chapter 8 answers various objections directed either against STC in particular or against theories of the general category to which it belongs. Finally, by way of rear-guard action, Part IV (Chapters 9-10) undertakes the defense of a certain view about the object-dependence of thoughtcontents that was built into TC at the outset, surveying (in Chapter 9) the arguments for that view and attempting (in Chapter 10) to rebut some rival accounts of the data.
xviii
Introduction
NOTES 1 Three features are usually cited as individually sufficient conditions for a transitive verb ‘V’ to
qualify as a so-called intensional transitive: (i) the principle of the Substitutivity of Identity appears to fail when applied to the complement of ‘V’ or to other terms occurring therein; (ii) certain quantifier phrases in the complement of ‘V’ admit of a special ‘narrow-scope’ reading; (iii) existential commitments normally associated with terms are cancelled with those terms occur as or within the complement of ‘V’. Thus, e.g., ‘Tom was expecting Mark Twain’ and ‘Tom was expecting Sam Clemens’ might fail of equivalence despite the truth of ‘Mark Twain = Sam Clemens’; ‘Mary seeks a mate’ may be true even though there is no particular mate she seeks; and the truth of ‘Homer worshipped Zeus’ is compatible with the non-existence of Zeus. 2 In tandem with mental reference there is presumably mental predication of various properties and relations. Depending on one’s account of the act of mental predication, it may involve mental reference to these predicated properties and relations in the course of predicating them—e.g., thinking that Socrates is wise may involve mental reference both to Socrates and wisdom in the course of mentally predicating the latter of the former. 3 If we were discussing the direct-object attitudes associated with intensional transitives, we might need to broaden this account of mental reference. However, the present account can apply to the object-oriented attitudes even if they are not reducible to propositional attitudes—so long, that is, as possession of one of the former entails possession of certain of the latter. Thus, e.g., if X worships Y, then surely X must have certain beliefs putatively ‘about Y’—that Y exists, that Y is worthy of worship, etc. If the thought-content of a belief that Y is F determines a satisfaction condition of which Y is a constituent, then X will count as mentally referring to Y by dint of worshipping Y. Of course, where Y does not exist (e.g., where X is worshipping Zeus) then it is an open question whether and how the belief that Y is F could determine a satisfaction condition of which Y is a constituent (unless, that is, we are prepared not only to countenance a being-existence distinction but also to count Y as a non-existent being). (Cf. Chapter 1, Sections 1.1-1.3.) 4 This strategy was first recommended in Boër and Lycan (1980) for dealing with the peculiarities of self-regarding belief reports but later renounced in Boër and Lycan (1986). Similar strategies have subsequently been adopted by neo-Russellians like Nathan Salmon (1986), Mark Richard (1987), and Scott Soames (1987a, 1987b, 2002). Interestingly, Richard too has recanted in (1990) and remains unrepentant.
PART I
PRELIMINARIES
CHAPTER 1
TERMS OF THE ART
Every philosophical discipline and sub-discipline has its proprietary jargon. The study of the propositional attitudes and the language of attitude-ascription is no exception. This Chapter, which is intended mainly for the reader who is unfamiliar with the argot of the attitudes, introduces the salient technical vocabulary and, where its usage is unclear, specifies the way it will be used in the present work.
1.1
SOME TYPES OF INTENTIONALITY
By dint of possessing satisfaction conditions, belief-states and other propositional attitudes are prime examples of what philosophers have called intentional states (note the second ‘t’). On the traditional characterization stemming from Brentano (1874), an act or state is deemed intentional if it is essentially ‘aimed at’, ‘directed upon’, or ‘about’something. Thus, e.g., a belief that Socrates was wise is essentially about Socrates and being wise—in the sense that it is impossible for a state-token to count as a belief that Socrates was wise unless it is connected to Socrates and wisdom in the relevant way (whatever that is).1 The items at which an intentional state is thus directed are called its intentional objects. Although these metaphors of aiming and directing are richly suggestive, they are not very helpful in giving a characterization of intentionality that is precise enough to be useful. To make matters worse, different philosophers have employed the notion of intentionality in a variety of non-equivalent ways. It will therefore be helpful to distinguish several different things that might be meant by calling a state intentional so as to fix on the one most germane to our discussion. One thing that is sometimes meant by calling a state intentional is just that it is or involves a propositional attitude of some sort—i.e., that being in the state in question entails bearing a certain attitudinal relation to a thought-content. Let us call this the cognitive intentionality of a state. Derivatively, a relation may itself be called cognitively intentional when bearing it to entities of the appropriate sorts constitutes or entails being in a cognitively intentional state. Believing and mentally referring are thus, trivially, cognitively intentional relations. To explain the nature 3
4
Chapter 1
of thought-contents and the belief relation is ipso facto to explain the cognitive intentionality of belief and mental reference. A second, even weaker thing that might be meant by calling a state intentional is that being in it entails being in one or more states having conditions of satisfaction and their concomitant quasi-semantical features. Let us call this the semantical intentionality of a state. Since thought-contents asymmetrically determine conditions of satisfaction, all cognitively intentional states will be semantically intentional. But the converse may not be true. We sometimes are willing to attribute satisfaction conditions to a state but are reluctant to credit it with a full-blown thought-content. For having a particular thought-content is intuitively connected with having specific concepts, whereas possession of satisfaction conditions is not. Thus, e.g., we may be willing to credit a dog with something like the desire that food now be in its dish on the ground that the dog is in a psychological state which has a functional role similar to that of a desire in humans and which would be satisfied by food now being in its dish. But even if we are not averse to the idea that dogs enjoy certain simple concepts or some analogue thereof, we may well be loath to attribute to the dog the specific concepts ‘food’, ‘dish’, ‘belonging to’, ‘I’ and ‘now’ that seem to be connected with the thought-content that food now be in my dish. This is reflected in the fact that it seems more accurate to report the dog’s alleged desires, beliefs, etc. in a noncommittal, relational way rather than a notional way—i.e., to say things like ‘The dog believes, of the food and his dish, that the former is in the latter’ rather than ‘The dog believes that the food is in his dish’. Derivatively, a relation may itself be called semantically intentional when bearing it to entities of the appropriate categories constitutes or entails being in a semantically intentional state. Believing and mentally referring are (again, trivially) semantically as well as cognitively intentional relations. According to some philosophers—most notably, Christopher Peacocke (1992, 1994, 1998, 2001)— certain perceptual states/relations may also be semantically but not cognitively intentional. Whether, in contrast to the conceptually articulated content of the propositional attitudes, there is such non-conceptual content is a highly controversial matter. Fortunately, our project does not require taking a stand on the reality of such non-conceptual content, and so we shall say no more about it here. There are at least two other, metaphysically more exciting-sounding things that philosophers have meant by calling a state intentional. Typically, these involve being a relational state in which the relation in question is independently deemed intentional in virtue of possessing certain peculiar features. As a preliminary to spelling out these features, we need a roster of the various categories of entities to which people might be thought to bear relations in general. For the sake of argument, let us take these to include at least individuals, propositions, states-ofaffairs, universals (properties and relations), and perhaps events (insofar as events are construed as non-individuals). For the present, let us suppose that this list is complete. (If additional categories need to be added, the following remarks can
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obviously be adapted to the expanded list). On this assumption, (P1) will be an ontological principle acceptable to all parties: (P1)
Everything is either an individual, a proposition, a state-of-affairs, an event, a property, or a relation.
Now there is a view of existence, stemming from the pioneering work of Gottlob Frege and Bertrand Russell and receiving its most famous contemporary expression in W. V. O. Quine’s essay ‘On What There Is’ (Quine, 1953), which rejects any existence-being distinction and holds that there are no non-existent beings of any sort. On such a view, what there is = what exists; so the field of every nonempty relation consists solely of existing things. Let us call this view Actualism and its adherents Actualists. Strict Nominalists, who countenance the existence of nothing but concrete individuals, are of course Actualists in our sense; but an Actualist need not be a strict Nominalist. An Actualist who admits the existence of something other than concrete individuals may be called a ‘tolerant’ Actualist. Some tolerant Actualists with Nominalist sympathies (e.g., Quine himself) limit their tolerance to the category of individuals: beyond concrete individuals, they admit the existence only of certain special non-spatiotemporal individuals—sets being their favorite candidate. In contrast, tolerant Actualists without Nominalist scruples (e.g., Plantinga, 1974) are willing to grant the existence of things belonging to other ontological categories, such as properties, relations, and propositions. A tolerant Actualist, whether nominalistically inclined or not, might be struck by the fact that some of the items in his ontological inventory fail to participate in the real world: non-concrete individuals are all causally inert; some states-of-affairs fail to obtain; some properties and relations are not exemplified; and so on. These non-participating entities may seem less robust, more shadowy and insubstantial, than their participating counterparts. In calling certain relations ‘intentional’, then, the tolerant Actualist may merely wish to draw our attention to the fact that these relations are, so speak, participation-independent—i.e., that they are capable of relating us (or other concrete existents) to certain abstract entities regardless of whether the latter participate in the relevant way. More precisely, we may give the following neutral definition: (D1)
X participates in the world =df . If X is an individual then X exists and is located in space-time; if X is a proposition then X exists and is true; if X is a state-of-affairs then X exists and obtains; if X is a property or relation then X exists and is exemplified; and if X is an event, then X exists and X occurs.
For an Actualist, of course, the inclusion of ‘exists’ in the definiens of (D1) is redundant. But a non-Actualist would presumably hold that nonexistent beings do not participate in the world any more than do, say, existing but unexemplified
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properties. Consequently, (D1) has been so formulated as to make the notion useful to Actualists and non-Actualists alike. (If accommodating the possible truth of Cartesian Dualism is a desideratum, the phrase ‘located in space-time’ in (D1) could be understood to include location in time but not in space.) Given the principle (P1) and our definition (D1), the theorem (T1) now follows trivially: (T1) All things that participate in the world are things that exist. The converse of (T1) is, of course, tendentious: our tolerant Actualist rejects it. Now a thing that does not participate in the world is either a non-existent or nonspatiotemporal individual, a non-existent or false proposition, a non-existent or non-obtaining state-of-affairs, a non-existent or unexemplified property or relation, or a non-existent or non-occurring event. So we may give the following, more precise definition of participation-independence as it applies to relations: (D2)
R is a participation-independent relation =df . It is possible for some existing thing to bear R to some being that does not participate in the world.
For example, mental reference might be deemed an intentional relation simply on the ground that one can think about abstract as well as concrete individuals (and/or about unexemplified properties as well as exemplified ones; and/or about non-obtaining states-of-affairs as well as facts; etc.). Although a tolerant Actualist who countenances the existence of relations at all is likely to accept that some are participation-independent, it is important to note that (D2) does not restrict the relata of such relations to existing things. (D2)’s definiens merely requires that an existent might bear such a relation R to a non-participating thing. So from the fact that one bears R to something it does not follow that one bears R to something that participates in the world. If it should turn out that there also are non-existent things, nothing in (D2) prevents one from bearing to nonexistent things a participation-independent relation like mental reference. No one but the most austere Nominalist is likely to balk at the suggestion that there are participation-independent relations in this sense. Indeed, when the belief relation is characterized in one of the traditional ways—e.g., as relating people to statesof-affairs regardless of whether the latter obtain, or to propositions regardless of their truth-value, or to properties regardless of whether they are exemplified—then believing will clearly count as a participation-independent relation. A relation’s being participation-independent, or a state’s being such that occupying it entails bearing a participation-independent relation to something, may thus be taken to constitute the weak metaphysical intentionality of that relation or state. In calling a state or relation ‘intentional’, however, some philosophers have had in mind a stronger kind of metaphysical intentionality. These philosophers
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have held that the twin hallmarks of an intentional relation in this stronger sense are what (following Smith and McIntyre (1982)) may be called ‘existenceindependence’ and ‘concept-dependence’. Unlike the relatively benign notion of participation-independence, however, the notions of existence-independence and concept-dependence are difficult to formulate coherently without certain departures from Actualism and the classical logic it typically espouses. The naïve and natural way of expressing a relation’s existence-independence is to say that it can relate us (or other existents) to various things ‘regardless of whether the latter things exist’. This is sometimes put by saying that such relations can relate us to something without there being any existing thing to which they relate us. Thus, it may be said, a man who seeks the Fountain of Youth or who worships Zeus is surely seeking or worshipping something—for it seems we cannot truly say that he seeks or worships nothing at all—but there is no existing thing such that he is seeking or worshipping it. Seeking and worshipping seem ontologically indifferent to the existence of that towards which they are directed. Taking all this at face value would give us the definition (D3): (D3) R is an existence-independent relation =df . It is possible for some existing thing to bear R to some being that is not an existing being. The applicability of (D3), however, depends on how we interpret the key words ‘some’ and ‘existing’ in its definiens. By the lights of Actualism and classical logic, the ingredient quantifiers in (D3) would be construed objectually and their domain would be identified with the class of existents: to exist is to fall within the range of the quantifiers. But on this interpretation of (D3) there obviously could not be any existence-independent or concept-dependent relations. For it is clearly not possible for an existing thing to bear a relation to something—i.e., to some existing thing—which is not an existing thing! For this reason, philosophers committed to the classical approach are likely express doubts about whether so-called intentional relations are really relations at all. An extreme expression of this doubt might take the form of a proposal to assimilate predicates like ‘seeks the Fountain of Youth’ and ‘worships Zeus’ to such fused idioms as ‘kicked the bucket’, i.e., to treat them as expressions devoid of logical complexity, hence as not really containing an independently significant relational verb and singular term. Concept-dependence, the second traditional hallmark of intentionality in the strong metaphysical sense, is an even more perplexing notion. Let us approach it via the familiar story of Oedipus. Oedipus wanted to marry Jocasta. Unbeknownst to him, however, Jocasta was his mother. But Oedipus, one is inclined to say, certainly never wanted to marry his own mother, as is evidenced by his grisly reaction to discovering that he has done so. So whether he wanted to marry the woman in question seems to depend on who he thought of her as being. In other words, the relation wants to marry appears to be mediated by its subject’s conception of its object’s identity. This is sometimes put by saying that one bears an intentional relation like
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wants to marry to something only under a certain description or representation of that thing. Prima facie, then, it looks as if we should characterize concept-dependence by (CD): (CD)
R is a concept-dependent relation =df . It is possible that, for some objects x and y and properties F and G, x bears R to y qua the thing which is F, but x does not bear R to y qua the thing which is G.
No doubt there is something right about (CD), but it proves difficult to articulate precisely what that something is without making concept-dependence into something paradoxical. In particular, (CD) may suggest that a concept-dependent relation can literally fail to respect the identity of its terms—i.e., that there could be items a, b, c such that b = c and a bears R to b, but a does not bear R to c! Indeed, this would follow logically from (CD) if (CD)’s definiens were crudely symbolized as Possibly (∃x)(∃y)(∃F)(∃G)(y = the F & y = the G & R(x, the F) & ∼R(x, the G)). But accepting this suggestion would be fatal. The very idea of a relation that fails to respect the identity of its terms runs afoul of the following two principles (in which the property and relation quantifiers are to be taken objectually): (P2)
For any objects x and y: if x = y then, for any property F, x has F iff y has F.2
(P3)
Necessarily, for any binary relation R and objects x and y: x bears R to y iff y has the relational property being a thing z such that x bears R to z (symbolized ‘[λz Rxz]’).
(P2), of course, is Leibniz’s Law, also known as the Principle of the Indiscernibility of Identicals. (P3) is simply the principle of property abstraction/concretion that grounds the intuitive truth of a statement like ‘John loves Mary iff Mary has the property being loved by John’. Insofar as one countenances objectual quantification over properties and relations in the first place, both principles seem incontestable (and will be so treated here). But (P2) and (P3) have (T2) as an immediate consequence: (T2)
For any objects x, y, z, and any binary relation R: if y = z and x bears R to y, then x bears R to z.
For if x bears R to y, then by (P3) there is a property [λz Rxz] which is exemplified by y. And if y = z, then by (P2) z must have this property too, whence by (T2) again, it follows that x bears R to z. (This derivation of (T2) does not beg the question by using the standard substitution rule for identity—viz., from formula
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φ and equation α = β to infer φ(α//β). Someone who thought that conceptdependent relations really could fail to respect the identity of their terms would of course reject the substitution rule for identity.) So whatever it may mean to say that a relation R is concept-dependent, it cannot on pain of glaring absurdity mean that R is a counterexample to the theorem (T2). 1.2 THE SUBSTITUTIONAL APPROACH AND ITS PROBLEMS So far we have failed to find a non-paradoxical way of understanding existenceindependence and concept-dependence along classical lines. In this connection, it is often suggested that sentences like ‘Homer worshipped something’, in the only sense in which they are true, do not involve standard objectual quantifiers but employ instead substitutional quantifiers, which can be promiscuously applied to any part of a sentence that falls within the stipulated substitution-class regardless of whether that part is independently referential or not. (Where ‘’ and ‘’ are respectively ‘universal’ and ‘existential’ substitutional quantifiers of a language L and α is a variable of L with stipulated substitution class C of expressions of L: (α)φ is true in L iff φ(β/α) is true for every β ∈ C; and (x)φ is true in L iff φ(β/α) is true for at least one β ∈ C.) Where ‘’ and ‘’ are so understood, and the substitution class for boldfaced variables is taken as the class of ordinary English singular terms, (D3sub ) captures the proposed interpretation of (D3): (D3sub ) R is an existence-independent relation =def . It is possible that (x) (y) (x exists and x bears R to y, but y does not exist). By the lights of (D3sub ), seeking and worshipping are existence-independent relations since, e.g., it is possible (because actually the case) that Homer existed and worshipped Zeus although Zeus does not exist; and it is possible (because actually the case) that Ponce de Leon existed and sought the Fountain of Youth although the Fountain of Youth does not exist. Substitutional quantification also provides a non-toxic way of understanding concept-dependence, for it permits us to formulate something perfectly intelligible that might be meant by saying that a concept-dependent relation is one that can fail to respect the identity of its terms—viz., (D4sub ): (D4sub ) R is a concept-dependent relation =def . It is possible that (x)(y) (z)(y = z & x bears R to y & ∼(x bears R to z)). Thus the scenario described in (1) is certainly possible: (1)
Jocasta = Oedipus’s mother, and Oedipus wants to marry Jocasta, but Oedipus does not want to marry his mother.
But (1) entails (2): (2)
(x)(y)(z)(y = z & x wants to marry y & ∼(x wants to marry z)).
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It follows by (D4sub ) that wanting to marry counts as a concept-dependent relation. Contrasting marrying with wanting to marry, we find that by (D4sub ) the former is not concept-dependent, for (3) is a necessary truth: (3)
(x)(y)(z)((y = z & x marries y) → x marries z).
We could then lay it down that a binary relation R is a metaphysically intentional relation in the strong sense iff R is both an existence-independent relation in the sense of (D3sub ) and concept-dependent relation in the sense of (D4sub ). And we could say that a state s is metaphysically intentional in the strong sense iff there is a binary relation R such that, for any x, x’s being in state s entails (y)(R is a metaphysically intentional relation in the strong sense & x bears R to y). On this approach, the official sufficient condition for strong metaphysical intentionality of a state s would be (4): (4)
(∃R){An agent a’s being in s entails [(w)aRw & Possibly(x)(y)(x exists and xRy, but y does not exist) & Possibly(x)(y)(z) (y = z & xRy & ∼xRz)]}.
The canonical specification of a state s as a belief-state (or as any other propositional attitude for that matter) will automatically yield a value for ‘R’ which shows, by the lights of the suggested substitutional definition, that s exhibits strong metaphysical intentionality. Consider, e.g., the state believing that Zeus exists. Now (5) obviously entails (6): (5)
a is in the state believing that Zeus exists.
(6) a believes that Zeus exists. Then it is easy to see that (7) will be true:3 (7)
(w)(a believes that w exists) & Possibly(x)(y)(x exists and x believes that y exists, but y does not exist) & Possibly(x)(y)(z)(y = z & x believes that y exists & ∼(x believes that z exists)).
Assuming the complex predicate ‘· · · believes that · · · exists’ in (7) expresses a binary relation of some sort, (4) now follows. Despite its undeniable formal attractions, however, there are reasons for suspecting that the substitutional approach is too weak to capture what is traditionally intended by talk of existence-independence and concept-dependence. Although the substitutional reading of Something is such that Homer worshipped it but it does not exist.
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as (y)(Homer worshipped y, but y does not exist) makes the former sentence true, it does so at the cost of undermining the project for which it was enlisted, viz., making sense of the idea that there are or could be genuine relations that are existence-independent. For ‘Homer worshipped Zeus’ will indeed imply ‘Homer worshipped something’ when the latter is read as ‘(y)(Homer worshipped y)’, but it will do so for the same uninteresting reason that the idiom ‘Homer kicked the bucket’will imply ‘Homer kicked something’when this is read as ‘(y)(Homer kicked y)’—a fact which strongly suggests that ‘Homer worshipped Zeus’, like ‘Homer kicked the bucket’, does not assert any real relation between Homer and something else (the ‘something’ in ‘something else’ being a classically interpreted objectual existential quantifier). Now those who maintain that it is possible for an existing thing to bear an intentional relation to some being that does not exist are, of course, logically committed to its being possible that there are things that don’t exist. Moreover, there is no obvious reason to suppose that every non-existent thing would have to have a name. (Indeed, for all we know, the number of non-existent things might be so large as to preclude the possibility of naming all of them.) So those who allow the possibility of there being things that don’t exist might well want to accept (8): (8)
It is possible that some things that don’t exist are nameless.
But on the substitutional approach, (8) would be codified as (9): (9)
It is possible that (y)(y does not exist & y is nameless),
Yet—on the plausible assumption that, for any name α, the claim α is nameless is self-refuting—(9) could not be true! It is also worrisome that, on the substitutional reading, the truth-value of sentences like ‘Homer worshipped something’ will inappropriately depend on contingent facts about what singular referential devices our language happens to contain. For consider English∗ , which is just English minus all singular terms other than ‘Homer’. The sentence ‘Homer worshipped something’ (construed as ‘(y)(Homer worshipped y)’) will be false in English∗ , since—assuming that Homer did not worship himself—the open sentence ‘Homer worshipped y’ has no true substitution-instances in English∗ . Now it is normally supposed that correct translation of sentences devoid of context-dependent elements preserves their truthvalue; and since English∗ is just a fragment of English, homophonic translation of the former into the latter is surely in order. But ‘Homer worshipped something’ is true in English, which contains the empty name ‘Zeus’ and hence the presumably true substitution-instance ‘Homer worshipped Zeus’. This divergence in truth-value
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is very puzzling, since the two sentences in question consist of exactly the same three words in exactly the same grammatical pattern, and those words in that pattern intuitively have the same meaning in both English and English∗ since they are correct translations of one another. What this anomaly suggests is that the substitutional reading fails to capture what people are trying to express when, while themselves regarding Homer’s gods as mere mythology, they insist that Homer nonetheless worshipped something. A similar problem arises in connection with concept-dependence. For the second conjunct of (7)—viz., Possibly(x)(y)(x exists and x believes that y exists, but y does not exist) & Possibly(x)(y)(z)(y = z & x believes that y exists & ∼(x believes that z exists)) —is, as we saw, true in English but will be false in English∗ . But again, why should the truth-value of what we are trying to express by ‘R is a concept-dependent relation’ depend on whether we speak English or English∗ ? 1.3
NON-ACTUALISM
Let us try a different, more robust way of understanding existence-independence and concept-dependence. The kind of ontological approach which seems to lie behind most endorsements of existence-independent relations (and which will be adopted here) is one which acknowledges a basic distinction between existence or actuality4 on the one hand and being on the other. For lack of a better name, let us call this view Non-Actualism. A common reaction to the non-Actualist’s proposal of a being-existence distinction is the worry it that entails commitment to various entities of dubious stature—legions of possible fat men crowding every doorway, herds of unicorns prancing through mythological fields, square circles, and who knows what other creatures of darkness dwelling jenseits von Sein und Nichtsein. This an overreaction: the mere claim that there are things that don’t exist (are not actual) carries no commitment to any particular inventory of non-existents. Of course, particular ontological commitments would inevitably attend any attempt to explain a being-existence distinction, since the assertion of ‘There are non-actual things’ invites the question ‘Such as. . .?’. So, before attempting a non-Actualist gloss on existence-independence and concept-dependence, it will be worthwhile digressing for a moment to discuss at least one possible metaphysical basis for a being-existence distinction that does not license ontological profligacy. 1.3.1 The Being-Existence Distinction: A Proposal Where N is an entity of a given type, let us say that a property EN of things of that type is an individual essence of N just in case (i) EN is exemplifiable (i.e., possibly,
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something has EN ) and (ii) necessarily, a thing exemplifies EN just in case it is identical with N. If there is such a property as being N (traditionally called the haecceity of N), then it would trivially be an individual essence of N. But not all individual essences need be haecceities. If, e.g., there are such things as numbers, then the number 2 presumably has the individual essence being an even prime, which is not an haecceity but rather a purely qualitative property. Now familiar individuals, properties and relations seem to have ‘identities’ in the sense that there is something about them that makes them particular things they are. This at least suggests that we might connect existence/actuality with having an identity by taking the principle (E!) as axiomatic: (E!) A being is an existent/actual being iff some individual essence of it is exemplified. Accordingly, something is a non-existent/non-actual being iff no individual essence of it is exemplified. This leaves open, however, two ways that a being N might qualify as non-existent/non-actual: N might enjoy an individual essence that is unexemplified, or N might lack an individual essence altogether. So-called merely possible individuals (of which fictional characters are popular examples) would be of the former sort. If, e.g., one thinks that there is an individual essence of Superman—a property ESuperman which is exemplified in some possible world and is such that a thing possesses it in a given world iff that thing is Superman in that world—then one will count Superman as a non-existent thing that nonetheless might have existed, i.e., exists in some possible world other than ours. (It is perhaps worth pointing out in this connection that at least some Actualists—e.g., Plantinga and his followers—are willing to accept individual essences and to treat the unexemplified ones as surrogates for the Possiblist’s merely possible individuals, which they vigorously reject.) On the other hand, one might take the opposing view that fictional entities are essentially fictional in the sense that they could not be real. On such a view nothing, no matter what properties it had, could actually be Superman (or Kryptonite, for that matter): at best it would be an imitation, not the individual that the salient story is about. Looked at in this latter way, the fictional Superman is a being without an individual essence: there simply is no exemplifiable property the instantiation of which is metaphysically necessary and sufficient for identity with Superman. (This fact, of course, need not interfere with our allowing that all beings are self-identical.) Let us say that a being is ordinary (in our proprietary sense) just in case it is possible that it should exist/be actual; and let us say that a being is abstract (in our proprietary sense) just in case it cannot exist/be actual. Given the gloss on existence/actuality provided by the principle (E!), fictional characters viewed in the first way (as mere possibilia) would be ordinary albeit non-existent things; but viewed in the second way (as incapable of being real) they would be abstract individuals. Given (E!) and our definition of an individual essence as a possibly
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exemplified property of a certain sort, it follows that an abstract entity (in our sense), being necessarily non-existent, lacks an individual essence altogether. A fortiori, then, abstract entities in our sense lack haecceities.5 It should be emphasized, however, that this result does not entail repudiation of the vaunted ‘no entity without identity’ principle in the special case of abstract objects: it merely requires that their identity conditions be articulated in a way that does not presuppose that they are identifiable by the properties they exemplify. Trivially, actual individuals will be identifiable by their properties: the principle of the Identity of Indiscernibles will hold for them. (The same, it will be assumed, is true of ordinary individuals in general.) But there will be no guarantee that the Identity of Indiscernibles holds for abstract individuals. Instead, in the formalism of Chapter 4, identity for abstract individuals will be defined in such a way as to leave open the possibility that numerically distinct abstract individuals might exemplify exactly the same properties. Since, as Platonists, we regard the realm of actual properties and relations as a plenum, we shall take it as axiomatic that any property or relation which might exist at all (i.e., which is ordinary) not only does but must exist. Given (E!), this has the result that the Identity of Indiscernibles holds for ordinary properties and relations as well (though, as will be seen in Chapter 4, this is not how we shall officially define their identity). While we are thus committed to the view that there are no ‘merely possible’ properties or relations, we shall remain neutral on the issue of merely possible individuals. The admission of unexemplified individual essences does not commit us to positing non-actual individuals whose essences they are; indeed, Plantinga may be right in holding that the availability of the former makes positing the latter superfluous. A fortiori, there is no commitment to bizarre impossibilia like square circles: no being, ordinary or actual, can be a square circle. (There is, of course, the unexemplifiable ordinary property being a square circle.) The only non-actual individuals our theory requires are certain abstract ones.6 Additionally, and much more important for our purposes, we shall also require a variety of abstract properties. Now if Superman-qua-essentially-fictional-being is an example of an abstract individual, what might be an intuitive example of an abstract property or relation? The properties attributed to fictional beings in their host stories (e.g., being able to leap tall buildings in a single bound and being able to run faster than a speeding bullet) are typically ordinary, hence actual ones, even though these properties and relations may not in fact be exemplified by anything at all. Nevertheless, fictional stories sometimes describe and assign names to essentially fictional properties. In the classic science fiction of Edgar Rice Burroughs, we find descriptions of eightlegged Martian beasts called ‘thoats’. At the beginning of Chapter 3 of Llana of Gathol, Burroughs writes: There are two species of thoat on Mars: the small comparatively docile breed used by the red Martians as saddle animals and, to a lesser extent, as beasts of burden on the farms that border the great irrigation canals; and then there are the huge, vicious, unruly beats that the green warriors use exclusively as steeds
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of war. These creatures tower fully ten feet at the shoulder. They have four legs on either side and a broad, flat tail, larger at the tip than at the root, that they hold straight out behind while running. Their gaping mounts split their heads from their snouts to their long, massive necks. Their bodies, the upper portion of which is a dark slate color and exceedingly smooth and glossy, are entirely devoid of hair. Their bellies are white, and their legs shade gradually from the slate color of their bodies to a vivid yellow at the feet, which are heavily padded and nailless. Thoats constitute an essentially fictional natural kind, and being a thoat is an essentially fictional zoological property. No matter what turned out to be true of a property, nothing could compel us to identify it with being a thoat. For all that, however, there is such a property as being a thoat—though of course nothing does (and perhaps nothing could) exemplify it. It is an abstract property in our sense, not an ordinary property like being a camel. Essentially fictional entities are usually severely underdescribed, but this is not why they lack individual essences. In principle, Burroughs could have invented an extensive biology and evolutionary history for thoats, reaching all the way back to the primordial Martian ooze. Nevertheless, actually discovering on Mars a genuine natural kind K (perhaps a long extinct species) that fits the expanded description would not amount to discovering that Ks are thoats or that thoats once existed on Mars, much less license identifying the property belonging to K with the property being a thoat. (All of this is, of course, compatible with its being predictable that readers of Burroughs’ stories would quickly dub the newly discovered Ks ‘thoats’in Burroughs’honor, thereby initiating a new chain of usage whose adherents might correctly call Ks ‘thoats’ after all.) Assuming that the foregoing has provided some substance to the being-existence distinction, let us return to the question of the role of that distinction in explicating intentionality. 1.3.2 The Non-Actualist Approach to Existence-Independence and Concept-Dependence On the non-Actualist approach to defining existence-independence and conceptdependence, the ingredient quantifiers are again construed objectually but their domain is now taken to be the class of beings, some of which are existents and some of which are not. Being is expressed by the quantifier ‘some’ and its colloquial variants (symbolized by ‘∃’), whereas existence is expressed by the predicates ‘exists’ and ‘is actual’ (symbolized by ‘E!’). Understood as (D3NA ) below, (D3) is then a perfectly intelligible definition of existence-independence which does not prejudge the issue of whether anything falls under it: (D3NA ) R is an existence-independent relation =def . Possibly(∃x)(∃y)(E!(x) & xRy & ∼ E!(y)). By the lights of (D3NA ) and (T1), existence-independence entails, but is of course not entailed by, participation-independence.
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An isomorphic non-Actualist strategy (a version of so-called Possibilism) could be obtained by invoking the apparatus of possible worlds, with the actual world and its contents taken to constitute the genuine existents, the merely possible worlds and their inhabitants regarded as non-existent beings ontologically inferior to existing things, and the domain of the quantifiers comprising all that is possible—i.e., actual or merely possible. A binary relation R would then be deemed existence-independent just in case an actual thing could bear R to some merely possible (i.e., non-actual) thing. Relations of belief and mental reference might well be existence-independent in this modal sense as well, the former potentially relating us to something like merely possible states-of-affairs and the latter to certain non-existent constituents of such states-of-affairs. Given the isomorphism with the strategy that exploits an existence-being distinction, and considering the relative simplicity of latter, we shall not pursue the modal version any further here. Returning to (D3), now officially understood as (D3NA ), it should be clear that most familiar relations, including any which involve a causal or spatial connection between their relata, will fail to be existence-independent. If, e.g., one smells or is six miles from something, then there is some existing thing such that one smells or is six miles from it. On the other hand, if there are any non-existent entities at all, there will automatically be some existence-independent relations (e.g., being discernible from) that every existent bears to every non-existent;7 and there will be others, like having in mind (mental reference), which some existents bear to some of these non-existents. What, then, about concept-dependence? As we saw earlier, we cannot coherently replace the substitutional quantifiers in (D4sub ) by their objectual counterparts. There is, however, a perfectly intelligible property in the neighborhood that a genuine relation might well have. For a natural way of understanding (CD)’s talk of x’s bearing a relation to y qua F-thing is to regard it as involving x’s representations of y. The idea, then, is that a concept-dependent relation R is mediated by representations in the sense that for x to bear R to y, x must be behaviorally attuned to the intrinsic features of some (verbal or non-verbal) representation that in turn is connected with y in the right sort of way. Where y is an object of thought, a representation r’s being connected with y in the right sort of way might consist in r’s being a sort of ‘presentation’ of y (e.g., a current percept or memory-image causally based on y, a public or private name or description that denotes y, etc.). Where y is a thought-content, the proper sort of connection between r and y would presumably consist in r’s ‘expressing’ y—i.e., in r’s being not so much name-like as sentence-like, having a truth or satisfaction condition somehow determined by y. (If there are languages of thought, their singular terms would do the presenting and their formulas the expressing.) We may sum this up in (D5): (D5)
R is a concept-dependent relation =def . For any objects x and y, x’s bearing R to y entails that, for some representation z and some
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behavior-determining relation Q: (a) x bears Q to z; and (b) either (i) z depicts y to x [i.e., z is or contains something which represents y to x], or (ii) z expresses y [i.e., z is a representation with a satisfaction condition that it derives from y]; and (c) for any representation r that depicts or expresses y, whether x bears Q to r depends on r’s having one or more of a certain range of intrinsic features [i.e., there is a set F of intrinsic features of x’s representations such that, for any representation r that expresses or depicts y for x: x bears Q to r iff r exemplifies some feature in F]. The binary relation wants to marry will be concept-dependent according to (D5) if it turns out that a’s wanting to marry b entails a’s bearing to a certain style of representation of b (e.g., a visual impression of b as from a certain angle) a certain behavior-determining relation which a is not thereby guaranteed to bear to any other representation of b which is not of that style (e.g., an auditory impression of b, or a visual impression of b as from a different angle). This is a relatively modest but respectable thing that might be meant by those who say that one bears a concept-dependent relation R to something only under a certain specification. As defined via (D5), concept-dependent relations are in complete compliance with (T2). For precisely this reason, however, it might be thought that (D5) fails to capture what it should. After all, wasn’t the concept-dependence of the binary relation wants to marry supposed to explain how it could be the case that Oedipus wanted to marry Jocasta but did not want to marry his mother? Indeed, doesn’t our avowed allegiance to the principles (P2) and (P3) preclude our defining any possible feature of relations that would explain this? For by (P3) we have (10)
Necessarily, Jocasta has the property being a thing such that Oedipus wants to marry it just in case Oedipus wants to marry Jocasta.
So from (11) we may infer (12): (11)
Oedipus wants to marry Jocasta.
(12)
Jocasta has the property being a thing such that Oedipus wants to marry it.
But (13) is stipulated to be true: (13)
Jocasta = the mother of Oedipus.
So by (P2), we may infer (14): (14) The mother of Oedipus exemplifies the property being a thing such that Oedipus wants to marry it.
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And so by (P3) again we infer (15): (15)
Oedipus wants to marry the mother of Oedipus.
So how could (11) and (13) be true and yet (15) be false? The answer, of course, is that each of (11) and (15) is ambiguous as between a strong, notional reading on which it reports how Oedipus conceives the desired state-of-affairs and a weak, relational reading on which it merely reports what objects are involved in that state-of-affairs, without undertaking any commitment as to how Oedipus conceives anything. On the relational readings of (11) and (15), the inference from (11) and (13) to (15) is valid. This is unsurprising, since on these readings (11) and (15) merely report Oedipus as having a desire, the object of which happens to be his mother Jocasta, to the effect that he (Oedipus) marries her. But on their notional readings, we cannot infer (12) and (14) from (11) and (13). For all that (P3) requires is that the property in question be exemplified by whatever is alluded to by ‘Jocasta’ and ‘the mother of Oedipus’ in (11) and (15) respectively on their notional readings. But, so far at least, it is an open question just what these terms do allude to on those readings. Intuitively, the notional readings somehow involve Oedipus representing the woman in question respectively ‘as Jocasta’ and ‘as his mother’, and so the abstracted property being a thing such that Oedipus wants to marry it may, for all that (P3) says, not be a property of a person but instead be a property of something more exotic, perhaps a person-qua-individual-of-a-certainkind or a person-qua-represented-in-a-certain-way, the ontology of which remains to be determined. Clearly, a theory of belief and its attribution is needed to sort this out. A variety of familiar resources are available for explaining the illusion of noncompliance with (T2). One such ploy lurks just below the surface of remarks about bearing attitudinal relations to things only under a description: it is the idea such relations have hidden parameters, extra argument-places in their logical forms not reflected in their normal verbal expressions. The values of these hidden parameters would be the sorts of representations quantified over in (D5), or perhaps other entities from which these representations could be somehow recovered. Apparent non-compliance with (T2) is then easily explained. For the facts that b = c and that R(a, b, r) need not entail that R(a, c, r ) where r is a representation distinct from r. Insofar as the representation-parameter remains tacit, it will superficially appear that we have a binary relation that violates (T2). A second strategy is to invoke contextual dependence in our talk about R. The relation R itself is not accorded extra argument-places but its verbal expression ‘R’is held to be context-sensitive in such a way that the assertive utterance of ‘b = c and R(a, b)’may be logically compatible with the assertive utterance of ‘∼ R(a, c)’when these utterances occur in suitably different contexts. (e.g., ‘R’ might be analysed as the complex binary predicate ‘[λxy (∃r)Gxry]’, where the domain of the quantifier in question is a contextually restricted set of mediating representations, different
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such restrictions being operative on the occasions when ‘b = c and R(a, b)’ and ‘∼ R(a, c)’are respectively uttered.) Although it appears that (T2) has been violated, in fact it is not the same relation that is being called ‘R’ in the two cases. Yet a third strategy would claim that when (T2) seems to fail, the apparent relata of R are not its real relata. Perhaps, that is, the fact that the term ‘b’ occurs twice in ‘b = c and R(a, b)’ has misled us into supposing that it is functioning exactly the same way in both places, e.g., that its semantic contribution is just the object b. But this supposition is not mandatory. After all, when a name occurs in a sentence both inside and outside direct quotation it is natural to view the latter occurrence as referring to the name’s bearer but the former occurrence as referring to the wordtype of which it is a token. So the semantic contribution made by a term might depend on where it occurs in a sentence, in consequence of which the items which ‘R(a, b)’ and ‘R(a, c)’ claim to be related to a are not the ones of which identity is asserted in ‘b = c’. The claims ‘b = c’, ‘R(a, b)’ and ‘∼ R(a, c)’ might then form a consistent triad. In addition, there is an ambiguity in the preposition ‘about’ that may create the false impression that a relation like having a belief about (or, more generally, thinking about) can fail to respect the identity of its terms. For there is a sense of ‘about’ in which it is true that, e.g., a belief about the Morning Star is not ipso facto a belief about the Evening Star, despite the fact that the Morning Star = the Evening Star. This, however, is presumably the sense of ‘about’ in which ‘A has a belief about (i.e., believes something about) N’ merits a notional paraphrase like ‘For some G, A believes that N is G’. But although it is notorious that (16) together with (17) does not entail (18), this fact has no tendency to show that having a belief about is a relation which does not respect the identity of its terms: (16) The Morning Star = the Evening Star. (17)
For some G, A believes that the Morning Star is G.
(18)
For some G, A believes that the Evening Star is G.
For, given the notional paraphrase, having a belief about is the corresponding abstracted relation [λxy (∃G)(x believes that y is G)], which, as we saw above, cannot automatically be assumed to take an ordinary individual as its second relatum. One may concede that, in the foregoing sense, the belief that the Morning Star is G is distinct from the belief that the Evening Star is G while still insisting that, in another perfectly good sense of ‘about’, these distinct beliefs are both about one and the same thing (Venus) regardless of what we call it. This is presumably the sense in which ‘A has a belief about (i.e., believes something about) N’ merits a weaker, relational paraphrase like ‘For some G, A believes, of N, that it is G’ or ‘For some G, A believes N to be G’. And, of course, (16) together with (19) does
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entail (20): (19)
For some G, A believes, of the Morning Star, that it is G.
(20)
For some G, A believes, of the Evening Star, that it is G.
Assuming, then, that alleged failures of (T2) are merely apparent and can be explained away compatibly with accepting (D5), let us characterize the strong metaphysical intentionality of a relation in terms of its being both existence-independent in the sense of (D3NA ) and concept-dependent in the sense of (D5). And let us say that a state is metaphysically intentional in this strong sense just in case occupying that state entails standing in at least one such relation to some being. As we saw above, it is not especially contentious to regard mental reference as a participation-independent relation, hence as metaphysically intentional in the weak sense. But it is controversial whether mental reference is metaphysically intentional in the strong sense. To be sure, by our ordinary practices of belief reporting, the likes of ‘Some people believe that Atlantis sank into sea’ and ‘Some people believed that Phlogiston is a chemical substance’ are counted as true. But one might shy away from concluding that the truth of these reports implies that the people in question were intentionally related to a certain non-existent continent and a certain non-existent substance (i.e., that they bore a dyadic relation of mental reference to Atlantis and Phlogiston respectively). However, since we have chosen to acknowledge a being-existence distinction, there is no particular reason to balk at regarding mental reference as an existence-independent relation, since by itself this commits us to no particular view about which things belong in its range. (Indeed, in Chapter 4 it will be made clear that our official view involves a commitment to only one special sort of non-actual entity—the so-called A-objects—and that other, more familiar putative non-existents such as mythical beings and fictional characters are to be countenanced only insofar as they are analyzed in terms of A-objects.) Whether the belief relation is similarly existence-independent is not settled merely by acknowledgement of a being-existence distinction. For as yet we have merely spoken of belief as a relation to a ‘thought-content’ but have offered no explanation of what thought-contents are. If thought-contents could be identified with the likes of propositions, states-of-affairs, or ordinary properties, and if in good Platonic fashion such entities were taken to exist regardless of whether they participate in the world, then there would be no reason to regard the belief relation itself as existence-independent even if mental reference were so regarded—unless, that is, we had some ground for thinking that a thought-content, so construed, cannot determine a satisfaction condition in which a non-existent figures. But this is precisely the sort of ground that could only arise from and be assessed within a comprehensive theory of the nature of thought-contents and attitudinal relations to them.
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Is mental reference also concept-dependent? By (D5) it would be sufficient for mental reference to be concept-dependent that x’s mentally referring to (thinking about) y should entail that, for some representation z, some intrinsic feature f of z, and some behavior-determining relation Q: (a) x bears Q to z; (b) z contains something which expresses or depicts y to x; (c) whether x bears Q to a representation that depicts or expresses y depends on that representation’s having one or more of a certain range of intrinsic features. Given our earlier characterization of mental reference to an item—as a matter of being in a thought-state with a thought-content which determines a satisfaction condition of which that item is a constituent—the plausibility of this entailment rests squarely on plausibility of viewing the belief relation as itself concept-dependent. So the prior question is whether belief is a representationally mediated relation to a content (taking ‘representation(al)’ in the widest possible sense). More precisely, the question is whether x’s believing a thought-content y requires that, for some representation z and some behavior-determining relation Q: (a) x bears Q to z; (b) z has a satisfaction condition determined by y; and (c) whether x bears Q to a representation that depicts or expresses y depends on that representation’s having one or more of a certain range of intrinsic features. If the belief relation to a thought-content is thus representationally mediated, then it is natural to expect that the ingredient representation whose satisfaction condition derives from that thought-content will involve something that represents to the believer the various constituents of that satisfaction condition, hence that the believer will count as thinking about (mentally referring to) those very constituents. But whether and how belief is thus mediated is, once again, precisely the kind of question we need a theory of the propositional attitudes to settle. 1.4
INTENSIONALITY AND EXTENSIONALITY
The intentionality of belief-states is reflected in the so-called intensionality (note the ‘s’) of the sentences used to ascribe them. Indeed, widespread adoption of the Quinean practice of semantic ascent has led concern with the latter feature to eclipse concern with the former. It is customary nowadays to define intensional sentences negatively, as non-extensional ones. So we will need a working definition of ‘extensional sentence’. As a preliminary, let us define some ancillary notions. First, we provisionally take the (putative) denoting terms of English to be its proper names, indexicals, demonstratives, and mass terms. (Later, certain additions will be made to this list). Second, we allow English+ to be any expansion of English obtained by adding zero or more new denoting terms and predicates to its lexicon. Third, we understand a reading of an English sentence to be a fully disambiguated version of that sentence, expressed in a regimented version of English+ that permits
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the use of variables and corresponding quantificational idioms like ‘Some thing x is such that · · · x · · · ’. Then a declarative sentence of English+ is deemed extensional on a reading S iff the reading S satisfies all of the following Extensionality Principles: Strong Existential Generalization Principle: For any denoting term D and variable v foreign to S, if S has the form · · · D · · · then from S one may validly infer Some existing thing v is such that · · · v · · ·. Replacement Principle for coextensive predicates: For any n-ary predicate expressions P and Q of English+ (n ≥ 1), if P occurs in S, then from S and For any objects x1 , . . . , xn , either P(x1 , . . . , xn ) and Q(x1 , . . . , xn ), or neither P(x1 , . . . , xn ) nor Q(x1 , . . . , xn ) one may validly infer any sentence that results from replacing one or more occurrences of P in S by Q. Replacement Principle for materially equivalent sentences: For any sentences P and Q of English+ , if P occurs in S, then from S and Either P and Q, or neither P nor Q one may validly infer any sentence that results from replacing one or more occurrences of P in S by Q. Principle of Substitutivity of Identity: For any denoting terms D and E of English+ , if S has the form · · · D · · ·, then from S and an equation of the form D = E [or E = D] one may validly infer any sentence that results from substituting E for one or more occurrences of D in S. The relativization to readings is cumbersome but unavoidable when dealing with natural languages, which are rife with lexical and grammatical ambiguity. It is only relative to a reading of its constituent sentences that a natural language argument can be said to be valid or not. (e.g., the validity of the argument from (21a) to (21b) obviously depends on disambiguating the phrase ‘visiting relatives’: (21)
a. John believes that visiting relatives can be boring. b. John believes a certain activity to be potentially boring.)
The fuss about English+ is necessary to prevent a sentence from counting as extensional by vacuously satisfying the four principles—i.e., where no counterexample to the inferences in question exists simply because there are not enough names or predicates to formulate one. Since the English+ sentences in question may contain various context-dependent items such as indexicals, demonstratives, tensed verbs, etc., it is important to be clear exactly what is meant by saying that an inference involving English+ sentences is valid or not. Particular inferences are sometimes characterized as valid when no inference ‘of the same form’has true premises and a false conclusion. Given that we are not ruling out the possibility that English+ contains names of non-existents and predicates that signify intentional properties or relations, this way of characterizing validity is not open to us. For, superficially at least, the inference from (22a) to
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(22b) has the same form as the inference from (23a) to (23b): (22)
a. John kissed Mary. b. Some existing thing is such that John kissed it.
(23)
a. Erik the Red worshipped Odin. b. Some existing thing is such that Erik the Red worshipped it.
But (23a) is true and (23b) is, we suppose, false; yet we do not for that reason reject the inference from (22a) to (22b) as invalid! Otherwise, we should end by counting every atomic sentence as non-extensional. So we must take a different tack. To begin with, we shall suppose that, in the first instance, it is the readings of sentences that express propositions at contexts, so that talk about the proposition expressed at a context c by an English sentence on such-and-such a reading is just talk about the proposition expressed at c by that reading. We further suppose that an English sentence on a given reading has, as hypothetically uttered in a context c, whatever truth-value and modal status pertains to the proposition expressed in c by that reading. Accordingly, we lay down the following criterion: An inference from English+ sentences S1 , . . . , Sn to the English+ sentence S0 is valid (relative to a specified sequence <S1 , . . . , Sn , S0 > of readings for these sentences) iff: for every context c, the propositions expressed in c by S1 , . . . , Sn jointly entail the proposition expressed in c by S0 (i.e., it is not possible that the former propositions are all true but the latter proposition is false). By this criterion, the inference from (22a) to (22b) above is valid but the inference from (23a) to (23b) is not. With validity thus understood, (22a) is an extensional sentence and (23a) is not. We may then say that an English+ sentence is intensional on a reading S just in case S fails to satisfy at least one of the four Extensionality principles. Every ascription of belief having the canonical form ‘A believes that P’ trivially counts as an intensional sentence on all of its admissible readings, since the Replacement Principle for materially equivalent sentences always fails when applied to the sentence occupying the position of ‘P’. Otherwise, we could not attribute to a person belief in a particular truth (or falsehood) without being committed to attributing to that person belief in every truth (or falsehood). We should further expect the Replacement Principle for coextensive predicates to fail for any predicate in a belief ascription’s ‘that’-clause. This owes to the fact that, for any such predicate, we can always concoct a coextensive predicate containing alien conceptual material and/or logical structure whose addition to the ‘that’-clause threatens to falsify the resulting belief ascription. Consider, e.g., ‘barks’ as it occurs in (24): (24) Tom believes that Fido barks.
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Trivially, ‘x barks’ is coextensive with ‘x barks, and the Axiom of Choice is equivalent to Zorn’s Lemma’, since it is a necessary truth that the Axiom of Choice is equivalent to Zorn’s Lemma. But, absent extra premises about Tom’s mathematical knowledge, it does not appear that from (24) we can validly infer (25): (25) Tom believes that Fido barks and the Axiom of Choice is equivalent to Zorn’s Lemma. Belief ascriptions with ‘that’-clauses containing denoting terms all appear to have legitimate readings (even if these are not always the most natural ones) on which the Principle of Substitutivity of Identity fails for those terms. Given the truth of instances of ‘A believes that · · · D · · · ’ and ‘D = E’, the truth of the corresponding instance ‘A believes that · · · E · · · ’ is not guaranteed. Thus, e.g., on the most natural readings of (26a-c), (26c) cannot be validly inferred from (26a) and (26b): (26)
a. Homer believed that the sea is full of water. b. Water = H2 O. c. Homer believed that the sea is full of H2 O.
For the author of the Odyssey presumably knew no chemistry. Similarly, on the most natural readings of (27a-c), (27c) cannot be validly inferred from (27a) and (27b): (27)
a. No rational person believes that Stalingrad = Stalingrad. b. Stalingrad = Volgagrad. c. No rational person believes that Stalingrad = Volgagrad.
Mere rationality, alas, does not confer substantive geographical knowledge. Admittedly, the interpretation of a belief ascription that first comes to mind is sometimes not one on which it obviously violates the Substitutivity Principle. Thus, e.g., it may not be at all obvious that (28c) fails to follow from (28a) and (28b) when (as the pictorial annotation ‘[ Venus]’ is meant to capture) these are thought of as sequentially uttered by someone who publicly ostends Venus in connection with both tokens of the italicized demonstrative: (28)
a. Tom believes that Venus is a planet. b. That [ Venus] = Venus c. Tom believes that that [ Venus] is a planet.
For (28a) is normally heard as implying (29), which, together with (28b), implies (30): (29) Venus is something Tom believes to be a planet. (30)
That [ Venus] is something Tom believes to be a planet.
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And it is normally hard to hear much difference between (30) and (28c). Even here, however, one can get the opposite effect by dint of supplying a suitable (if fanciful) background story. Suppose that Tom has observed Venus and other extraterrestrial planets only at night and that he loudly insists that no extraterrestrial planet is observable during daylight hours. If we now imagine the time of utterance to be shortly after daybreak and the ostension to rely on Venus being seen against the morning sky, it is much easier to hear (28a) and (28b) in such a way that that (28c) does not follow from them. After all, if we were to produce Tom and to ask him, while pointing to Venus, ‘Do you believe that that is a planet?’ (or the equivalent in his language if he does not speak English), he would presumably answer in the negative given his avowed view that other planets can only be seen at night. And there is a reading of (28c) to which this would matter, viz., one on which (28c), unlike (29), would intuitively ascribe to Tom a certain visually demonstrative way of thinking of Venus. This dependence of our ability and inclination to hear a certain reading on background stories is not confined to belief reports employing demonstrative vocabulary. There are further cases like (31), in which one’s inclination to hear a reading on which (31a) and (31b) imply (31c) varies with different assumptions about how the subject arrived at his belief: (31)
a. Igor believes that the cleverest spy is the most successful spy. b. Natasha is (=) the cleverest spy. c. Igor believes that Natasha is the most successful spy.
Suppose we are told that Igor has never had any contact with Natasha but has deduced that the cleverest spy must be the most successful spy from propositions which he believes on general (e.g., statistical) grounds alone: viz., that there is a spy cleverer than any other, that there is a spy more successful than any other, and that no one could be maximally clever at spying without being maximally successful at it. Then we would most likely hear (31a) as ascribing a merely ‘general’ belief to Igor, and our acceptance of (31a) and (31b) would not be likely to induce us to accept (31c). On the other hand, if we are told that Igor formed his belief that the cleverest spy is the most successful spy as a direct result of being introduced to Natasha by name at her KGB retirement celebration and hearing her honored as the world’s cleverest and most successful spy, then it is natural to hear (31c) as being a consequence of (31a) and (31b). Some belief ascriptions with ‘that’-clauses containing denoting terms have readings on which they obey the Strong Existential Generalization Principle, and some do not. Thus, e.g., both (32a) and (32b) would normally be taken to imply (32c): (32)
a. Galileo believed that Venus is a planet. b. Galileo believed that that [ Venus] is a planet. c. Some existing thing is such that Galileo believed that it is a planet.
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In contrast, consider the case of Tom, a classical scholar who remembers every line of the Odyssey and can recite it word-for-word. The truth of (33a) then seems unassailable, but (33b) seems plainly false: (33)
a. Tom believes that Odysseus escaped from the Cyclops. b. Some existing thing is such that Tom believes that it escaped from the Cyclops.
Whatever ontic status (if any) Odysseus and his fellow fictional characters may enjoy does not include existing. On the Actualist view that everything exists—i.e., that there are no non-existing entities—the word ‘existing’ in ‘Some existing thing is such that. . .’ is of course redundant. On the non-Actualist view adopted here, which concedes that some things do not exist (i.e., that some things are non-existing things), a sentence of the sort ‘Some existing thing is such that · · · it · · · ’ implies but is not implied by a sentence of the corresponding sort ‘Something is such that · · · it · · · ’. For the non-Actualist, there is thus a point to distinguishing the Strong Existential Generalization Principle from the following: Weak Existential Generalization Principle: For any denoting term D and variable v foreign to S, if S has the form · · · D · · ·, then from S one may validly infer Something v is such that · · · v · · ·. Obviously, one way in which a belief report could fail to obey the strong version of the principle is by failing to obey even the weak version. The non-Actualist will not regard this as the typical case but will take the standard case to be one in which the strong but not the weak version fails. Thus, e.g., a non-Actualist who regards fictional characters as non-existent entities in the domain of ‘something’ will take the standard case to be illustrated by the likes of (33a), which fails to imply (33b) but does (by such a non-Actualist’s lights) imply (34): (34) Something [viz., Odysseus] is such that Tom believes that it escaped from the Cyclops. Indeed, it is an open question whether there are any belief reports to which the Weak Existential Generalization Principle (as understood by the non-Actualist) does not apply. It has been suggested (Zalta, 1988) that the story of Igor rehearsed above provides such a case. The story provided a reading on which (31a) and (31b) together failed to imply (31c). That same reading appears to be one on which (31a) fails to imply even (35a), let alone (35b): (35)
a. Something is such that Igor believes that it is the most successful spy.
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b. Some existing thing is such that Igor believes that it is the most successful spy. However, it is controversial whether this failure of (31a) to imply (35a) constitutes a counterexample to the Weak Existential Generalization Principle. For the status of the ingredient definite description ‘the cleverest spy’ as a genuine denoting term in its own right has been open to dispute ever since Russell first presented his Theory of Descriptions. In later chapters we will undertake a commitment to there being one very special sort of non-actual entity. But we are also persuaded by the Russellian view that natural language definite descriptions are not, logically speaking, denoting terms. So we will not count the foregoing example as a counterexample to the Weak Existential Generalization Principle so long as that principle is restricted to English+ . Indeed, if this principle is understood as restricted to ordinary English, and if English definite descriptions are not counted as denoting terms, then the principle seems to have no clear exceptions at all.8 (Alleged counterexamples using vacuous demonstratives run afoul of serious doubts as to whether belief reports whose content-clauses contain such expressions actually say anything that could be literally true or false—on which, cf. Chapter 9.) As propositional attitude ascriptions, then, belief reports are thoroughly intensional: each has a permissible reading on which violates one or more of the four Extensionality Principles. Of course, ascriptions of belief and other propositional attitudes are by no means unique in this respect. Sentences of the form ‘Necessarily, P’ (even where ‘P’ itself is purely extensional) provide familiar, uncontroversial counterexamples to the two Replacement Principles. Whether such modal sentences also provide counterexamples to Substitutivity and Strong Existential Generalization is a matter of controversy, the outcome depending heavily on whether definite descriptions are to be counted as denoting terms and whether names and demonstratives are to be regarded as rigid designators (i.e., as picking out the same thing with respect to every possible world in which that thing exists9 ). Insofar as there is current consensus on such matters, it favors the view that the mere presence of modal operators like ‘necessarily’ and ‘possibly’ does not, by itself, threaten either Substitutivity or Strong Existential Generalization.10 1.5
HYPER-INTENSIONALITY
There are, of course, related principles violated by every belief ascription (on some reading thereof) but not by every modal sentence. Consider, e.g., the modalized versions of the two Replacement principles: Replacement Principle for necessarily coextensive predicates: For any n-ary predicate expressions P and Q of English+ (n ≥ 1), if P occurs in S, then from S and Necessarily, for any objects x1 , . . . , xn , either P(x1 , . . . , xn ) and
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Q(x1 , . . . , xn ), or neither P(x1 , . . . , xn ) nor Q(x1 , . . . , xn ) one may validly infer any sentence that results from replacing one or more occurrences of P in S by Q. Replacement Principle for necessarily equivalent sentences: For any English sentences P and Q, if P occurs in S, then from S and Necessarily, either P and Q, or neither P nor Q one may validly infer any sentence that results from replacing one or more occurrences of P in S by Q. Modal operators are insensitive to the differences between necessarily coextensive predicates and necessarily equivalent sentences, but belief ascriptions are not. The strategy used earlier to show the failure of the Replacement Principle for coextensive predicates already involved necessarily coextensive predicates and so equally shows that the modalized version of the principle fails for belief reports. Moreover, our beliefs are no more closed under logical equivalence than they are under material equivalence. Someone could believe, e.g., that every set has a choice-function without ipso facto believing that every set can be placed in 1-1 correspondence with some ordinal. But the set-theoretic propositions in question (which formulate the Axiom of Choice and the Numeration Theorem respectively) are necessarily equivalent. Finally, let us broaden the Principle of Substitutivity of Identity by extending the class of (putative) denoting terms to include predicate terms and sentences as well, taking predicate terms to denote properties or relations and sentences to denote propositions. Fully spelled out by cases, the broadened Principle of Substitutivity of Identity will then read as follows (where S(E//D) abbreviates the result of substituting E for one or more occurrences of D in S : Principle of Substitutivity of Identity [Broadened Version]: 1. For any proper names, demonstratives, or mass terms D and E of English+ , if S contains D, then from S and an equation of the form D = E [or E = D] one may validly infer S(E//D); and 2. For any n-ary predicate terms F and G of English+ (n ≥ 1), if S contains F, then from S and an equation of the form being x1 , . . . , xn such that F(x1 , . . . , xn ) = being x1 , . . . , xn such that G(x1 , . . . , xn ) [or its converse] one may validly infer S(G//F); and 3. For any sentences P and Q of English+ , if S contains P [i.e., if P is a subformula of S], then from S and an equation of the form the proposition that P = the proposition that Q [or its converse] one may validly infer S(Q//P). (Intuitions about propositional identity tend to be weaker than intuitions about the identity of properties and relations. For expository purposes we provisionally assume that atomic propositions R1 (a1 , . . . , an ) and R2 (b1 , . . . , bn ) are identical iff R1 = R2 and aj = bj for 1 ≤ j ≤ n.)
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The broadened Principle of Substitutivity of Identity would thus license both inferences like (36), in which the locus of substitution is the predicate position, as well as inferences like (37), in which the locus of substitution is the subject position: (36)
Ralph is a lawyer. Being a lawyer = being an attorney. ∴ Ralph is an attorney.
(37)
Celibacy is a virtue. Celibacy = Abstinence from sexual relations. ∴ Abstinence from sexual relations is a virtue.
Since it extends to sentences, the broadened Substitutivity Principle will also license inferences like (38): (38)
It is logically impossible that Lincoln was a lawyer but not a lawyer. The proposition that Lincoln was a lawyer = the proposition that Lincoln was an attorney. ∴ It is logically impossible that that Lincoln was an attorney but not a lawyer.
In contrast, many belief reports violate this broadened version of the Substitutivity Principle on their most natural readings. While (36), (37) and (38) above were valid, the corresponding inferences (39), (40) and (41) below are not valid when the constituent sentences receive their normal interpretations: (39)
No rational person believes that some lawyers are not lawyers. Being a lawyer = being an attorney. ∴ No rational person believes that some lawyers are not attorneys.
(40)
No rational person believes that celibacy is not the same property as celibacy. Celibacy = Abstinence from sexual relations. ∴ No rational person believes that celibacy is not the same property as abstinence from sexual relations.
(41)
No rational person believes that Lincoln was a lawyer but not a lawyer.
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The proposition that Lincoln was a lawyer = the proposition that Lincoln was an attorney. ∴ No rational person believes that Lincoln was an attorney but not a lawyer.
In each of (39)-(41) the premises are plausibly true. But there are certainly imaginable situations in which a perfectly rational but suitably ignorant person might be duped (by lies, misread literature, etc.) into thinking, on the one hand, that lawyers are to attorneys in the American judicial system as barristers are to solicitors in the British system and, on the other hand, that celibacy is a religiously based abstinence from sexual relations. Regarding predicates as denoting terms has the consequence that sentences which fail the broadened version of the Substitutivity Principle also fail the modalized Replacement Principles for predicates and sentences. For predicates denoting the same property are necessarily coextensive, and sentences denoting the same proposition are necessarily equivalent. So if a sentence permits the internal interchange of necessarily coextensive predicates and sentences salva veritate it must similarly permit the interchange of predicates denoting the same property and sentences denoting the same proposition, hence failure to tolerate the latter kind of exchange implies failure to tolerate the former kind. Failing the modalized Replacement Principles for predicates and sentences is not, however, sufficient for failing the broadened Substitutivity Principle. It is possible to conform to the latter principle despite failing the former because, on the one hand, even necessarily coextensive properties might be distinct (as is plausibly the case, e.g., with Triangularity and Trilaterality, or with the properties being a natural number between 1 and 3 and being an even prime number) and, on the other hand, even necessarily equivalent propositions might be distinct (as, e.g., the necessary proposition that 2 is prime is intuitively distinct from the equally necessary, hence necessarily equivalent, proposition that 7 + 5 = 12). Interestingly, failure to conform to the broadened Substitutivity Principle separates belief ascriptions not only from modal sentences (when the latter contain no psychological vocabulary) but also from attributions of ‘direct-object’ intentional states made using certain intensional transitive verbs. Consider, e.g., the intensional transitives ‘exalt’ and ‘depict’ (neither of which is obviously analyzable as a disguised propositional attitude). The inferences (42) and (43) seem perfectly valid:11 (42) Tom exalts celibacy. Celibacy = Abstinence from sexual relations. ∴ Tom exalts abstinence from sexual relations.
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(43) Tom depicted a warlock. Being a warlock = being a male witch. ∴ Tom depicted a male witch.
Where the intentional relation in question is directed at a particular rather than a universal, matters are a bit more complicated. ‘Tom worships the Sun’ and ‘the Sun = the Star around which Earth orbits’ seems to imply ‘Tom worships the Star around which Earth orbits’. But if the putative individual is a non-existent, the status of the relevant equations may not be clear. Do ‘Tom worships Hera’ and ‘Hera = the wife of Zeus’ entail ‘Tom worships the wife of Zeus’? If it is possible for ‘Hera = the wife of Zeus’ to be literally true or false, despite Hera and Zeus being non-existent, intuition seems to favor the validity of the argument. Otherwise, it is not clear what one should say. Also, if the intentional relation in question is not primitive but can be analyzed in terms of propositional attitudes, the substitution inference may fail—but for reasons traceable solely to its involving those attitudes. Something like this probably explains why there are not only readings of the sentences involved on which the inference (44) is valid but also readings of those sentences on which the inference is invalid: (44)
Oedipus lusts after the woman he just met. The woman Oedipus just met = his mother. ∴ Oedipus lusts after his mother.
For ‘A lusts after B’ is plausibly analyzed as involving a propositional attitude ascription like ‘A wants it to be the case that A-self has sexual relations with B’, so the reading of (44) on which it is invalid is just the one giving the narrowest possible scope to the quantifier-phrases ‘the woman he just met’ and ‘the mother of Oedipus’ in the first premise and conclusion respectively. Let us say, then, that a sentence of English is hyper-intensional on a given reading just in case the broadened Substitutivity of Identity Principle fails for it on that reading. Any belief ascription in the canonical ‘A believes that P’ format will have at least one admissible interpretation on which it is hyper-intensional. This is clearly so when ‘P’ contains non-logical vocabulary, and it remains so even in the limiting case in which ‘P’ is a wholly general sentence like ‘Everything is the same as something or other’. For, insofar as we have intuitions about propositional identity, ‘Everything is the same as something or other’and ‘For each thing there are one or more things with which it is identical’ would seem to express the very same proposition. But the behavior of some beginning logic students on symbolization
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quizzes attests to the invalidity of the inference (45): (45)
Even the dullest logic student believes that if everything is numerically the same as something or other, then everything is numerically the same as something or other. The proposition that everything is numerically the same as something or other = the proposition that for each thing there are one or more things with which it is identical. ∴ Even the dullest logic student believes that if everything is numerically the same as something or other, then for each thing there are one or more things with which it is identical.
It is their hyper-intensionality that marks out ascriptions of belief (and other propositional attitudes) as special among intensional sentences, distinguishing them even from intensional transitive constructions (at least to the extent that the latter are not analyzable in terms of propositional attitudes).
1.6
OPACITY AND TRANSPARENCY
The locus of the substitution failures in a sentence of the form ‘A believes that P’ is typically the embedded sentence ‘P’. Of course, by putting in place of ‘A’ a definite description that incorporates propositional attitude ascriptions—e.g., a description of the sort ‘the person who believes that · · · D · · · ’—it is possible to construct examples in which the subject term ‘A’ also resists substitution, but these cases are parasitic on substitution failures in the sentences embedded within those terms. An explanation of hyper-intensionality will need a more discriminating vocabulary to sort these matters out. From Quine (1960) we borrow the ideas of the ‘substitutional transparency/opacity’and ‘quantificational transparency/opacity’of a term position in a sentence (or complex term) on one of its admissible readings. Since natural language definite descriptions are not being treated as denoting terms at all, let alone as complex ones, the ‘positions’ they superficially occupy will not be counted as genuine term positions. But since the class of denoting terms has been expanded to include predicate terms and sentences, complex denoting terms will include the likes of ‘(the property) being F’, ‘(the relation) x bearing R to y’, and ‘(the proposition) that S’, in which the optional parenthetical phrases may be regarded as pleonastic. Where a and b are denoting terms, v is a variable, and a occupies the term position pE in the expression E, let E(b/a[pE ]) be the result of substituting b for a at the position pE and let E(v/a[pE ]) be the result of substituting v for a at the
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position pE . Then, relative to a given reading of a sentence S: The term position pS in S is said to be substitutionally transparent or substitutionally opaque according as the inference from S and b = a to S(b/a[pS ]) is valid or not on that reading of S; and The term position pS in S is said to be quantificationally transparent or quantificationally opaque according as the inference from S to Some existing thing v is such that S(v/a[pS ] [v being foreign to E] is valid or not on that reading of S. Similarly, relative to a given reading of a complex term T : The term position pT in T is said to be substitutionally transparent or substitutionally opaque according as the inference from b = a to T = T (b/a[pT ]) is valid or not on that reading of T ; and The term position pT in T is said to be quantificationally transparent or quantificationally opaque according as the inference from the inference from T = T to Some existing thing v is such that T = T (v/a[pT ])—or to Some existing thing v is such that T (v/a[pT ]) = T —is valid or not on that reading of T [v being foreign to E]. It follows from the definitions above that a sentence is hyper-intensional on a reading just in case, as so interpreted, one or more term positions in it are substitutionally opaque. Derivatively, a particular occurrence of a term T in a sentence or complex term E may be called transparent/opaque in one of these ways when it occupies a term position in E that is correspondingly transparent/opaque. Similarly, a term T may be said to occur transparently/opaquely in a sentence or complex term E in one of these ways when there is at least one occurrence of it in E that is correspondingly transparent/opaque. Substitutional opacity/transparency and quantificational opacity/transparency are not necessarily coextensive phenomena. We saw, e.g., that the position occupied by ‘water’ in ‘Homer believed that the sea is full of water’ is substitutionally opaque. But, intuitively at least, that position is not quantificationally opaque, because ‘Homer believed that the sea is full of water’ seems to imply ‘Some existing thing [viz., water] is such that Homer believed that the sea is full of it’. That the word ‘water’ may not ‘merely’ be referring to water in that sentential context does not preclude its referring to water, an actual substance. Indeed, if natural language definite descriptions are not counted as denoting terms, it seems that clear cases of quantificational opacity will arise only in sentences or complex terms containing proper names like ‘Zeus’ and ‘Phlogiston’ (which, if they name anything at all, presumably name non-actual things). Since the proper treatment of sentences containing so-called empty names is a large and controversial matter in its own
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right, we propose to sidestep it here and to concentrate only on belief ascriptions all of whose constituent terms are presumed to denote real things (individuals, properties, or relations). (Some reasons for doing so are to be found in Chapter 9). So it is substitutional transparency and opacity that will concern us hereafter. Accordingly, unless otherwise indicated, we shall henceforth understand ‘transparent’ and ‘opaque’ as short for ‘substitutionally transparent’ and ‘substitutionally opaque’ respectively. Also, we shall henceforth use ‘Substitutivity Principle’ to mean the broadened Substitutivity Principle, which counts both predicate terms and sentences as denoting terms. 1.7
DE RE / DE DICTO / DE SE
In discussions of ascriptions of propositional attitudes, one frequently encounters the technical expressions ‘de re’ and ‘de dicto’. Unfortunately, it is not always perfectly clear just what this terminology means. So before availing ourselves of it, some definitions are in order. The original home of the ‘de re’ / ‘de dicto’ terminology was the discussion of alethic modality, where necessity or possibility de dicto concerns the modal status of a proposition (dictum), and necessity or possibility de re concerns the modal character of a certain property of an object (res). Thus, e.g., a sentence like (46) The number of planets is necessarily odd. is often said to be ambiguous: taken one way, it (incorrectly) attributes necessity to the proposition The number of planets is odd ; taken another way, it (correctly) attributes to the number of planets (viz., the number 9) the property being necessarily odd. Since the former necessity is de dicto and the latter de re, it is natural to call the two interpretations of (46) its de dicto and de re readings respectively. This way of talking suggests, of course, that the de dicto/de re distinction is fundamentally ontological (a matter of the metaphysics of propositional necessity and essential properties) and only derivatively a linguistic matter. Now as far as superficial grammar goes, saying of the proposition a is F that it is necessary and saying of the object a that it has the property being necessarily F are respectively analogous to saying of the proposition a is F that it is believed by so-and-so and saying of the object a that it has the property being believed by so-and-so to be F. This grammatical analogy has encouraged use of the ‘de re’ / ‘de dicto’ terminology in contemporary discussions of the propositional attitudes as well. Thus, e.g., (47a) is often held to be ambiguous, having one reading on which it is synonymous with (47b) and another on which it is synonymous with (47c): (47)
a. Igor believes that the cleverest spy is a successful spy. b. The proposition the cleverest spy is a successful spy is believed by Igor.
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c. The cleverest spy has the property being believed by Igor to be a successful spy. Taken in the first way, (47a) is said to ascribe a ‘de dicto belief’, and taken in the second way (47a) is said to ascribe a ‘de re belief’. Unfortunately, this talk of ascribing de re or de dicto beliefs can be misleading, owing to an ambiguity in the noun ‘belief’. Sometimes ‘belief’ means belief-state (type or token), as when we say that beliefs causally interact with desires and lead to the formation of certain intentions. But sometimes ‘belief’ means thoughtcontent, as when we say that certain beliefs are true, false, shared by many people, etc. Now when ‘belief’ means thought-content, talk of reporting de re or de dicto beliefs suggests that belief-states reported in these different ways ipso facto have different contents. One who takes a belief-state to involve a relation to a proposition might then be tempted to suppose that the content of a de dicto belief is a wholly general proposition and the content of a de re belief is a singular proposition. Thus, e.g., the two readings of (47a) might be seen as relating Igor to two quite different propositions—perhaps to a general proposition like There is a cleverest spy and she is a successful spy in the case of (47b) and to a special singular proposition like That woman is a successful spy in the case of (47c). On the other hand, if belief-state is meant, then talk of ascribing de re or de dicto beliefs suggests that there are different kinds of believing, hence that the verb ‘believe’ is ambiguous as between relational and notional senses. Such a view may be coupled with the ‘different contents’ view alluded to above: e.g., it might be held that notional believing relates an agent to a proposition whereas relational believing relates an agent to an n-tuple of objects and an n-ary attribute. Of course, both suggestions might ultimately turn out to be correct: perhaps there really are different kinds of belief relations, and perhaps each relates its subject to different sorts of entity. But it would be tendentious in the extreme to saddle use of the ‘de re / de dicto’ idiom with such heavy philosophical baggage in advance of any demonstrated need for it. In the interest of neutrality, then, we shall initially use ‘de re’ and ‘de dicto’ merely to signify ways of reporting attitudes. Where ‘V’ is an attitudinal verb, a report of the form ‘A Vs that P’ is purely de dicto/purely de re iff every term position in the embedded sentence ‘P’ is an opaque/transparent position in ‘A Vs that P’. Of course, there can be mixed attitude reports which are neither purely de dicto nor purely de re—i.e., in which some but not all term positions in the embedded sentence ‘P’ are transparent positions in ‘A Vs that P’. We shall use ‘de re’, unqualified, to cover both the pure de re and the mixed cases. A de re report may be said to be de re with respect to any item denoted by a term occupying a transparent position in that report. An important special case is provided by reports of the form ‘A Vs that (· · · M · · ·)’, where ‘M’ is either the explicitly reflexive construction ‘he himself’ / ‘she herself’ or a bare personal pronoun that is taken in context to be short for such a construction. Self-regarding attitude reports of this form are nowadays called ‘de
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se’. The question arises as to whether, in such a case, the embedded expression ‘M’ is to be regarded as a term, and whether the position it occupies is to count as a term position in ‘(· · · M · · ·)’. While it would be possible to treat such reflexive pronouns as free-standing terms (as Frege apparently did), it will prove technically more useful to regard them as surface reflections of underlying bound variables— assimilating ‘(· · · M · · ·)’ to ‘(· · · x-self · · ·)’—and thus not to count the superficial positions these pronouns occupy as authentic term positions in the sense invoked in our definition of opacity and transparency. Accordingly, the status of a de se report ‘A Vs that (· · · x-self · · ·)’ as purely de dicto, purely de re, or a mixed case will depend solely on the opacity or transparency of any genuine term positions therein that fall within the ‘that’-clause. Now the ability to explain the relevant data about belief reports of the foregoing sorts without proliferating kinds of belief relations or kinds of entities to which they may relate us, while perhaps not strictly an adequacy condition on theories of the propositional attitudes and their ascription, would certainly be a methodological merit of any candidate theory. The theory TC to be constructed in Chapters 4-5 will have this feature. Although by the lights of TC the entities (viz., thoughtcontents) to which the belief relation relates the believer will all be of the same ontological category, there will nonetheless prove to be internal differences among them that generate a derivative, ontological sense in which one could sensibly speak of thought-contents themselves as being de re, de dicto or de se (see Section 4.3.8 of Chapter 4). But until we are in a position to characterize these thought-contents and hence to spell out this derivative sense, we shall use ‘de re’, ‘de dicto’ and ‘de se’ only to signify modes of reporting.12 (Not surprisingly, it will turn out that what is alleged by a belief report which is de re / de dicto / de se in the linguistic sense is, in effect, that the subject bears the unitary belief relation to a thought-content which is de re / de dicto / de se in TC’s special ontological sense.) NOTES 1 This leaves open whether someone who is connected to Socrates and wisdom in the relevant way could have been in the same physical state without being so connected. If intentional states supervene locally on non-intentional individualistic facts about persons, then the answer is negative. If intentional states supervene (not locally but) globally on non-intentional facts about persons and their external environments, then the answer is affirmative. 2 For the sake of brevity, ‘if and only if’ will often be written ‘iff’. 3 The first conjunct of (7) follows from (6). The second conjunct of (7) follows from the truth of such sentences as ‘Homer exists and Homer believes that Zeus exists, but Zeus does not exist’. Finally, the third conjunct of (7) follows from the truth of sentences like ‘Zeus = the purely mythical king of the Greek gods; and Homer believes that Zeus is a god, but Homer does not believe that the purely mythical king of the Greek gods exists’. 4 As we shall use these expressions, ‘exists’ and ‘is actual’ are synonyms. Unfortunately, some philosophers use ‘actual’ in ways that involve a contrast between actual existents and non-actual existents. Frege, an Actualist in our proprietary sense, characterizes actuality (Wirklichkeit) in terms of concreteness and causal involvement, maintaining that there also exist non-actual objects such as
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numbers and senses. David Lewis, whose modal realism makes him an Actualist in our sense, treats ‘actual’ as an indexical like ‘here’ (cf. Lewis, 1986). So for Lewis too there exist non-actual things in the sense that from the standpoint of any given world there exist things not belonging to that world. 5 This result may seem to run afoul of a certain principle of parity—proposed and defended by Gary Rosenkrantz (1993: 13–14)—which maintains that if one thing has an haecceity then everything does. His argument for this principle depends, however, upon the dubious assumption that it is always legitimate to infer from the truth of a sentence of the form ‘(∃x)(x = N)’ that there is a corresponding proposition that something is identical to N, hence a corresponding property (haecceity) being identical to N. But in Chapters 4 and 5 we adopt for the articulation of our theory a formal system (derived from Zalta 1988) within which (a) there are two basic kinds of predications—familiar exemplification predications and special ‘encoding’ predications—; (b) ‘=’ is defined via certain encoding predications; and (c) sentences containing encoding predications or expressions which are defined in terms of them do not generate additional properties, relations or propositions. (Indeed, in this formalism one cannot legitimately form λ-expressions that would purport to denote such items: e.g., both ‘[λx x = N]’ and ‘[λ (∃x)(x = N)]’ are ill-formed. Only for identity of ordinary objects (symbolized ‘=E ’), which is subject to the Identity of Indiscernibles, are we allowed to form property-designators like ‘[λx x =E N]’ and proposition-designators like ‘[λ (∃x)(x =E N)]’. Of course, Rosenkrantz’s principle of parity holds trivially for any ordinary object o, since [λx x =E o] will be its haecceity. 6 The theory of abstract objects presented in Zalta (1988) allows that an abstract individual might encode any first-order properties whatever, even contradictory ones like being square and being circular—though of course no object could simultaneously exemplify them. The abstract individual which encodes just these two properties might be pressed into service for the analysis of discourse and reasoning about ‘the square circle’. 7 From a non-Actualist perspective, any existent being, x, is ipso facto discernible from any nonexistent being, y, because x will always exemplify a property (viz., existing/being actual) that y does not. If a type theory is imposed, then for each logical type t there will be a discernibility relation [λxt yt (∃F )(Fx & ∼ Fy)] for items of that type. So every existent of a given type would bear that relation to every non-existent of that type. 8 Our ultimate theory of thought-contents and the belief relation (Chapters 4-5) will be articulated in an intensional formal language which, for purely technical purposes, contains certain (rigidified) definite descriptions as singular terms subject to a Free Logic. Some of these descriptive terms will be axiomatically guaranteed to denote certain non-actual entities; the remaining, ‘ordinary’ descriptions carry no denotational warranty. Consequently, the analogue of the Weak Existential Generalization Principle will not hold for sentences of that language that contain any ordinary definite descriptions, but will hold for all other sentences of our formalism. 9 This informal account of rigidity leaves open the question of what, if anything, a rigid designator of an object x designates at worlds in which x does not exist. Following Salmon (1981), we might call a rigid designator of x persistently rigid if it designates nothing at all with respect to worlds in which x does not exist; and we might call a rigid designator of x obstinately rigid if it continues to designate x even in worlds in which x does not exist. Recanati (1993) reminds us that Kripke’s notion of a rigid designator should not be confused with the richer ‘Millean’ notion of a directly referential term, since the latter involves the idea of a rigid designator lacking any connotation that determines what it designates at a given world. 10 Thus, e.g., if officially recognized denoting terms like proper names are treated as rigid designators, then there is no way in which sentences like ‘Necessarily, if Mark Twain existed, then he was Mark Twain’ and ‘Mark Twain = Sam Clemens’ could both be true without ‘Necessarily, if Mark Twain existed, then he was Sam Clemens’ also being true. 11 Since there are no witches, what is presumably at issue in (43) is that ‘narrow-scope’ or ‘nonspecific’ reading of its quantifier phrase complement that is peculiar to intensional transitives.
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12 Occasionally, in discussing an author (e.g., Roderick Chisholm) who uses ‘de re’, ‘de dicto’, and
‘de se’ as modifiers of ‘belief’ and ‘believes’, we shall lapse into similar usage on stylistic grounds. Even so, remarks like ‘A believes de dicto that P’ or ‘A has the de dicto belief that P’ are still to be understood as short for the more cumbersome ‘ “A believes that P” is true on its de dicto reading’ or ‘A has the belief reported de dicto by “A believes that P” ’.
CHAPTER 2
ADEQUACY CONDITIONS AND FAILED THEORIES
As a prelude to the technicalities, the present Chapter formulates some major adequacy conditions on the project at hand, sketches certain historically influential theories of belief—those of Gottlob Frege, Bertrand Russell, and Roderick Chisholm—and shows how they fail to satisfy various of these requirements. In later Chapters, useful elements of these failed theories will be incorporated into our own account in a way that ensures that the resulting view meets all the relevant adequacy conditions. 2.1
SOME GENERAL ADEQUACY CONDITIONS
The proposed conditions are of two sorts: metaphysical constraints on any account of the nature of belief and semantical constraints on any account of the truth conditions of belief ascriptions. To begin with, a candidate theory B of the nature of belief is adequate only if B satisfies at least the following metaphysical requirements (I)-(VII): I. B should provide an ontological assay of belief-states that grounds their intentionality (in all four of the senses distinguished in the previous chapter). In brief, B must provide an account of what thought-contents are, how they figure in states of belief, how they determine conditions of satisfaction for those states, how these conditions of satisfaction may have various items as constituents, and how states of belief, as relations to thought-contents, involve relations that are both existence- (hence participation-) independent and concept-dependent. II. B must permit generalization in some natural way to propositional attitudes other than belief. That is, B should suggest what is common to beliefs, intentions, desires, and the like qua contentful psychological attitudes. (Though perhaps not a strict adequacy condition, forging a link between propositional attitude reports and indirect speech reports would certainly be a nice-making feature in view of the many obvious parallels between the logical behavior of ‘believes that’ and ‘says that’ constructions.) 39
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III. With the possible exception of quotation names, constructions employed by B must neither overtly nor covertly evince substitutional opacity: B should not exploit the very features it is trying to explain (or explain away). Whether or not an exception must be made for standard quotation names depends on whether such a name q of an expression e is counted as containing a genuine occurrence of e, or is instead regarded as a semantically simple (albeit suggestively shaped) name of e. To avoid the need for special dispensation, we shall officially treat quotation names in the latter way—as semantically unstructured—hence will regard the apparent occurrence of ‘Cicero’ in ‘Cicero’ as spurious, like the specious occurrence of ‘can’ in ‘canary’.1 IV. B must usefully connect with the body of issues about the mechanics of believing. How does one get related to a thought-content by the belief relation? How can being so related to such an entity have any causal-explanatory power anent one’s behavior? Insofar as these and similar questions are left dangling, we lack a psychologically plausible picture of what beliefs are. V. B must not invoke unusual entities—complexes, senses, propositions, or whatever—unless it provides both existence-conditions and identityconditions for them. This is an ontological requirement and must be sharply distinguished from the demand for epistemic ‘criteria’ of existence and identity. To specify what it is for things of a certain putative kind to exist or to be identical with one another need not be to specify how one could tell (i.e., come to know) whether they exist or are identical. VI. B must provide an account of thought-contents on which they are potentially public. In other words, B must allow that different people can take the same or different attitudes towards the very same thought-content. In connection with the semantics of belief reports, B must thus provide for the possible truth of reports of the forms ‘Everybody believes that S’, ‘Many people believe that S’, ‘There is something that everyone believes’, etc. (This is closely connected with the generalization requirement mentioned above, for we would like to be able to handle locutions like ‘Fred said something that everyone believes’ and ‘Bob doesn’t believe anything unless he wants it to be true’ as straightforward cases of quantification over thought-contents.) VII. If B analyses believing that P in terms of its being the case that Q, then this analysis, when applied to nested beliefs, should not succumb to the Paradox of Analysis by entailing that to believe that X believes that P = to believe that Q. Otherwise, any account of the belief that P which, like Fregean theories and many of their rivals, invokes items not overtly mentioned in ‘P’—e.g., senses, mental representations, possible worlds, causal chains, etc.—will be doomed to failure. For one could presumably believe that X believes that P without thereby believing (indeed, while explicitly disbelieving) that X is related to any such additional foreign items (cf. Forbes (1993)).
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Furthermore, any semantics S for belief ascriptions will itself be adequate only if S satisfies the semantical requirements (VIII)-(XI): VIII. S must systematically sort out the different truth conditions attaching to the various possible pure and mixed de re and de dicto readings of (non-iterated) belief ascriptions in a way that captures the logical relations between these various readings. As an example of the effect of this variety of readings, consider the arguments (1)-(2): (1)
a. Fred believes that Stalin was a tyrant. b. Stalin = Iosif Dzhugashvili. ∴ c. Fred believes that Iosif Dzhugashvili was a tyrant.
(2)
a. Fred believes that Stalin was a tyrant. b. Being a tyrant = being a despot. ∴ c. Fred believes that Stalin was a despot.
It appears that any combination of verdicts about the validity or invalidity of (1)-(2) is such that at least one reading of the first premise and conclusion of each will support it. S must accommodate this appearance, either (as we shall) by accepting it as veridical and explaining why things are as they seem, or by rejecting it as delusory and explaining how so many people have been misled into thinking that such a variety of readings is semantically possible. IX. S must capture what is distinctive about so-called de se belief reports and explain their relation to corresponding de re and de dicto belief reports. Consider, e.g., (3) and (4): (3)
John believes that he himself is in danger.
(4)
John believes that John is in danger.
Why does (3) seem logically stronger than (4) when (4) is taken de re with respect to the embedded name ‘John’ but logically independent of (4) when the latter is taken purely de dicto? And what is it about the greater strength of (3) that allows (3) but not (4) to explain certain behavior on John’s part in special situations? (E.g., (3), but not (4), seems to explain why John, suffering from amnesia and hence ignorant of his own identity, curls up in a ball at the sight of a charging grizzly bear). A closely related issue concerns the influence of context on the relative interpretation of belief reports of the form ‘I believe that I am F’ and those of the form ‘N believes that I am F’ where ‘N’ is a term other than ‘I’. Consider, e.g., the following scenario: Bob [addressing Ted] first says: ‘I believe that I am overweight.’ Bob [addressing Ted] then says: ‘You believe that I am overweight.’
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It is natural to give the first sentence Bob utters a de se reading and to treat the second as a de dicto ascription to Ted of a belief which has the same truth condition as the belief Bob avows (viz., Bob’s being overweight) but a different thought-content. On this interpretation, Bob avows in his first utterance the belief that he-himself is overweight, but in his second utterance he ascribes to Ted the different belief that he [Bob-as-contextually-identified] is overweight. So construed, the ‘I’ in the contentclause of the latter ascription occurs opaquely and is not replaceable salva vertitate by just any term referring to Bob. (Crudely put, it might be contextually required that Ted think of Bob indexically as ‘you’or ‘the man addressing me’or some such.) Yet it is also possible to hear both sentences as de dicto reports of beliefs with the same thought-content, viz., that he [Bob-as-contextually-identified] is overweight. This would be natural, e.g., in a context in which Bob and Ted are discussing how Bob looks in certain childhood photographs. Correlatively, if Bob and Ted each utter ‘I believe that I am overweight’, there is a clear sense in which the beliefs they express have the same content despite being about different people: viz., each man expresses the belief that he-himself is overweight. In this case, the second occurrence of ‘I’ in the sentence they utter could without loss of meaning be replaced by ‘I-myself’, making it clear that each man is avowing a de se belief. But there is also a de dicto reading of their two utterances on which the beliefs they express differ in content in a way not reducible to the mere fact that they are about different people, a reading on which Bob is avowing the belief that he [Bob-as-contextually-identified] is overweight, but on which Ted’s utterance avows the belief that he [Ted-as-contextually-identified] is overweight—as, e.g., in a context in which Bob and Ted are comparing childhood photographs of each other, or standing side by side in front of a mirror at their health club. S must be able to provide thought-contents that support all these distinctions. X. S must extend in a natural way to iterated belief ascriptions, i.e., to attributions of nested beliefs of the sort reported by (5): (5)
Mortimer believes that Natasha believes that the earth is flat.
In particular, if S takes opacity as a semantic datum, it should allow that reports of beliefs about beliefs have the full range of purely de dicto, purely de re, and mixed interpretations that they intuitively appear to have. XI. Finally, S must solve or dissolve standard conundrums about ascribing beliefs to people who are variously confused, deceived, or mistaken about certain linguistic and/or extra-linguistic facts. Two such puzzles in particular, one owing to Saul Kripke (1979) and the other to David Austin (1990), must be addressed by any semantics for belief reports. Kripke’s puzzle concerns Pierre, a monolingual French-speaker who learns English later in life by the direct immersion method. As a child in France, while still monolingual, Pierre is told stories (in French) about a beautiful city called ‘Londres’
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and comes to assent to ‘Londres est jolie’. Later, he is transported to an ugly slum in London and forced to learn English from scratch, without benefit of interpreters. He learns that ‘London’ is the name of the surrounding city. Being confined to the slum, he naturally comes to assent to ‘London is not pretty’. Of course, he is unaware that the city he calls ‘Londres’ when speaking his native French is the very same city that he calls ‘London’ when speaking his newly acquired English. Now our usual practices of translation and de dicto belief ascription, Kripke maintains, rely upon the following two principles: The Disquotation Principle (‘S’ being schematic for any univocal sentence of English free of indexicals, demonstratives, and the like): If a normal English speaker, on reflection, sincerely assents to ‘S’, then he believes that S. The Translation Principle: For any languages L and L , if a sentence σ of L is true-in-L, then any (correct) translation of σ into L must be true-in-L . The looming paradox Kripke finds here is that these two principles—together with the acceptability of any instance of the Tarski schema ‘ “S” is true ≡ S’—seem to license both the de dicto report ‘Pierre believes that London is pretty’ and the de dicto report ‘Pierre believes that London is not pretty’, hence to warrant attributing to Pierre contradictory beliefs, despite the fact that Pierre may simultaneously be supposed perfectly rational and logically infallible!2 Kripke, who seeks to undermine arguments for opacity that are based on our standard principles of belief ascription, concludes that these principles are somehow flawed and hence that the arguments based on them are untrustworthy. In contrast, any theory of belief and the truth-conditions of belief attributions that accepts opacity as a genuine semantic datum had better dispel the air of paradox created by the story of Pierre. David Austin’s puzzle concerns Smith, a medical student who has learned to focus his eyes independently of one another. As a result, Smith is able to enjoy two independent visual fields under certain circumstances—e.g., when looking at a specimen through a microscope with his left eye and, at the same time, looking at a second specimen though a second microscope with his right eye. Now imagine an experiment in which, instead of two microscopes, two independently adjustable tubes are attached to Smith’s eyes and directed by the experimenter at a uniformly illuminated sheet of red plastic, so that the contents of Smith’s two visual fields are two qualitatively indiscernible red spots. Smith knows all the details of the experimental set-up except one: viz., the particular way in which the experimenter has subsequently oriented the two tubes vis-à-vis the red plastic sheet. In the context of the experiment, Smith uses tokens of ‘this’ to refer to the red spot he sees with his left eye, and he uses tokens of ‘that’ to refer to the red spot he sees with his right eye. Smith acknowledges the spots’ color by saying to himself ‘This is red and that is red’ and acknowledges their existence by saying to himself ‘This = this and
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that = that’. Knowing that he cannot tell how the experimenter has oriented the tubes, Smith then wonders aloud ‘Is this identical to that?’. Unbeknownst to Smith, however, the two tubes are pointed at exactly the same spot on the red plastic sheet. The trouble begins when we ask whether Smith believes what he would express by ‘This = that’. One the one hand, there is reason to think that it is not that case that Smith believes what he would express by ‘This = that’, for otherwise he would have no ground for asking ‘Is this identical to that?’. On the other hand, there is reason to think that Smith does believe what he would express by ‘This = that’. For in the context of Smith’s employment of them, ‘this’ and ‘that’ both refer to the very same spot, and the phenomenal contents of Smith’s two visual fields are ex hypothesi intrinsically indiscernible. So it seems that ‘This = this’ and ‘That = that’ must have for him the very same content. If so, then ‘This = that’ will also have that content, in which case Smith, who presumably believes both what he expressed by saying ‘This = this’ and what he expressed by saying ‘That = that’, must also (paradoxically) believe what he would express by ‘This = that’. Any theory of belief as a dyadic relation to a content-entity (e.g., a Fregean Thought or Russellian proposition) must find a way to avoid this paradox. Only two escape routes are open to such a theory: on the one hand, it can attempt to distinguish Smith’s three beliefs by finding suitably distinct entities to serve as contents of his utterances of ‘This = this’, ‘That = that’, and ‘This = that’; or, on the other hand, it can attempt to identify Smith’s three beliefs by finding grounds to deny that his asking ‘Is this identical to that?’ shows that he fails to believe what he would express by ‘This = that’. In addition to meeting the foregoing general requirements, both B and S should of course be able to answer any further, theory-specific objections that have been raised against accounts of the particular kind they offer. In the case of the sample theories adduced in this chapter, various such theory-specific objections will be discussed. Which if any of them will prove to be relevant to our own view is a matter taken up in Chapters 7-8. Prior to presenting our own account and showing that meets all the general adequacy conditions and can answer relevant theory-specific objections, it would be nice to have demonstrated that no known rival can do likewise. In view of the number of such rivals proposed in the last hundred years and the complexity of the dialogue between their proponents, such a synoptic undertaking would require a lengthy book in its own right and so will not be attempted here. Still, it will be useful to give a brief illustration of how four historically important and radically different lines of attack fall short of satisfying our criteria. The approaches in question fall into two kinds, which may roughly be styled ‘propositional’ and ‘non-propositional’. As representative propositional approaches, we shall examine Frege’s theory of Thoughts and Russell’s early theory of propositional complexes. As representative non-propositional approaches, we shall scrutinize Russell’s later ‘multiple relation’ theory and Roderick Chisholm’s contemporary ‘property attribution’ theory. Beyond their historical interest, there is
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a self-serving reason for choosing these four theories: certain elements of each will be incorporated into our own account, where they will be connected in a way that exploits their usefulness while avoiding the problems they caused in their original environments. 2.2
FREGE’S THEORY OF THOUGHTS
Frege’s theory, as originally formulated in ‘Über Sinn und Bedeutung’ (Frege 1892a) and presented later in ‘Der Gedanke’ (Frege 1918), involves the following ontological and semantic ingredients. On the ontological side, Frege maintains that beyond the mental and physical realms there is a third, abstract realm inhabited by senses and logical entities (the latter including Fregean functions and their value-ranges, of which the two truth-values are special cases). The denizens of this third realm exist independently of anything mental or physical but are in principle capable of being cognitively grasped by minds. Senses are modes of presentation of (putative) entities from the three realms—i.e., ways in which minds might think of (conceive) such things.3 To think about an entity is, inter alia, to grasp a sense that presents it. Among senses, pride of place is given to so-called Thoughts, the modes of presentation of truth-values. Thoughts are, in effect, ways one might take things-as-conceived-in-certain-ways to stand to one another—as when, e.g., one takes an object which one conceives as the F to have a property which one conceives as being G, thereby thinking the Thought that the F is a G. Thoughts are thus complexes that somehow contain modes of presentation of the various things (objects, relations, logical operations, etc.) that they are about. To grasp a Thought is to grasp a way it might be with these things, a piece of (true or false) information. So conceived, Thoughts are not only the contents of the psychological attitudes but also the basic bearers of truth-value and hence the things with whose character and interrelations the science of logic is primarily concerned. On the semantic side, Frege maintains that linguistic expressions of the various basic sorts (singular terms, n-ary predicates, truth-functional connectives, and quantifiers) first become meaningful by being conventionally associated with (coming to express) appropriate senses, where this association may in some cases be speaker-specific rather than community-wide. Once associated with a sense, an expression will refer to or designate whatever its sense presents.4 Expression and presentation are thus primary: the relation of reference/designation is merely their relative product. (Although Frege recognizes the possibility of senses that fail to present anything, he holds that a properly scientific language would disallow such senses for its words.) As regards the nature of senses, Frege is exasperatingly coy. He remarks in passing that the sense of certain singular terms (‘Proper Names’ [Eigennamen] in his idiosyncratic jargon) may be articulated via certain definite descriptions. Many (though not all) commentators have seen these remarks as reflecting the underlying view that the sense of a singular term is or somehow determines a uniqueness property, i.e., a property of the sort being uniquely
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F (or: being the F). For working purposes, let us sidestep the exegetical controversy and assume that this was in fact Frege’s view. Then the referent (if any) of a singular term would then be whatever exemplifies this correlated uniqueness property. The reference of an n-ary predicate is taken to be a function from n-tuples of objects to truth-values. Frege (1892b) calls the reference of a unary predicate a ‘concept’ and uses the term ‘relation’ for the references of all other predicates. The status of the senses of predicates is much less clear. Frege’s official ontology recognizes only two basic categories of entities: functions and objects. Functions are ‘unsaturated’ entities that correlate items; objects are ‘complete’ or ‘saturated’ entities. The correlations that functions generate (their ‘value-ranges’) are objects in their own right (which serve as Frege’s substitute for sets). Frege clearly regards the senses of singular terms as likewise being objects of some sort. But he appears ambivalent about the proper categorization of the senses of predicates. Sometimes a predicate sense would appear to be an object that determines identifying characteristics of a Fregean concept or relation. On other occasions, the sense of an n-ary predicate appears to be an n-ary function—i.e., a function from n-tuples of singular-term senses to Thoughts. In any event, Frege always regards declarative sentences themselves as complex singular terms that (putatively5 ) refer to truthvalues. An atomic sentence like ‘Fido snores’ will have as its sense the Thought that Fido snores—where this Thought somehow contains the senses of both ‘Fido’ and ‘snores’—and will have as its reference whichever truth-value is the truth-value thereof that Fido snores. Since he championed opacity as a semantic datum, Frege needed some explanation of the unusual behavior of propositional attitude ascriptions. His justly famous solution in ‘Über Sinn und Bedeutung’ was to distinguish between the ordinary or ‘direct’ sense and reference of an expression and various oblique or ‘indirect’ senses and references that it acquires as it is embedded under one or more verbs of propositional attitude. To put it another way, the notion of an expression’s sense and reference is to be relativized to its grammatical position in a sentence. In application to a belief report like ‘Ralph believes that Fido snores’, the strategy is simple: relative to their locations in this sentence, ‘Ralph’ and ‘believes’ have their ordinary senses and references; however, when embedded in the ‘that’-clause ‘that Fido snores’, the words ‘Fido’ and ‘snores’ do not have their ordinary referents but take instead their ordinary senses as their new (indirect) referents, while taking on new (indirect) senses that present those ordinary senses. Consequently, the clause ‘that Fido snores’ in the belief report designates the Thought composed of those ordinary senses, viz., the Thought that Fido snores, and the report is true iff Ralph stands in the belief relation to that Thought. The invalidity of the argument form (6) is thus neatly explained: (6)
a. X believes that F(a) b. a = b ∴ c. X believes that F(b).
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For the truth of (6b) ensures only that ‘a’ and ‘b’ have the same ordinary reference, not that their ordinary sense is the same. But if their ordinary senses differ, so will their indirect references in (6a) and (6c), with the result that the terms ‘that F(a)’and ‘that F(b)’ will designate different Thoughts, the former of which X may believe without believing the latter! Moreover, although Frege must reject the principle of Substitutivity of Identity as a formal syntactic inference rule, his solution permits him to maintain a modified semantic Principle of Extensionality: viz., coreferential terms may be replaced salva veritate at any position in a sentence provided their references are the same relative to that position in that sentence. In its original version, Frege’s theory clearly fails to meet most of our general adequacy conditions, though it may prove possible to supplement his view so as to meet at least some of the remaining conditions without sacrificing the basic spirit of his approach. To begin with, it is concerned exclusively with the purely de dicto attitude ascriptions and wholly opaque indirect discourse constructions: as the view stands, it has nothing to say about de re belief reports. Commentators, however, have suggested a variety of plausible remedies for this omission (cf., e.g., Dummett (1973) and Kaplan (1968)). Since a Fregean Thought is supposedly a complex of senses which is somehow isomorphic to the formula of Frege’s Conceptual Notation that canonically expresses it, the interpretation of (7) on which ‘Venus’ occurs transparently, might be accorded a logical form like (8): (7)
Galileo believed that Venus is a planet.
(8)
(∃σ)(Presents(σ, Venus) & Believed (Galileo, [Planet]∧ σ)).
Here the variable ‘σ’ ranges over individual senses, ‘[ ]’ is an operator that forms a name of the sense of whatever expression it encloses, and ‘∧ ’ signifies the appropriate concatenation of senses (so that the complex term ‘[Planet] ∧ σ’ names the relevant atomic Thought). Perhaps Frege could have accommodated de re ascriptions of belief in some such way. But his ability to handle de se belief attributions like (9) is in serious doubt: (9)
Gustav believed that he himself had been wounded.
Frege seems to regard ‘he himself’ as a free-standing term which, in the context of the clause ‘that he himself had been wounded’, designates the allegedly special way in which Gustav alone can identify himself—viz., that self-identifying sense, presenting Gustav but accessible to Gustav alone, which he associates with his own uses of the first-person singular personal pronoun. In other words, Frege appears to propose for (9) an analysis like (10): (10)
(∃σ)(SelfIdentifies(σ, Gustav) & Presents(σ, Gustav) & Believed (Gustav, [Wounded ]∧ σ)).
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This at least has the merit of explaining the obvious logical relationships between (9) and the corresponding de re attribution. But as a general account of de se belief reports, this line is not promising. In the first place, the appeal to essentially private self-identifying senses flagrantly undercuts Frege’s leading idea that Thoughts are in principle shareable. Worse, these essentially private self-identifying senses are even more mysterious than ordinary, sharable senses. For we can at least get a tenuous grip on the notion of an ordinary sense by thinking of it as essentially involving one or more properties of the thing (if any) that it presents, so that presentation itself can be understood in terms of the unique instantiation of those properties. No such route to understanding self-identifying senses is available. Not even an appeal to haecceities will help, for Gustav’s haecceity (if such there be) is just the non-qualitative property being Gustav. But Gustav’s haecceity could just as well be involved in someone else’s sense for the name ‘Gustav’: nothing prevents someone other than Gustav from identifying Gustav via this property. The problem here is of course connected with Frege’s conspicuous failure to provide adequate criteria of existence and identity even for ordinary senses—despite his earlier insistence (in Frege (1884)) that the provision of identity-criteria is an adequacy condition on the introduction of new objects into a theory. Where senses are concerned, Frege’s procedure was instead to mark out a number of theoretical jobs that allegedly must be done by something—e.g., accounting for the possible cognitive difference between equations of the forms ‘a = a’and ‘a = b’, explaining opacity phenomena in attitude reports and indirect speech constructions, providing for the objectivity and communicability of scientific and mathematical information, etc.—and then to characterize senses functionally as the entities that fill these roles. Though it may be useful as a heuristic device, this procedure does not automatically provide a functional definition. For the most it tells us is that each role must be filled by something or other. But without existence- and identity-criteria for senses, we cannot have any assurance that they constitute a determinate kind of entity in the first place, let alone that they uniquely fulfill the functions in question. Indeed, it is widely noted that Frege invokes so many disparate logical, linguistic, and psychological jobs for senses to perform that it is far from obvious that any single kind of entity could accomplish them all. In particular, much grief results from Frege’s tendency to treat senses both as the linguistic meanings of words (at least in an ideal, context-free language) and as constituents of the Thoughts expressed by sentences formed from those words. This invites an unfortunate conflation of linguistic synonymy with expressing the same sense. One result of such conflation is that, appearances to the contrary notwithstanding, there could not be any synonyms even within an idealized version of a natural language, in which all sentences are eternalized, purged of vagueness and ambiguity, and regimented in Frege’s formal notation! In Frege’s semantics, sameness of ordinary or direct sense presumably guarantees sameness of oblique or indirect sense at every level of embedding, so that expressions of, say, idealized
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English with the same sense would be everywhere interchangeable in its sentences salva veritate. But, as Benson Mates (1950) pointed out, any two distinct singular terms ‘a’ and ‘b’ or distinct general terms ‘F’ and ‘G’ seemingly fail to be interchangeable salva veritate in certain multiply embedded environments. Thus, e.g., the inferences from (11a) to (11b) and from (12a) to (12b)—or their counterparts in idealized English—are bound to fail when the ingredient sentences are accorded purely de dicto readings: (11)
a. Nobody can rationally doubt that anyone who believes that a = a thereby believes that a = a. b. Nobody can rationally doubt that anyone who believes that a = a thereby believes that a = b.
(12)
a. Nobody can rationally doubt that anyone who believes that all Fs are Fs thereby believes that all Fs are Fs. b. Nobody can rationally doubt that anyone who believes that all Fs are Fs thereby believes that all Fs are Gs.
So no two singular or general terms even of idealized English could ever have the same sense, and hence they could never be synonyms. Now one might argue on Frege’s behalf that this problem is not a fatal, since ‘sense’ is a technical notion whose job-description does not obviously require the existence in one and the same language of distinct expressions having the same sense. (The italicized qualification is crucial, since Frege clearly does require that the same Thought can be expressed by distinct sentences in different languages.) Be that as it may, however, insofar as synonymy is identified with expressing the same sense, intraliguistic synonymy will be impossible (though interlinguistic synonymy would remain a possibility). Quite apart from any entanglement with the notion of synonymy, Frege says things that threaten his view with outright inconsistency by implying that there are distinct expressions of a given language (in his case, German) that have the same sense. For if this were not possible, it would surely be impossible for distinct sentences of that language to express the same Thought. Yet Frege insists, e.g., that (German) sentences containing distinct indexicals can, if uttered in appropriate contexts, express the same Thought. In English, sentences like ‘My rent is due today’ (uttered by Gustav on a given day) and ‘My rent was due yesterday’ (uttered by Gustav on the following day) serve to illustrate his point.6 Frege also claims that the grammatical shift between active and passive voice constructions does not affect the Thought expressed, so that ‘Brutus stabbed Caesar’ and ‘Caesar was stabbed by Brutus’ can express the same Thought (which is why Frege’s Conceptual Notation symbolizes both in the same way). He even goes so far as to suggest that certain simple syntactic operations that ‘obviously’ preserve logical equivalence—e.g., commutation of conjunctions—also preserve identity of the Thought expressed.
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Needless to say, evaluation of these claims would require knowing a necessary and sufficient condition for two different sentences to express the same Thought. Frege’s own candidate for such a condition is the following (cf. Dummett 1991: 171): (FC)
Sentence S1 expresses the same Thought as sentence S2 iff: it is impossible for a person simultaneously to grasp both the Thought expressed by S1 and the Thought expressed by S2 without immediately recognizing that they must have the same truth-value.
Now (FC) does license Frege’s various claims about identity of Thoughts expressed. But, as Dummett points out, (FC) is seriously defective as a putative sufficient condition and so cannot really vindicate those claims. For one thing, (FC) would license the claim that (13a) and (13b) both express the same Thought: (13)
a. Cato killed Cato. b. Cato committed suicide.
But on Fregean grounds this result would in turn entail the falsehood (14): (14) Whoever believes that Cato killed Cato believes that Cato committed suicide. The problem, of course, is that someone (a child, perhaps) may possess the concept ‘kill’ but lack the more sophisticated concept ‘commit suicide’. Intuitively, the Thoughts expressed by (13a) and (13b), though logically equivalent, have distinct constituents—hence the attractiveness of symbolizing (13a) and (13b) differently as, say, (15a) and (15b) respectively: (15)
a. Killed (Cato, Cato). b. [λx Killed (x, x)](Cato).
An adequate sufficient condition for the identity of Thoughts expressed must take account of the way in which the grammatical differences between sentences like (13a) and (13b) are reflected in differences between the constituents (senses) in the Thoughts they express. But it is unlikely that this can be done in the absence of some defensible theory about the existence- and identity-conditions for Thoughts and other senses as such. One of the most serious shortcomings of Frege’s theory, noted in Kripke (1979) and stressed in Schiffer (1992), concerns its inability to allow for the straightforward truth of de dicto reports of shared beliefs. Consider, e.g., a claim like (16) in the
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mouth of a normal English-speaking utterer u: (16)
Everyone who has seen Paris believes that Paris is beautiful.
It seems entirely plausible to assume that the content-clause ‘that Paris is beautiful’ is semantically univocal. In Fregean semantics, this means that there is a unique Thought —presumably the one u would express by uttering ‘Paris is beautiful’ in isolation—which is designated by ‘that Paris is beautiful’, so that (16) is true in u’s mouth just in case every person who has seen Paris stands in the belief relation to . Fregean Thoughts/sentence-meanings, however, are composed of senses/wordmeanings: there would have to be a particular sense/word-meaning [Paris] and a particular sense/word-meaning [beautiful] of which is uniquely composed. But the senses that compose a Thought are modes of presentation, determinate ways of thinking of certain (putative) objects. So Frege’s semantics appears to have the consequence that (16), as uttered by a normal English-speaker, is true only if all the people who see Paris believe it to be beautiful under [Paris]—i.e., that they all think of Paris under exactly the same mode of presentation (indeed, the very one employed by u)! This, however, is wildly implausible, at least insofar as a mode of presentation is understood to be anything like a way of thinking of an object. Surely the truth of (16) should be compatible with the fact (which Frege himself concedes) that people’s ways of thinking of an object could be diverse and idiosyncratic. The problem of existence- and identity-conditions arises again in connection with iterated belief reports. For Frege’s official view is that there is a hierarchy of indirect senses and references corresponding to the levels of embedding in a nested ‘that’clause. Thus, e.g., his account of the truth condition of (5) [‘Mortimer believes that Natasha believes that the earth is flat’] involves not only the ordinary or direct sense of the sentence ‘Natasha believes that the earth is flat’ but also a mysterious indirect sense of the embedded sentence ‘the earth is flat’ distinct from its direct sense (which is the Thought that the earth is flat). While capable of coherent formal articulation (as, e.g., in Church (1951)), this feature of Frege’s view has struck most readers from Russell onwards as extremely counterintuitive. Our grip on the notion of sense, tenuous as it was for direct senses, gives way completely when we attempt to climb this hierarchy of indirect senses. (Dummett (1973) has argued that this hierarchy is a dispensable feature of Frege’s view, so perhaps iterated belief ascriptions will not pose quite the problem for Frege that they initially seem to.)7 It is generally agreed that Frege’s few brief remarks on context-dependent expressions provide no workable theory of indexicals and demonstratives or of the de dicto belief reports that employ them (cf., e.g., Perry (1977) and Burge (1979)). So it is unclear whether one could provide a ‘Fregean’ solution to Austin’s Two Tubes Puzzle without serious violence to Frege’s original position. Subsequent work by Fregeans on demonstrative thought (e.g., Forbes (1987)) may provide a broadly
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Fregean framework for handling Austin’s problem, but the matter is controversial and we cannot pursue it further in this brief review. It may seem that Frege would be equally unable to cope with Kripke’s puzzle about Pierre. Certainly this is Kripke’s view of the matter: indeed, he takes the puzzle to undercut the usual arguments for the opacity of attitude reports. Here, however, there are some conservative defensive moves that a Fregean sense-theorist might make. In particular, William Taschek (1988) reminds us that the Fregean’s point of attack on so-called Millianism is not the latter’s doctrine of direct reference for proper names—i.e., the doctrine that the semantical function of a proper name is everywhere just that of (rigidly) designating its bearer—but is instead the strong substitution principle that it authorizes, which licenses the interchange of co-designative proper names in all (non-quotational) linguistic environments. For Frege and his followers take the standard intuitions about opacity to show that such substitutions, when made within propositional attitude reports, can differentially effect the cognitive significance (Erkenntniswert) of the sentences involved. To defuse the Fregean attack, the Millean must show that the absurdities alleged to follow from adopting his strong substitution principle can be derived without using any principle that licenses substitutions that can differentially effect the cognitive significance (sense) of the sentences involved. The question is whether Kripke’s story about Pierre really shows this. Taschek (op. cit.) forcefully argues that it does not. For, on the one hand, a Fregean understanding of the Translation Principle (including its homophonic version) requires both that the idiolects of individual speakers be counted as languages too and that strictly correct translation (as opposed to the rough-and-ready paraphrases we often settle for) must preserve cognitive significance. But, on the other hand, Kripke’s use of the Translation Principle does not conform to these requirements: This is evident when—despite the undeniable fact that, for Jones, ‘Cicero’ and ‘Tully’ differ in cognitive significance—Kripke allows that ‘A proposal that “Cicero” and “Tully” are interchangeable amounts to a homophonic “translation” of English into itself in which “Cicero” is mapped into “Tully” and vice versa, while the rest is left fixed’. And it is no less clear that, for Pierre, ‘London’ and ‘Londres’ differ in cognitive significance. (Taschek 1988: 103) The Fregean thus has no reason to be perplexed. For, by his lights, whether we accept ‘Pierre believes that London is pretty’ or ‘Pierre believes that London is not pretty’ in the context of Kripke’s story will depend on whether we regard ‘London’ as being used therein with the same sense that Pierre attaches to his uses of ‘Londres’ or with the same sense that Pierre attaches to his uses of ‘London’. And in the likely event that we are unclear about just what senses Pierre attaches to these names, we will not know which, if any, of these claims to accept. But this, as Taschek rightly observes, is no puzzle. Frege’s account provides no connections to the mechanics of believing, since ‘grasping’ (i.e., entertaining) is left as a primitive relation between two radically
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different sorts of objects: thinkers and Thoughts—the latter being languageindependent abstract objects of some sort that can serve as the senses of sentences. Now while it may be a truism that to think of an object is to think of it in some way or other, there is a serious question about the coherence of Frege’s apparent identification of thinking of an object in a given way with grasping a sense that presents that object. For if that sense is itself just another object that the thinker has in mind, a vicious infinite regress looms: to have that sense in mind would require grasping yet another sense that presents it, and so on ad infinitum. But if not in terms of identity, how we are to understand the relation between grasping a sense of an object and having it in mind? A persistent thought among some admirers of Frege is that augmenting his ontology with the apparatus of possible worlds would solve many of the problems he faced. Certainly some advantages would accrue. Alongside Frege’s purely extensional notion of ‘concepts’ and ‘relations’ (understood respectively as unary and n-ary (n > 1) functions from objects to truth-values) one could then appeal to predicate intensions, understood as functions from possible worlds to Fregean concepts and relations defined over the objects in those worlds. These predicate intensions could then be drafted to play the role of predicate senses. Similarly, the role of singular term senses could played by individual intensions, understood as functions from possible worlds to particular objects in those worlds. A first-order atomic Thought could then be identified with a structured entity (perhaps a finite sequence) whose constituents are an n-ary predicate intension and n individual intensions. Given appropriate intensions for logical operators, Thoughts in general could be identified with suitably structured systems of intensions. Provided that these structured systems are themselves sets of some sort (e.g., nested sequences that mimic the syntactic structure of sentences), our misgivings about existence- and identityconditions for senses might be assuaged, for existence- and identity-conditions for sets are provided by standard set theories. Moreover, logically equivalent Thoughts would not have to be implausibly identified with one another, as they would have to be if Thoughts were directly identified with sets of possible worlds. As sets, the atomic Thoughts and will be distinct so long as f = g or a1 = b1 or . . . or an = bn . Thus, e.g., the Thought that zero is less than one and the Thought that one is greater than zero would be numerically distinct because the corresponding intensions they contain are pairwise distinct. But these two Thoughts are logically equivalent because both are true in every possible world: each is such that, in any possible world W , the pair of values of its ingredient individual intensions at W is mapped onto the True by the value of its ingredient predicate intension at W . So, in principle, someone could stand in the belief relation to the one Thought but not to the other despite their strict equivalence—surely a welcome result. It is unlikely, however, that Frege could in this way meet the demand for property-tracking versus transworld extension-tracking involved in certain de re belief reports. For even in his augmented ontology the nearest analogue to the notion of a property would be that of a unary predicate intension. Yet this
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notion is still inadequate to explain the difference between (17) and (18) taken purely de re: (17)
Gustav believes that the Greek letter ‘’ is a triangle.
(18)
Gustav believes that the Greek letter ‘’ is a trilateral.
When all their term-positions are construed as transparent, each reports Gustav as believing, of ‘’ and a certain property, that the former has the latter. But each involves a different property, which is why (17) and (18) would still be heard as inequivalent despite the fact that the predicate intension of ‘is a triangle’ is the very same set as the predicate intension of ‘is a trilateral’: viz., that function f from possible worlds to Fregean concepts such that f (W ) is that function from objects in W to truth-values which maps an object onto the True if it is a triangle/trilateral, and which maps an object onto the false otherwise. Worse still, such possible-worlds versions of Fregeanism—at least those based on some standard set theory—can easily run afoul of the Axiom of Foundation when attempting to provide for the various mixed readings in iterated belief reports. For this theoretical reason Max Cresswell (1985: Ch. 10) declares that sentences like (19)
Mortimer believes that Natasha believes that the earth is flat.
cannot coherently be given any pure or mixed de re reading on which the second occurrence of ‘believes’ is transparent, because (on his possible-worlds version of Fregeanism) this would require the function which is the intension of ‘believes’ to take itself as argument. This rejection seems ad hoc, indicating a limitation of his semantical framework rather than any anomaly in the data.8 Suppose Mortimer, having been asked for his opinion as to whether Natasha has any position on the Flat Earth Hypothesis, says ‘Uncritical belief is what I take to be her attitude towards that hypothesis’. It is hard not to hear this as warranting precisely the disputed reading of (19). Moreover, there does seem to be a de re reading of (19) on which it implies and is implied by (20): (20)
Mortimer believes that Natasha thinks that the earth is flat.
This needs explaining. 2.3
RUSSELL’S PROPOSITIONAL AND MULTIPLE-RELATION THEORIES
Like Frege, Russell (1903, 1904) began by regarding judgment as a simple binary relation between a judging mind and a judicable content, the latter being a special kind of mind-independent, non-linguistic complex of entities, which he called
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a ‘proposition’. Unlike Frege, however, Russell took the constituents of these complexes to be the real (or—early on—even unreal) individuals, properties, and relations that we normally suppose ourselves to be thinking and talking about, as well as various logical operations and other propositions constructed from these basic ingredients. A Russellian proposition, like a Fregean Thought, mimics the structure of the declarative sentence we use to express it (at least when we are speaking in an Ideal Language) but, unlike a Fregean Thought, is composed not of senses but of the presumed referents of the logical and non-logical words in that sentence. Truth is treated as an unanalysable property: it is simply a brute fact that some propositions do, and others do not, exemplify it. As Russell quickly came to see, the problem of existence- and identity-conditions for these propositions is acute. Given what little he says about them, it is obviously tempting to identify them with set-theoretic constructs of some sort: e.g., the proposition that Bob loves Sue might be identified with the nested sequence <[λxy Loves(x, y)],>. This strategy is undeniably attractive in light of the simple extensional identity-conditions for sets, and for this reason it has been favored by some of Russell’s contemporary followers. But it is not available to Russell himself, for he notoriously denied that there are any such things as sets or classes! (To be an individual in his ontology, a thing must be a potential object of acquaintance—a requirement that rules out sets and classes, since these are normally understood to be abstract individuals.) Yet if a proposition does not unite its elements in the manner of a set, what sort of unity could a proposition have? An attractive place to look for the requisite unity of properties, relations, and individuals is in the ontological category of facts. The fact that Bob loves Sue exists iff Bob loves Sue (i.e., iff the relation [λxy Loves(x, y)] obtains between them); and facts are intuitively identical iff they involve the same individuals, properties, and relations arranged in the same way—though it is no trivial matter to explain just what ‘arranged in the same way’ means. Moreover, Russell firmly believed that there are such things as facts: they are a basic category in his ontology. The obvious problem, of course, is posed by the existence of false beliefs. ‘Fred believes that Bob loves Sue’ can still be true even when ‘Bob loves Sue’ is false; but then there is no fact that Bob loves Sue, hence nothing to be the content of Fred’s belief. If propositions are supposed to be fact-like complexes of individuals, properties and relations, then false propositions now appear to be impossible! Unless the individuals appropriately exemplify the properties and relations in question, there will be nothing that unifies these disparate elements into a free-standing whole that can serve as second relatum of the belief relation. This problem of the unity of false propositions, together with an acquired distaste for positing non-existent entities as potential objects of thought, ultimately led Russell to reject both the existence of propositions and the conception of belief as a dyadic relation in favor of his infamous ‘multiple relation’ theory of judgment (hereafter: MRTJ). According to his new theory, the desired unity resides not in
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what is believed but in the act of believing. As we shall see, however, this approach merely trades one set of internal problems for another. Since Russell presented several versions of MRTJ, a brief review of its career will be helpful.9 Russell intended the theory to cover all the propositional attitudes, but for simplicity we shall confine attention to belief. Now according to Russell (1910), a belief ascription of the superficial form (21) A believes that R(a1 , . . . , an ) is no longer to be analyzed as a binary predication (22)
B(A, that-R(a1 , . . . , an ))
in which ‘that-R(a1 , . . . , an )’ names a proposition but rather as the (n + 2)-ary predication (23)
B (A, R, a1 , . . . , an )
in which the believer A is directly related to the n + 1 entities R, a1 , . . . , an mentioned by the terms of the complement clause ‘R(a1 , . . . , an )’ in (21)—where it is now assumed that R, a1 , . . . , an actually exist. (Beliefs putatively about nonexistents are now to be handled via the Theory of Descriptions, on which see below.) Russell’s terminology varies from one presentation to the next, so we shall adopt the following standardization proposed by Nicholas Griffin (1985): A is the subject of the judgment schematized in (23); R, a1 , . . . , an are its objects; its subject and objects together comprise its terms; B is its main relation and R is its subordinate relation. The main relation together with all its terms (i.e., the n + 3 entities B, A, R, a1 , . . . , an ) comprise the constituents of the judgment. Since Russell maintains that the constituents of a judgment are the same regardless of the judgment’s truth-value, he must hold that the existence of the subordinate relation R does not depend on whether it actually relates the particular objects a1 , . . . , an . Otherwise, there would be no subordinate relation to serve as object of thought when the belief reported in (21)/(23) is false. This metaphysical commitment anent the existence conditions for properties and relations is, however, already implicit in Russell’s Platonic conception of universals. In the context of Russell’s type theory, MRTJ is forced to regard the English verb ‘believe’ as being, from a logical standpoint, infinitely ambiguous. Even in the case of belief ascriptions like (21), in which the complement clause is atomic, ‘believes’ will not be univocal. Instead, for each n ≥ 1 and each list of (simple10 ) types t1 , . . . , tn , there is an (n + 2)-ary predicate of type , t1 , . . . , tn > (i being the type of individuals) designating a (weakly intentional) belief relation of
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like type. By itself this extravagance is not fatal, but one would hope that something could be said about this huge family of relations that would explain why they are all belief relations. Russell then introduces truth and falsity as typed properties of judgments (i.e., judgmental facts).11 Claims of the form (24) are to be replaced by claims of the corresponding form (25), where (25) is defined by (26): (24) The elementary proposition that R(a1 , . . . , an ) is true. (25)
Beliefs that R(a1 , . . . , an ) have elementary truth.
(26) There exists a fact of a1 , . . . , an standing in the relation R. To extend the account from elementary to general judgments, Russell defines (27) as (28): (27)
Beliefs that (∀x)F(x) have second-order truth.
(28)
For any item a, Beliefs that F(a) have elementary truth.12
Although the gloss on (23) gives us some intuitive grip on the sort of multiple relation allegedly attributed by (21), we are not given any corresponding analysis of (29) that would reveal how general beliefs are supposed to involve a multiple relation: (29)
A believes that (∀x)F(x).
For that matter, beyond the decidedly retrograde suggestion in (1910/11) and (1992) that an ascription of negative belief like (30)
A believes that ∼ R(a1 , . . . , an )
could be replaced by (31)
D(A, R, a1 , . . . , an )
—where D is the disbelief-relation—Russell never indicates how MRTJ analyzes belief ascriptions with truth-functionally complex complement clauses! If belief is understood to include tacit belief, then we might just barely get away with rewriting (32) as (33): (32) A believes that [R(a1 , . . . , an ) & S(b1 , . . . , bk )] (33)
[A believes that R(a1 , . . . , an )] & [A believes that S(b1 , . . . , bk )].
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But even on this relaxed conception of belief, the possibility of A’s indifference prevents us from analyzing (34) as (35): (34)
A believes that [R(a1 , . . . , an ) ∨ S(b1 , . . . , bk )]
(35)
[A believes that R(a1 , . . . , an )] ∨ [A believes that S(b1 , . . . , bk )].
In general, the fact that one cannot replace truth-functional equivalences inside attitudinal contexts salva veritate seems to block any natural way of extending Russell’s suggestion. Perhaps he could include logical operations among the objects of judgment, so that, where V is the operation of disjunction, (34) could be analyzed as (36): (36)
B(A,V, R, a1 , . . . , an , S, b1 , . . . , bk ).
But he shows no sign of favoring such a move; indeed, he was moved by Wittgenstein to deny the existence of such entities as logical operations. (Nor could V be identified with the relation [λpq p ∨ q], inasmuch as this would require treating ‘p’ and ‘q’ as propositional variables!) Other technical problems for Russell’s theory arise when it tries to account, on the one hand, for the internal difference between (37) and (38) and, on the other hand, for the fact that (37)-(38) make sense whereas (39)-(40) do not: (37)
A believes that a precedes b.
(38)
A believes that b precedes a.
(39)
A believes that b a precedes.
(40)
A believes that precedes b a.
Again following Griffin (1985), these two difficulties will be called ‘the Direction Problem’ and ‘the Nonsense Problem’ respectively. In (37)-(40) the subordinate relation (precedence) is merely a term of the main relation (belief), and there is nothing in the theory so far which differentiates (37) from (38) or which excludes the likes of (39) and (40)! By the time of writing (1912), Russell thought that the Direction Problem could be solved simply by appealing to the direction of the main relation itself (which, unlike the subordinate relation, will be an actually instantiated relation for which the notion of direction makes sense). In other words, it is the particular act of believing that ‘puts the terms in the right order’. In his unfinished 1913 book manuscript Russell abandoned this ploy on the basis of the following, less than pellucid argument: Suppose we wish to understand ‘A and B are similar’. It is essential that our thought should, as is said, ‘unite’ or ‘synthesize’ the two terms and the relation;
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but we cannot actually ‘unite’ them, since either A and B are similar, in which case they are already united, or they are dissimilar, in which case no amount of thinking can force them to become united (Russell 1992: 116).13 He follows this argument with his new proposal: The process of uniting which we can effect in thought is the process of bringing them into relation with the general [logical] form of dual complexes. (loc. cit.) Thus begins Russell’s final attempt to rescue MRTJ by invoking so-called logical forms as additional terms of the judgment relation and introducing a supplementary notion of ‘the position of a constituent within a complex’. Initially, he characterizes elementary logical forms by means of their names: the name of an elementary logical form is obtained from an elementary sentence by replacing all its nonlogical vocabulary with variables of appropriate types. (He never says how this would extend to names of nonelementary logical forms.) This looks as if it solves the Nonsense Problem trivially: type-restrictions on names of logical forms ensure that there is no logical form R(x, y) in which a and b can be anything other than arguments to the relation of precedence. But it still doesn’t solve the Direction Problem. It might be thought that (37) could be analyzed as (37∗ ) and (38) as (38∗ ): (37∗ ) B(A, Rxy, precedence, a, b) (38∗ ) B(A, Ryx, precedence, a, b). But for this to work, some convention on order of substitution is clearly needed. Perhaps we could build this into the relation B. Even so, however, this introduction of logical forms as abstract templates of some sort creates a fatal difficulty. The ‘variable elements’ in logical forms are supposedly represented in their names by free variables, as in (37∗ ) and (38∗ ); but then (37∗ ) and (38∗ )—unlike the sentences they are supposed to analyze—are no longer complete sentences at all! Realizing the need to be clearer about the nature of logical forms, Russell goes on to identify them with certain ‘purely general logical facts’: e.g., the logical form (or structure) of an n-ary elementary complex is said to be the logical fact that (∃R)(∃x1 ) . . . (∃xn )R(x1 , . . . , xn ). To handle the Direction Problem, Russell defines, for each n-ary relation R, (what amounts to) the positional relation ‘x is the nth term of R in complex y’. Then he defines the ‘complex’ a-precedes-b as the complex C such that (i) C’s constituents are a, b, and the (directionless) relation S of sequence, (ii) C’s logical form is the logical fact that (∃R)(∃x1 )(∃x2 )Rx1 x2 and (iii) a is the first term of S in C and b is the second term of S in C. The judgment that a precedes b is then interpreted as the judgment that the complex a-precedes-b exists. Unfortunately, Russell provides no clue as to how this new existential judgment is itself to be understood as involving a multiple relation!14 Moreover, in the belief
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that a precedes b, the order of the subordinate relation’s terms is now determined by the positional relations: there is nothing left for the logical form to do except to carry information about the number and relative types of the constituents in the complex a-precedes-b. How it does this, and how doing so obviates the Nonsense Problem, is left obscure, since we are given no account of how the mind relates the objects of a belief with a logical form. Russell abandoned his book manuscript, but although he would continue to champion MRTJ as late as his famous logical atomism lectures (Russell 1918/19), he never supplied the missing ingredients. For the most part, the problems we have so far noted in connection with Russell’s propositional and non-propositional theories of judgment have been theory-specific ones, self-inflicted injuries as it were. But even if these difficulties could somehow be sorted out (on which, see Chapter 3), the resulting theories would seem to apply only to purely de re belief reports, since they provide no room for failure of Substitutivity in belief ascriptions or anywhere else. As represented in Russell’s notation, the only admissible readings of English sentences will be those on which every term position is transparent! Russell, of course, had read Frege and was perfectly aware of the kind of linguistic data that had occasioned Frege’s worries about opacity. Notoriously, however, Russell came to regard these apparent cases of opacity as ‘logical mirages’, illusions created by grammatical confusion over what constitutes a genuine singular term. In his celebrated essay ‘On Denoting’ (Russell, 1905), he exuded confidence that judicious use of his Theory of Descriptions would dispel these illusions, explaining away the alleged differences between de re and de dicto attitude reports in terms of syntactic distinctions of quantifier-scope. His strategy (described our terminology) is essentially as follows. First, Russell concedes that if, as Frege maintained, ascriptions of propositional attitude have de dicto readings on which some or all singular term positions in their content-clauses are opaque, then they will indeed provide counterexamples to the Substitutivity of Identity, the principle which sanctions inferences of the form (SI): (SI)
σ α=β σ(α//β) [or σ(β//α)].
For if σ is a propositional attitude ascription containing the singular term β opaquely within its ‘that’-clause, then the joint truth of σ and α = β would fail to guarantee the truth of σ(α//β). Thus, e.g., we would expect arguments like (41) and (42) to be straightforwardly invalid instances of (SI): (41)
a. Nobody who believes that De Fato was written by just one man doubts that the author of De Fato wrote De Fato.
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b. The author of De Fato = Cicero. c. Nobody who believes that De Fato was written by just one man doubts that Cicero wrote De Fato. (42)
a. Everyone who believes that Cicero exists believes that Cicero = Cicero. b. Tully = Cicero. c. Everyone who believes that Cicero exists believes that Cicero = Tully.
Second, Russell concedes that there is a reading on which arguments like (41) and (42) are invalid; but he argues that, when so interpreted, such arguments are not really of the form (SI), hence cannot count as counterexamples to it. According to his Theory of Descriptions, natural language definite descriptions (expressions of the form ‘the F’) are not genuine singular terms (individual constants) but are to be eliminated via his famous contextual definition (DD): (DD)
. . . the F . . . =def . Exactly one thing is F, and . . . it . . .. [In symbols: ‘(∃x)(Fx & (∀y)(Fy → y = x) & (. . . x . . .))’]
Relying on (DD), Russell insists that the logical form of (41a) on its alleged de dicto reading is not (43)—in which ‘a’ is a genuine singular term corresponding to ‘the author of De Fato’—but instead is (44): (43)
Nobody who believes that De Fato was written by just one man doubts [a wrote De Fato].
(44)
Nobody who believes that De Fato was written by just one man doubts [exactly one thing wrote De Fato and it wrote De Fato].
(The use of square brackets here and below is intended to be neutral as between Russell’s propositional theory and the various versions of MRTJ; for the former view, take a bracketed sentence to be a name of the proposition the sentence expresses; for the latter views, take a bracketed sentence to be a list of the objects of the attitudinal multiple relation in question, the appropriate placement of commas being understood.) There being no singular term in (44) corresponding to ‘a’ in (43), there is no question of the conclusion (45) arising from (44) by substitution of ‘Cicero’ for that term: (45)
Nobody who believes that De Fato was written by just one man doubts [Cicero wrote De Fato].
Invoking his doctrine that ordinary proper names like ‘Cicero’ and ‘Tully’ (as opposed to so-called logically proper names) are really conventional shorthand for certain definite descriptions, Russell similarly denies that (42) is really of the form (SI).
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Russell concludes that (for singular term positions at least) opacity is an illusion: the only real singular term positions in a sentence are those occupied by genuine singular terms (logically proper names) in the sentence’s logical form; and all such positions are, he maintains, fully transparent. If Russell is right, then the only logical difference between the alleged purely de dicto reading of (46a), on which ‘Wanda’s sister’ occurs opaquely, and a de re reading of (46a) on which ‘Wanda’s sister’ occurs transparently is the syntactic difference in quantifier-scope exhibited by (46b) and (46c) respectively: (46)
a. Fred believes that Bob loves Wanda’s sister. b. Fred believes [exactly one thing is a sister of Wanda, and Bob loves it]. c. Exactly one thing is a sister of Wanda, and Fred believes [Bob loves it].
Given the additional premiss ‘Sue = Wanda’s sister’ (i.e., ‘Exactly one thing is a sister of Wanda, and Sue = it’) and treating ‘Sue’ as a genuine singular term, the conclusion ‘Fred believes that Bob loves Sue’ is formally derivable from (46c) but not from (46b). In general, purely de dicto (or: purely de re) readings of attitude ascriptions would simply be those on which the relevant quantifiers are accorded the narrowest (or: widest) possible scope, with any mixed readings being those in which intermediate scopes are assigned. Certainly there is no denying the ingenuity of Russell’s strategy for dismissing allegations of opacity and accounting for the logical relations among so-called de dicto and de re attitude reports. Its adequacy, however, is far from evident. One obvious shortcoming is the lack of any explicit account of de se attitude reports. One may conjecture from various scattered remarks that Russell’s view was something like the following. Each person possesses a special logically proper name of him/herself. Each person’s special self-name is intelligible only to that person and cannot be synonymous with any definite description not containing it. Communicating with others about ourselves is only possible by using public language descriptions that advert to intersubjectively accessible objects, properties, and relations. Thus ‘I’, as used by an English-speaker in overt speech, must be regarded as shorthand for some suitable definite description—perhaps ‘the utterer of this sentence-token’. If this is correct, then Russell’s private self-names are analogous to Frege’s essentially private self-identifying senses and hence are subject to analogous criticisms. Perhaps the most serious problem with Russell’s strategy is the tendentiousness of his account of the content-clauses of de dicto ascriptions, for on his analysis such ascriptions would always attribute complex, logically sophisticated beliefs. While the definiens in Russell’s contextual definition (DD) may be logically equivalent to its definiendum, it is fallacious to suppose that this fact alone would warrant his practice of substituting the former for the latter under verbs of propositional attitude (as when, e.g., he translates (46a) as (46b)). For contexts like ‘X believes that [. . .]’, even if not opaque in our technical sense, remain resolutely intensional to the extent
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that they reject interchange salva vertitate of logically equivalent sentences. Even if Russell has shown that opacity is a grammatical illusion, nothing in his account demonstrates that belief and other propositional attitudes are closed under logical equivalence, and few would advocate such closure in the first place. Fred, it seems, could have the belief reported de dicto by (46a) even if he were an untutored and not-too-bright child. Russell’s account creates an uncomfortably large gap between the reporter’s description of the belief’s content and any description thereof that the believer could reasonably be expected to provide. By itself, this complaint may not be decisive, since a defender of Russell could always argue that the strong Disquotation Principle of belief attribution presupposed by this objection—roughly, where ‘S’ is an English sentence devoid of indexicals, demonstratives and the like: ‘A normal English speaker who is not reticent will be disposed to sincere reflective assent to ‘S’ if and only if he believes that S’—is itself dubious because it leads to Kripke’s puzzle about Pierre. If our remarks above about the potential Fregean response are on track, however, coping with the puzzle need not entail abandonment of the Disquotation Principle, in which case the ‘descriptive gap’ objection above still stands. In addition to being tendentious, Russell’s account of de dicto-de re distinction in terms of scope differences seems plainly incapable of capturing our intuitions about the de dicto interpretations of certain iterated attitude reports. Linsky (1967), drawing on Mates (1950), cites (47) as an example: (47)
John believes that {it might have been the case that [(George IV wanted to know whether Scott = the author of Waverly); but (George IV did not want to know whether exactly one individual wrote Waverly and it = Scott)]}.
Intuitively, this report has a de dicto reading on which it could well be true. The reading in question attributes to John the belief we would normally take him to express if, having mastered Russell’s Theory of Descriptions and having sincerely disavowed any personal views about the actual or possible authorship of Waverly, he were to criticize Russell by assertively uttering (48): (48)
But surely it might have been the case that George IV wanted to know whether Scott = the author of Waverly but not whether exactly one individual wrote Waverly and it = Scott!
In eliminating ‘the author of Waverly’ from (47), many different scope-distinctions could be made, but none of them will produce a paraphrase that attributes the intuitively appropriate belief. On the narrowest possible scope-assignment, (47) attributes to John the absurd belief that an explicit contradiction might be true, while every other scope-assignment runs afoul of John’s presumed lack of any personal views about the actual or possible authorship of Waverly.
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Independently of the foregoing criticism, it may be objected that Russell’s ‘logical mirage’ account extends to attitude reports allegedly containing opaque occurrences of ordinary proper names only courtesy of his ‘disguised description’ view of such names. But the Description Theory of Names is nowadays in general disrepute, it being widely held that the arguments of Kripke (1972) have definitively refuted both its Russellian version (on which ordinary names abbreviate certain definite descriptions) and its Fregean version (on which ordinary names have the same sense as certain definite descriptions). Why, then, was Russell so certain in the first place that the Substitutivity of Identity, once it is understood to apply only to logically proper names, is a logical law? Linsky (1967) suggests, quite plausibly, that Russell was conflating the syntactic inference rule (SI) with the metaphysical principle of the Indiscernibility of Identicals, viz., the principle that, for any objects x and y, x = y only if any property of x is a property of y. The Indiscernibility of Identicals, however, would only license unrestricted use of (SI) in the presence of the assumption that every open sentence expresses a property, so that, e.g., ‘N believes [. . . a . . .]’ would be logically equivalent by λ-conversion to ‘[λx N believes [. . . x . . .]](a)’ for any logically proper name ‘a’. But, as is well-known, this assumption would lead straight to paradox for predicates like ‘is non-self-exemplifying’ and the like. And even if the assumption is restricted so as not to apply to paradoxical predicates, it would be question-begging to apply it to an open sentence of the sort ‘N believes [. . . x . . .]’. For the property such a sentence expresses is being believed by N to be such that . . . it . . .; but the inference from (49) to (50) is not valid unless it is already taken for granted that the indicated occurrence of ‘a’ in (50) is transparent: (49)
a is believed by N to be such that …it . . . .
(50)
N believes [… a …].
If (50) has any reading on which ‘a’ occurs opaquely, then (50) will require for its truth more than a’s just having the property in question. Moreover, Russell’s crucial distinction between ordinary and logically proper names is vitiated by his inability to provide plausible examples of this logically special kind of name for which (SI) is supposed to be self-evidently valid. The only natural language candidates he ever proposes as logically proper names are pure demonstratives like ‘this’ and ‘that’ (no doubt because reference via pure demonstratives seems to lack any overt descriptive force). But even pure demonstratives seem capable of occurring opaquely in attitude ascriptions, as is attested by the intuitive invalidity of arguments like (51) when enunciated in certain contexts: (51)
a. Fred believes that this is the USS Cottonbottom. b. This = that. c. Fred believes that that is the USS Cottonbottom.
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Let the context in question be as follows. Fred is looking at a long dockside warehouse several blocks away; he sees a ship’s bow protruding from behind one end of the warehouse and a ship’s stern protruding from behind the opposite end. Because of the great length of the warehouse, he naturally assumes that the bow and stern in question must belong to different ships. He peeks through binoculars and observes the name ‘USS Cottonbottom’ emblazoned on the bow but, because of the angle, can see no identification on the stern. Now Wanda, the utterer of (51a-c), is standing alongside Fred and sees through her binoculars everything that he sees, but Wanda knows that the bow and stern they both see belong to a single, prodigiously long supertanker. In sequentially uttering (51a-c), Wanda points to the bow each time she uses ‘this’ and to the stern each time she uses ‘that’, relying on the familiar convention that one may demonstratively refer to an object by indicating a visible part of it. In the envisaged context, (51b) correctly reports an identity and (51a) correctly reports Fred’s visually based belief, but (51c) seems dead wrong in light of Fred’s ignorance. We can easily imagine him pointing first to the stern and then to the bow while proclaiming ‘No! That couldn’t be the USS Cottonbottom—it’s too far away from this!’ 2.4
CHISHOLM’S PROPERTY-ATTRIBUTION THEORY
Roderick Chisholm (1981) puts forward a view of thinking which takes thoughtstates to be essentially relational and which maintains that properly intentional notions cannot be eliminated from the characterization of these relations. As he sees it, the philosophical task is to achieve the formally tidiest and ontologically most economical non-reductive explication of intentionality. Accordingly, Chisholm allows himself only five primitive ontological predicates: ‘x exemplifies y’, ‘x is possibly such that it is F’, ‘x conceives y’, ‘x obtains’, and ‘x is a relation’. Properties are defined as those things which are possibly exemplified, and it is postulated that every property is possibly such as to be conceived. It is further laid down that any property (other than conceiving and what it entails) which is possibly unexemplified is possibly unexemplified-but-conceived. From this it follows that no property is conceivable only by reference to a contingent thing. The force of these requirements is thus to eliminate ‘singular’ properties such as being identical to Meinong and being the owner of this book. Properties, in Chisholm’s favored sense, are thus purely qualitative. States of affairs are defined as items which are (i) necessarily distinct from properties and relations, (ii) conceivable, and (iii) such that whoever conceives one conceives something which possibly obtains. Statesof-affairs which we would intuitively think of as non-compound are tied to sets of properties through a postulate which equates the obtaining of such states-ofaffairs with the exemplification either of all the properties in a certain non-empty set of properties or of none of the members of a certain nonempty set of properties (affirmative verses negative states of affairs). Since there are no singular properties in Chisholm’s ontology, this postulate has the effect of eliminating singular
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states-of-affairs such as Meinong’s being an Austrian, or someone’s owning this book. States-of-affairs, in the admissible sense, are purely qualitative and general. The power and ingenuity of Chisholm’s positive view emerges when we see how he proposes, within the confines of this purified ontology, to solve the problem of singular belief. Traditional relational theories invoke propositions as the second term of the belief relation and accordingly treat a singular belief report as a de dicto ascription of belief in a singular proposition. But, as Chisholm forcefully points out, the doctrine of singular propositions runs hopelessly aground on the case of those singular beliefs which are self-regarding (de se),15 such as my belief that I was born in California, your belief that you had parents, Jimmy Carter’s belief that he himself was once president, and so on. With respect to such beliefs, the proponent of singular propositions is driven to wild excesses in his attempt to say just what propositions are believed. (There appears, e.g., to be no such intersubjectively available proposition as that he himself was once president which Jimmy Carter and Bill Clinton might both truly believe). Accordingly, the proponent of singular propositions is forced to follow Frege in positing mysterious first-person propositions which embody the subject’s ineffable Ich-Vorstellung and consequently are accessible only to the subject. Nor does it help to posit two different belief-relations: say, dyadic ‘notional believing’, which relates the subject to an intersubjectively available proposition, versus triadic ‘relational believing’, which relates the subject to an n-ary attribute and n-tuple of individuals. For while such a ploy might aid in explaining the difference between de dicto and de re belief ascriptions, de se belief ascriptions (which attribute self-regarding beliefs) are importantly different from both, as is reflected in the logical relations among sentences of the forms (52)-(54) (where (53) is accorded its normal de dicto reading): (52) The F believes that he himself is G. (53) The F believes that the F is G. (54) The F believes, of the F, that he is G. For (52) implies, but is not implied by, (54); and (52) neither implies, nor is implied by, (53)! So, pursuing the proliferation tactic, one would be driven to posit yet a third kind of belief, the self-regarding kind, which would hover inexplicably between the other two. Chisholm’s solution (which resembles one independently worked out by David Lewis (1979)) is brilliantly simple: instead of invoking mysterious first-person propositions or proliferating belief relations, Chisholm inverts the traditional picture by taking self-regarding belief as fundamental. He then proceeds to show how what is attributed in de re and de dicto belief reports can be regarded, within the confines of his purified ontology, as species of such self-regarding belief. The key to this paradigm-shift is a new primitive doxastic locution: ‘x directly attributes
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z to y’. The concept of direct attribution is constrained by postulates which ensure that if x directly attributes z to y, then y = x and z is a property. Direct attributions are thus (in the alternative terminology employed in Lewis’s version) self-ascriptions of properties. Person x’s self-regarding belief that he himself is F may then be identified with x’s direct attribution of F-ness to x—or, more colloquially, with x’s self-ascription of F-ness. What is said here regarding belief may be extended, mutatis mutandis, to the other modes of thought by regarding them all as modifications of a single generic relation expressed by ‘x entertains F-ness of y (in mode M )’, a relation which a person bears solely to himself and some property or other. Belief could then be viewed as self-entertainment of some property in the doxastic mode. (Where the mode of entertainment is that of mere contemplation, Chisholm speaks of x ‘considering’ y as being F.) Rather than pursue this complication, however, let us follow Chisholm in concentrating on belief as the paradigm of thought and treating self-ascription as basic rather than as a mode of something else. Turning now to the question of belief ascribed de dicto and de re, we must inquire how Chisholm proposes to allow for ascription of beliefs that pertain to transcendent objects (i.e., to things other than the ascriber). This is accomplished by means of a derivative notion of indirect attribution of properties to objects qua objects related to the ascriber in certain ways. More precisely: x indirectly attributes F-ness to y (as the thing that x bears R to) if and only if (i) x bears R to y alone and (ii) x self-ascribes a property entailing the property of bearing R to just one thing and to a thing which is F. For short, we can say simply that x indirectly attributes F-ness to y—meaning thereby that there is some relation R such that x indirectly attributes F-ness to y as the thing to which x bears R. Now the key point is just that a person may indirectly attribute a property to himself without directly doing so, hence have a belief about himself which is nevertheless not a genuine self-regarding belief. What is asserted by belief reports of the forms (52) and (54), that is, may provisionally be captured in (52∗ ) and (54∗ ): (52∗ ) The F directly attributes to the F (self-ascribes) the property G. (54∗ ) The F self-ascribes or indirectly attributes to the F the property G. This explains why instances of (52) entail, but are not entailed by, corresponding instances of (54). What, then, is reported by the de dicto belief ascriptions which are instances of (53)? Chisholm regards them as reporting the acceptance of states-of-affairs (‘de dicto beliefs’ in his terminology), where by definition: The state-of-affairs that p is accepted by x if and only if exactly one state-ofaffairs is the state-of-affairs that p, and either x self-ascribes the property being
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such that p, or x indirectly attributes the property of obtaining to the state-ofaffairs that p as the thing x is conceiving in a certain way. Several points call for comment here. It will be remembered that, in Chisholm’s ontology, states-of-affairs as well as properties are required to be pure or qualitative; in particular, there are no singular states-of-affairs. It follows, then, that all de dicto beliefs are general in content. If an instance of (53) attributes a genuine de dicto belief to the F, it would presumably attribute something like the F’s acceptance of the state-of-affairs that there is one and only one F and it is G. What is asserted by instances of (53), then, might be captured schematically in (53∗ ): (53∗ ) There is exactly one state-of-affairs s that [one and only one thing is F and it is G] and the F either self-ascribes being such that [one and only one thing is F and it is G] or indirectly attributes obtaining to s as the thing he is conceiving in a certain way. Now even though there may well be such a unique state-of-affairs s, the F’s selfascribing G neither entails nor is entailed by his either self-ascribing being such that [one and only one thing is F and it is G ] or indirectly attributing obtainment to s qua thing he is conceiving in a certain way. This is why instances of (52) neither entail, nor are entailed by, corresponding instances of (53). A few cautionary words are now in order. Chisholm maintains that the locutions ‘x directly attributes z to y’ and ‘x conceives y’ express certain primitive intentional relations of which a person may be the subject. But it is important to see this talk of intentional relations in the proper light, lest it seem that Chisholm is committed to too much. As was pointed out earlier, some traditional discussions of intentional relations characterize them as possessing certain anomalous features: e.g., the ability to obtain between an existing and a non-existing entity, or the ability to ignore the identity of their terms, i.e., to obtain between x and y but not between x and z despite the fact that y = z. The sense in which Chisholm regards conception and self-ascription as primitive intentional relations is, however, much more modest than this. Self-ascription is directed in a primitive and unmediated way upon the self (the ascriber) and a property (in Chisholm’s highly restricted sense of ‘property’), and Chisholm distinguishes the existence of a property from the existence of something exemplifying that property, holding that there exist unexemplified (but not unexemplifiable) properties. The only sense in which he allows that self-ascription may relate a person to a ‘non-existent’ entity is that the property self-ascribed may not be exemplified by anything (as when, e.g., someone self-ascribes the property being king of France in 1983). Moreover, self-ascription is a relation which respects the identity of its terms: if F-ness = G-ness, then self-ascribing F-ness = self-ascribing G-ness.
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Matters are a bit more complicated with the relation of conceiving, since its objects may be of various ontological categories: one may conceive states-ofaffairs, properties, concrete and abstract particulars, and so on. Here too, however, Chisholm insists that the objects of conceiving straightforwardly exist: they are not mere possibilia or entities endowed with subsistence or some other non-standard mode of being. The case of states-of-affairs parallels that of properties, upon which we have already remarked. Although it might seem rather artificial to distinguish the existence of a state-of-affairs from its obtaining, the blow is softened by the connection which Chisholm makes between states-of-affairs and properties, for which the parallel distinction between existence and exemplification is more natural (at least for a Platonist), namely, that the obtaining of non-compound states-of-affairs is equivalent to the joint exemplification or a joint non-exemplification of certain sets of properties. The question of the identity-criteria for properties, states of affairs, and their ilk is a vexed one, but there is nothing in Chisholm’s account to suggest that the relation of conception fails to respect the identity of its terms any more than self-ascription does. (Indeed, were conception or self-ascription to behave in such an anomalous way, the grammatical object-positions in the verbs ‘conceive’ and ‘self-ascribe’ would be substitutionally opaque, so that the Chisholmian vocabulary could not be used to give a non-circular account of opacity in attitude ascriptions.) What we are asked to accept, then, is just that there are these two weakly intentional relations of conception and self-ascription—capable of obtaining between persons on the one hand and existing (though perhaps abstract and unexemplified or non-obtaining) entities such as properties and states-of-affairs on the other—and that their happening to relate appropriate items or not in any given case is a brute fact in the sense of not consisting in the presence of anything ontologically more fundamental. As explicated by indirect attribution, the notion of having a belief ‘about’ an object (a ‘de re belief’ in Chisholm’s terminology) is a very weak one, being merely a special case of the old Russellian idea of thinking of an object under a description. Russell contrasted this indirect way of reaching the object with the direct access provided by acquaintance, and many philosophers have followed Russell at least to the extent of supposing that genuine de re beliefs must involve some more intimate connection(s) between the self and the transcendent objects in virtue of which they are about the latter. Chisholm is at pains to show that his theory can accommodate these more demanding conceptions of de re belief where, as he puts it, the believer identifies the object as a thing which he (the believer) believes to have such-andsuch a property. There are, broadly speaking, four types of case Chisholm considers: self-identification, perceptual identification, epistemic identification, and a special ‘essential’ mode of identification for abstract (eternal) objects. Identifying oneself as the thing one believes to be F is simply a matter of selfascribing F-ness while considering one’s doing so (i.e., while self-entertaining in the contemplative mode the property being a self-ascriber of F-ness). Explanation of the other types of identification is more complicated, involving suitably adapted
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versions of concepts from Chisholm’s theories of knowledge and perception, some familiarity with which will be taken for granted it what follows. Let us say that x knows himself to be F just in case: he is F, he self-ascribes being F, and this self-ascription is evident to him. Let us say further that x perceptually takes y to have property F if and only if: there is a certain way in which y alone appears to x, and F-ness is a sensible property which x indirectly attributes to y as the thing appearing to him in that way. Assuming appropriately definability of ‘it is evident to x that y is F, we may then say that x perceives y to be F if and only if: y is F, x perceptually takes y to be F, and it is evident to x that y is F. Then we may characterized x’s perceptual identification of y as a thing he believes to be F in terms of the existence of some property G such that x perceives y to be G and self-ascribes the property of being such that the thing he perceives to be G is F. We turn next to epistemic identification of an object as a thing one believes to be F. Here the key notion is that of recognizing an object of indirect attribution under various descriptions. More precisely, x identifies y as a thing to which, under several descriptions, he indirectly attributes F-ness (i.e., epistemically identifies y as a thing he believes to be F) if and only if (i) x indirectly attributes F-ness to y, both as the thing to which he bears a certain relations R and as the thing to which he bears a certain relation S; (ii) x knows himself to bear R and S to the same thing; and (iii) his evidence for believing that he bears R to just one thing is independent of his evidence for believing that he bears S to just one thing. Finally, there is the special case in which x essentially identifies an eternal object y as something he believes to be F. This is a matter of x’s being uniquely related to y by means of some relation R and self-ascribing a certain property H which (a) entails F-ness if F-ness is entailed by the essence of y and (b) is necessarily such that whatever has it bears R to something having both the essence of y and F-ness. In sum, then, we may say that x has a ‘strong’ (some would say ‘genuine’) de re belief regarding an object y to the effect that it is F just in case, in one of the four senses above, x identifies y as a thing he believes to be F. (The extension of these remarks to de re beliefs with multiple objects, and to modes of thought other than the doxastic, is straightforward.) We may now see how Chisholm’s view fits into our initial characterization of the intentionality of thought, where we spoke of the contents, objects, and satisfaction conditions of thoughts. All belief is at bottom self-ascription of properties: the differences between de se, de dicto, and de re belief ascriptions are ultimately just differences in the kinds of properties whose self-ascription they report. Selfascription (direct attribution) involves primitive, unmediated mental reference to oneself, which thus deserves to be called the ‘direct object’ all of one’s beliefs. All other, ‘indirect objects’ of one’s beliefs, even in the strong de re cases, are picked out by relation to oneself, hence are referred to only indirectly, by description. (In other words, these indirect references, unlike direct reference to the self, are parasitic upon content.) Content may be similarly stratified. The ‘direct content’ of a belief state is the property which the owner of that state ultimately is
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self-ascribing; it’s ‘indirect content’ consists in those properties (if any) therein indirectly attributed to (indirect) objects. The association of a truth condition with a belief state is, intuitively, a matter of the direct content of the latter. On Chisholm’s view, however, it is not correct to say, as the traditional propositionalist account does, that contents themselves have truth conditions, since contents are now properties. Nor can we think of truth conditions themselves as possible states of affairs, since they would always have to be of the forbidden singular kind (i.e., of the sort ascriber-exemplifying-self-ascribed-property). Rather, it seems that we must regard talk about associated truth conditions as mere shorthand for talk about direct contents themselves. To say that one of x’s belief-states is true if and only if p (or has the truth condition that p, etc.) is just to say that its direct content is exemplified by x if and only if p. Rather than there being two explananda—viz., how thoughts are contentful and how their contentfulness determines a correlation with something else—only contentfulness calls for explanation. We have seen, in outline, how Chisholm proposes to account for the intentionality of thought (specifically, of beliefs). What remains to be seen is whether his theory is adequate to handle all of the relevant data. One crucial datum was touched upon in our initial characterization of intentionality as involving satisfaction conditions: namely, that one can think the impossible. Any adequate account of belief must explain how, e.g. someone can believe that p even though it is strictly impossible that p. It seems, however, that Chisholm’s purified ontology will prevent him from giving a fully general account of such beliefs. A case in point is someone’s belief that there is more than one even prime number. This is, it would seem, a purely general belief (a ‘de dicto belief’ in Chisholm’s sense) which any mathematically naive or confused person might have. Now according to Chisholm’s construal of de dicto belief, a person x has such a belief just in case there is a unique state of affairs s that [there is more than one even prime number] and either (a) x selfascribes the property being such that [there is more than one even prime number], or (b) x indirectly attributes obtainment to s qua thing he is conceiving in a certain way. Now if s is a state of affairs, then it follows on Chisholm’s definition that whoever conceives s conceives something which is possibly such that it obtains. But there cannot possibly be more than one even prime number, so in conceiving s one would not be conceiving something which might obtain. Therefore, Chisholm cannot allow that there is any such state of affairs as s to which (qua thing one is conceiving in a certain way) one might indirectly attribute obtainment. Nor can there be any such property as the property being such that there is more than one even prime number, since nothing could possibly exemplify such a property, and unexemplifiable properties are forbidden. It appears, then, that Chisholm’s account of belief must be modified, or else his ontology must be enriched. The proceeding problem is intimately connected with another. One of the curious features of belief ascriptions is that their content clauses are opaque to predicate replacement not only with respect to coextensive predicates but even with respect to synonymous predicates. The sentences ‘John believes that he owns a hinny’ and
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‘John believes that he owns an offspring of a male horse and a female donkey’ seemingly can differ in truth-value despite the synonymy of the predicates ‘hinny’ and ‘offspring of a male horse and a female donkey’. On Chisholm’s account, however, the truth of the former sentence consists in John’s self-ascribing the property owning a hinny. But the property being a hinny is identical to the property being an offspring of a male horse and a female donkey. So it follows that owning a hinny is the same property as owning an offspring of a male horse and a female donkey, hence that John’s self-ascription of the former property = his self-ascription of the latter property. But then the original sentences ‘John believes that he owns a hinny’ and ‘John believes that he owns an offspring of a male horse and a female donkey’ could not differ in truth value, since they report exactly the same thing. The connection with the problem of believing the impossible runs through one sort of reason we might give for the alleged truth-value divergence: namely, that John might believe that a hinny is not the offspring of a male horse and a female donkey—which is clearly a case of believing the impossible. It is worth noting that nothing in Chisholm’s account appears to permit a nonquestion-begging denial of the identity of the two properties mentioned above. One could not, e.g., deny their identity by claiming that they do not (in Chisholm’s sense) entail one another. Since their possible exemplifications are obviously connected in the right way, this claim could only mean that neither property is necessarily such that whoever conceives it conceives the other—i.e., that one can conceive the property being a hinny without conceiving the property being an offspring of a male horse and a female donkey (or vice versa). But conceiving is presumably a relation which respects the identity of its terms; so it would be question-begging to claim that one can conceive one of these properties without conceiving the other. Intuitively, they are the same property, so that to conceive one is to conceive the other. It appears, then, that Chisholm must either deny the intuitive data regarding predicate opacity or else regard direct attribution and/or conceiving as being intentional relations in the incurably problematic sense of being relations which somehow can obtain between x and (property) y without obtaining between x and z even though y = z! Another difficulty with Chisholm’s account is that it seems to sever certain intuitive connections between believing and the possession of various concepts. To avoid begging any questions in what follows, let us say that what Chisholm has defined is ‘belief ∗ ’, which may or may not coincide with our pre-analytic notion of belief. Then there appears to be some initial oddity in the fact that nothing in Chisholm’s definitions prevents one from directly or indirectly attributing properties that one is unable to conceive, so that nothing prevents one from having beliefs∗ whose direct or indirect contents involve properties beyond one’s conceptual ken. If, e.g., having the concept ‘airplane’ involves the ability to conceive the property being an airplane, then there seems to be no reason of principle why one should not be able, say, to believe oneself to be standing next to an airplane even though one lacks the very concept of an airplane—surely a counterintuitive
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result! To this it might with some justice be replied that possession of a concept is not the same thing as the ability to conceive the related property, for conceiving a property is a way of referring to it in thought, whereas attributing properties is a kind of mental predication. Thinking of oneself as being hungry is compatible with not yet having mentally singled out the property of being hungry. But taking this line only relocates the oddity. For if the intuitive constraint is not captured by conceiving qua mode of mental reference, then it seems that we should look to attribution, the mental analogue of predication. The suggestion, in other words, is that we think of having the concept of an F-thing (whatever that ultimately amounts to) as an essential part of the ability directly or indirectly to entertain (in whatever mode) the property of being an F-thing. This would certainly explain our reluctance to say that a member of a primitive tribe, coming across an airplane for the first time, believes that he is standing next to an airplane. Unfortunately, this natural way of capturing the intuitive conceptual repertoire constraint would be disastrous for Chisholm’s theory, which analyzes certain conceptually innocentlooking beliefs as beliefs∗ involving the attribution of suspiciously complex properties. Consider, e.g., our primitive tribesman—call him ‘Gornak’—staring in amazement at the airplane which has just crashed in front of his hut, deep in the unexplored forests of New Guinea. We may well suppose that Gornak has a simple indexical belief about this extraordinary object: he believes, say, that that thing is a demon. Chisholm would presumably regard this belief as a ‘strong’ de re belief ∗ , i.e., a case of Gornak’s perceptually (visually) identifying the airplane as a thing which he himself believes to be a demon. Such a belief ∗ is analysed as follows: there is some sensible property G such that Gornak sees that object to be G, and Gornak self-ascribes the property being an x such that there is one and only one y such that x sees y to be G and y is a demon. For concreteness, we may suppose that G is the property being-huge-silvery-bird-like. But self-ascription is definitive of belief ∗ de se, so if Gornak has the de re belief ∗ in question, he also has the de se belief ∗ that there is one and only one thing which he himself sees to be huge-silvery-bird-like, and it is a demon. On the proposed way of capturing the conceptual repertoire constraint, he could not have this belief ∗ unless he possessed the concept of seeing, or visual perception. And this, to put it mildly, seems a bit much to expect of poor Gornak! Primitive humans (not to mention monkeys, dogs, etc.) seemingly end up believing∗ things which it is highly doubtful that they really believe. By failing to provide a coherent locus for anything like a conceptual repertoire constraint, Chisholm creates the strong suspicion that the class of beliefs∗ does not coincide with the class of beliefs at all. What is suggested by the foregoing difficulty with de re beliefs about perceived particulars is that certain kinds of demonstrative reference to such particulars may be on the same footing with mental reference to the self, rather than being reducible to self-ascription of various properties. This is sometimes put by saying that there are ‘irreducible perceptual modes of presentation’, or ‘de re modes of presentation’,
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or ‘demonstrative ideas’ of objects. Some authors go so far as to suggest that demonstrative reference to particular thoughts and experiences is the primitive sort of mental reference, the self being referred to only indirectly as the owner of these items. Not surprisingly, there seem to be difficulties with ‘here’-thoughts that parallel those regarding ‘this’-thoughts. Egocentric spatial thinking gets short shrift from Chisholm: to think of a place as ‘here’is, we are told, just to think of it (indirectly) as ‘where I am’. On this view, what distinguishes ‘here’-thoughts from other thoughts about particular places is merely that the latter involve different and richer sorts of envisaged relations to oneself. All such thoughts are ultimately egocentric: ‘here’thoughts are just the simplest and least specific, for they involve no characterization of the self’s location beyond its being such. There is an undeniable attractiveness to this way of construing egocentric spatial thinking; indeed, it does seem to some to be self-evidently correct. But problems loom. Suppose person x is located at place y and has a belief which he would formulate for himself by something of the form ‘F(here)’, in which ‘here’ is the only singular term pertaining to a place. Now if, as Chisholm would have it, this belief is just a matter of x’s indirectly attributing F-ness to y qua place where he himself is, hence ultimately a matter of x’s being at y and self-ascribing the property of being situated at an F-place (or some richer property entailing this one), then there is no way of allowing that the (indirect) object of x’s belief could be any place other than y. Yet we do seem to be able to imagine cases in which the indirect object of x’s belief would be some place other than y. Consider the skeptic’s favorite scenario: x is, unbeknownst to himself, a brain in a vat at place y. Let us add to this that x has been attached, by remote control, to a cyborg whose body is a perfect replica of the one from which x was extracted—except, of course, that it has no brain of its own, only a piece of hardware which transmits afferent signals to x’s brain and passes along efferent signals from x’s brain to the body. The requisite operations having been done while x was unconscious, x supposes that all is normal. The body he sees and feels he naturally regards as his own familiar body. Now the obvious question arises: where is x? Since there is no spatio-temporal continuity between the cyborg and the previously incarnated x, it seems reasonable to continue identifying x with his living physical residue, the discorporated brain, and hence to say that x is wherever the mad scientists have stashed the latter. But the cyborg could be anywhere, say on the opposite side of the world. Now the problem is evident: x, who is located at y, judges, on the basis of perceptual input from the cyborg, which is currently at a distant spot z, some ‘F(here)’-thought. There is a strong intuition that, contra Chisholm, x is thinking about z and not about y. The ground of this intuition is that x’s perceptions and actions by his ‘body’ pertain exclusively to z: he is not even dispositionally linked to extra-cerebral goings-on at y in the same intimate way.16 The difficulties do not end here. Chisholm treats both ‘x believes that x-self is F’ and ‘x believes [accepts the state-of-affairs] that p’ as strictly defined in terms
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direct and indirect attribution. This would presumably make the property equation (55) analytically true: (55)
believing that x-self believes that x-self is in pain = believing that x-self is a self-ascriber of the property being in pain.
But now Chisholm faces the iteration problem mentioned in our initial statement of adequacy conditions. For consider the belief report (56): (56)
Nelson believes that he-himself believes that he-himself is in pain.
(issued, say, after Nelson proclaims ‘Not only am I in pain, but I believe that I am, and I believe that I believe that I am!). On Chisholm’s view, (56) should be analytically, hence necessarily, equivalent to (57): (57)
Nelson believes that he-himself is a self-ascriber of the property being in pain.
But Nelson could be a devout Nominalist, who vehemently rejects the existence of properties and other non-particulars. In such a case, (56) could easily be true while (57) is false. Finally, let us consider the impact of Kripke’s and Austin’s puzzles. Chisholm is well aware of the former. He prefaces his treatment of it with an argument for the conclusion that . . .if we are justified in using proper names to report other people’s beliefs (as in ‘Jones believed that Cicero was identical to Tully’), then the beliefs in question are in part beliefs about those names. (1981: 66) He then dismisses Kripke’s puzzle with the observation that The first sentence [‘Pierre believes that London is pretty’] is true in virtue of the fact that Pierre attributes to himself the property of being such that the thing he usually uses ‘Londres’ to designate is pretty. And the second sentence [‘Pierre believes that London is not pretty’] is true in virtue of the fact that he attributes to himself the property of being such that the thing he usually uses ‘London’ to designate is a thing that is not pretty. (1981: 67) The two facts in question being mutually compatible, the puzzle allegedly disappears. This quick dissolution of Kripke’s problem comes at the price of accepting two claims. The first is that, where ‘a’ is any proper name, there is a reading of the sentence ‘a is F’ on which its semantic value is not a proposition but a property— viz., being an x such that the thing x normally uses ‘a’ to designate is F—which
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would be self-ascribed by anyone who utters the sentence. And the second claim, whose plausibility rests mainly on that of the first, is that the reading in question is the one relevant to interpreting sentences of the form ‘x believes that a is F’ at least on those occasions when we are justified in asserting them. Unfortunately, the first claim reintroduces the ‘missing concepts’/‘alien complexity’ problem. For the truth of ‘x believes that a is F’ will involve x’s self-ascribing a complicated property which x may be unable to conceive. Surely, one would suppose, someone may believe that London is pretty even though he lacks the semantical concepts of quotation and designation (not to mention the logical concepts) involved in paraphrasing away the definite description ‘the thing x normally uses ‘a’ to designate’). Mastering the use of proper names in object-English, something that small children manage to do, does not seem to require competence in semantical meta-English. It would be nice to be able to solve or dissolve Kripke’s puzzle without the need to assume otherwise. Although Chisholm does not explicitly discuss Austin’s Two Tubes Puzzle, it is not difficult to predict the way in which he would diagnose Smith’s confusion. By Chisholm’s lights, Smith ‘perceptually identifies’ the spot he sees under the phenomenal description ‘the thing that now appears to me to be here/on the right/at the center of my right visual field’ and under the phenomenal description ‘the thing that now appears to me to be there/on the left/at the center of my left visual field’but fails to realize that it is one and the same thing to which he bears these perceptual relations. So in saying ‘This is red’, Smith indirectly attributes to the spot, as the thing that appears to him(self) to be on the right, the property being red. And in saying ‘that is red’, Smith indirectly attributes this same property to the spot, only now as the thing that appears to him(self) to be on the left. No problem now arises, for Smith’s beliefs are appropriately distinct. As Austin himself points out, however, this solution threatens to be unintelligible on Chisholm’s own principles. How can Chisholm differentiate what is expressed by such phrases as ‘appears to me to be here’ and ‘appears to me to be there’, or by ‘appears to me to be on the left’and ‘appears to me to be on the right’? Relations like x appears to y to be here and x appears to y to be on y’s right are not ‘pure’and hence must, by Chisholm’s lights, be further analyzable in non-indexical terms. But how? For someone like Chisholm, who is an adverbialist about perception, there are no such things as sense-data or visual fields and their parts to which one might appeal in crafting the requisite non-indexical analysis. And we have no corresponding notion of how to differentiate locative ‘aspects’ in these ways of being appeared to.
NOTES 1 Cf. Quine (1960: 143-144), where it is pointed out that such illusory occurrences could be
avoided altogether by dissolving quotation into spelling (i.e., by using names of the letters of the alphabet together with a concatenation operator). In practice, however, the latter strategy would be unnecessarily hard on the reader.
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2 The argument proceeds as follows. Since Pierre assents to ‘London is not pretty’, the Disquotation
Principle yields (i): (i) Pierre believes that London is not pretty. Since Pierre also assents to ‘Londres est jolie’, the French version of the Disquotation Principle entitles a French-speaker to assert Pierre croit que Londres est jolie. and hence, by the French version of the Tarski schema, to assert ‘Pierre croit que Londres est jolie’ est vrai (en Francais). Under translation into English, this truth becomes the truth ‘Pierre croit que Londres est jolie’ is true (in French). But the English translation of ‘Pierre croit que Londres est jolie’ is presumably just ‘Pierre believes that London is pretty.’ So by the Translation Principle again, we are entitled to assert ‘Pierre believes that London is pretty’ is true (in English). The Tarski-schema then yields (ii): (ii) Pierre believes that London is pretty. Kripke points out that if we are willing to strengthen the Disquotation Principle to a biconditional schema like A normal English speaker who is not reticent will be disposed to sincere assent to ‘S’ if and only if he believes that S., then we could derive the explicit contradictory of (ii), for it is stipulated that Pierre assents to ‘London is not pretty’ and is logically competent, in which case he would presumably not assent to ‘London is pretty’! 3 At one point Frege says that modes of presentation are ‘contained’ in senses, but the distinction between ‘being’ a mode of presentation and ‘containing’ one is not further exploited, so it is difficult to know what Frege had in mind. 4 In Frege (1960), Max Black’s original translation of Frege (1892a), ‘Bedeutung’and ‘Bezeichnung’ (which Frege uses interchangeably) are rendered as ‘reference’ and ‘designation’ respectively. 5 The qualification ‘putatively’ is required because of the truth-value gaps that appear to open up in connection with meaningful declarative sentences containing ‘empty’ terms—terms whose senses fail to present any referents. Sometimes Frege seems to regard such sentences as expressing perfectly respectable albeit truth-valueless Thoughts, but on other occasions he appears to back away from countenancing truth-valueless Thoughts, calling them instead ‘Scheingedanken’ (‘mock Thoughts’ or ‘pseudo-Thoughts’). No doubt part of his ambivalence on this issue owes to his conflation of sense and linguistic meaning.
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6 The presence in natural languages of indexicals and demonstratives—which intuitively retain a
constant meaning even when their reference shifts with context—ultimately undermines any attempt to equate Fregean sense with the ordinary notion of linguistic meaning. If Frege equated them, it was most likely because he was concerned primarily with idealized languages. See Burge (1979, 1990). 7 Frege’s theory involves certain weakly intentional relations as primitive: e.g., grasping relates us to senses, which are non-spatiotemporal entities; presentation relates these non-spatiotemporal entities to other things, which themselves might be non-spatiotemporal; expression relates wordtypes to senses, both of which are non-spatiotemporal entities. Since Frege’s account of fictional belief and the like exploits senses rather than positing any non-existent entities, he avoids the need for strongly intentional relations. 8 Of course it is open to the possible-worlds theorist to avoid the problem by adopting some nonstandard set theory (such as that of Aczel (1987)) in which nonwellfounded sets (hypersets) are allowed. A lucid discussion of this approach can be found in Barwise and Etchemendy (1987, Ch. 3). 9 Although an early form of MRTJ is tentatively proposed in (1906/08), the first version Russell publicly endorses appears in (1910). It is repeated in (1910/11), revised in (1912) and further revised in the posthumously published 1913 book manuscript (1992). Russell was still propounding MRTJ in print as late as (1918/19), but officially abandoned it the following year in (1919). 10 We ignore here the ramified version of Russell’s theory of types. In the simple type theory invoked here, i is the basic type (of individuals) and is a type if all of t1 , . . . , tn are. 11 Since there are presumably only finitely many such judgmental facts, it is unclear how Russell proposed to account for the truth-values of unjudged propositions. 12 Russell takes for granted here that all the belief-relations required by his theory are extensional. 13 Russell’s reasoning here is rather obscure. Of course thought cannot (in general) literally bring about the very connections it envisages as obtaining among objects in the extramental world! Who, except perhaps an extreme Idealist, would ever have supposed otherwise? The problem for MRTJ, surely, is to say what the multiple relation of believing does do with these objects. 14 Perhaps, taking a hint from the suggestion about general judgment in Russell and Whitehead (1910: Introd., Ch. II, pp. 45-46), we could regard existential judgment as a new binary relation E between persons and propositional functions, thus representing the judgment that the complex C exists by something like ‘E(A, (ˆu = C))’. Alternatively, we might invoke the property E of being exemplified by something and try to represent the existential judgment as ‘B(A, E,(ˆu = C))’. Of these ploys, the former seems more Russellian in spirit, especially since the latter would involve the very reification of logical constants that Russell later rejected. 15 Chisholm treats ‘de re’, ‘de dicto’, and ‘de se’ as adjectives modifying ‘belief’ and as adverbs modifying ‘believes’. Where possible without intolerable circumlocution, we have avoided this usage in favor of our neutral ‘linguistic’ alternative, on which ‘de re’, ‘de dicto’, and ‘de se’ characterize ways of reporting beliefs. 16 This line of argument is adapted from Evans (1982).
PART II
ONTOLOGY
CHAPTER 3
LOGICAL FORMS AND MENTAL REPRESENTATIONS: THE LESSON OF RUSSELL’S MULTIPLE RELATION THEORY OF JUDGMENT In Chapter 2 we sketched and criticized Russell’s infamous multiple relation theory of judgment, paying special attention to its final and most developed version, according to which the relata of judgment relations include not only the individuals, properties, and relations that the judgment is intuitively about but also a mysterious logical form that somehow encodes the pattern in which these constituents are judged to be arranged, thereby determining the judgment’s truth condition. On that version of the theory, it will be remembered, an atomic belief ascription of the superficial form (1) is to be analysed1 along the lines of (2), in which f is the yet-to-be-explained logical form of an n-ary predication and Bel is a yet-to-beexplained (n+3)ary relation of the appropriate logical type for relating items having the respective logical types of A, f , R, a1 , . . . , an : (1)
A believes that R(a1 , . . . , an )
(2)
Bel(A, f , R, a1 , . . . , an ).
The primary aim of this Chapter is to show how, by developing apparatus rooted in Russell’s own early work, we can provide explications of these logical forms and Bel-relations that will facilitate the formal reduction of Russell’s theory— suitably formalized as the system MRTJ—to a plausible representationalist theory, thereby vindicating his much-maligned account of judgment, at least as regards attitudes reported de re.2 The secondary aim of this Chapter is to extract from these explications of Russell’s logical forms and Bel-relations certain key insights that may be enlisted in the aid of a fully adequate account that extends to attitudes reported de dicto and de se. Section 3.1 briefly sketches the ideas behind MRTJ and presents some adequacy conditions on any reductive vindication of such a theory. Section 3.2 details the formalities of MRTJ: its base language, underlying logic, and some of its characteristic
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axioms. Section 3.3 adduces some general considerations about mental representation and, against the same formal background, discusses some salient axioms of a representationalist theory that treats thought as inner speech in one’s mental language. Section 3.4 provides the crucial definitions and axioms which, when added to to obtain the theory + , function as bridge principles allowing the formal reduction of MRTJ to + . Section 3.5 argues that this reduction constitutes a vindication inasmuch as MRTJ, reconstructed within + , meets the adequacy conditions laid down in Section 3.1. Finally, Section 3.6 discusses how + ’s explication of the logical forms and de re belief relations invoked by MRTJ might be further refined to serve a more ambitious account that extends to belief reported de dicto and de se—an account in which logical forms are transmogrified into an analogue of Fregean modes of presentation and the vast family of disparate Bel-relations are reunited into a single dyadic belief-relation.
3.1 ADEQUACY CONDITIONS ON THE REDUCTION Before becoming immersed in the technicalities of MRTJ’s axiomatization, it will be useful to articulate certain adequacy conditions specific to our program of reductive vindication. Suppose—as will transpire in the next section—that MRTJ is set out as a formalized theory in which the general notions of ‘belief’, ‘logical form’, and ‘determining a truth condition’ are taken as primitive, along with some notation for describing the logical complexity of the logical forms of particular beliefs. A reduction of MRTJ to another theory whose primitives are taken as antecedently understood will not be adequate for the purpose of vindicating the former’s notions of logical forms, multiple relations and the like unless the reduced version of MRTJ provides plausible analyses of beliefs of arbitrary complexity. One test of the plausibility of such analyses is their ability to accommodate and explain the intuitive validity or invalidity of certain inferences about people’s beliefs. It is, e.g., notorious that the Substitutivity of Identity seems to fail in inferences about psychological attitudes like belief. The reduced theory should offer some account of this which is consistent with MRTJ’s commitment to the Substitutivity of Identity. In sum, then, we have (C1) as an adequacy condition on the reduced version of MRTJ: (C1)
It should give a plausible analysis of ‘A believes that p’ and ‘The belief that p is true/false’ for all grammatically admissible replacements of ‘p’, not just for atomic ones like (1). In particular, this analysis should shed light upon alleged failures of the Substitutivity of Identity.
Moreover, because MRTJ eschews propositions in favor of a multiplicity of typed belief relations among logical forms and various non-propositional objects of belief, the reduced version of MRTJ must additionally meet the adequacy conditions
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(C2)-(C5): (C2)
It should reveal what is common to the members of the infinitely large family of differently typed belief relations (i.e., that in virtue of which they are belief -relations).
(C3)
It should incorporate a precise account of the nature of the posited logical forms.
(C4)
It should explain how the obtaining of a belief relation brings the objects of the belief into relation with a logical form so conceived; and this explanation should account for the role of logical forms in fixing the logical structure of a belief—explaining, e.g., (a) how a specific order is thereby imposed on the objects of the belief and (b) why certain possible orderings make sense but others do not.
(C5)
It should neither appeal to propositions nor use locutions that might seem to presuppose propositions for their interpretation—such as, e.g., undefined predicates that take nominalized sentences (as opposed to names of sentences) as arguments.
While Russell’s versions are set up to comply nominally with (C5), it is a matter of record that none ever came close to satisfying (C1)-(C4). This is not surprising, since everything clearly depends upon what is said, on the one hand, about the nature of the posited logical forms and, on the other hand, about the way in which belief (even when false) supposedly unites its objects with logical forms so conceived. But both of these topics ultimately remain mysterious in Russell’s writings. Let us see if we can dispel the mystery. 3.2 THE FORMALITIES OF MRTJ 3.2.1 The Base Language and Underlying Logic MRTJ, we shall assume, is articulated in a quantificational language L embodying a simple type theory in which the basic type is i (the type of individuals) and in which counts as a type if t1 , . . . , tn do.3 (Type indices appear as right superscripts on terms.) L contains variables of every type and a finite selection (borrowed from English) of primitive names for the individuals, properties and relations that serve as objects of judgment. (We use ‘name’ as a synonym for ‘constant’. When t = i, we will also call a name of type t a predicate of type t. The variables and names of a given type constitute the terms of that type.) Two sorts of complex terms are permitted. When α1t1 , . . . , αntn (n ≥ 1) are variables and φ is a formula in which none of α1 , . . . , αn occurs bound, L counts λ-abstracts of the form [λα1t1 . . . αntn : φ] as complex terms of type . And where β t is a variable occurring free but nowhere bound in the formula ψ, L counts a definite
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description of the form (ιβ t )ψ as a complex term of type t. For future reference, let us call a formula pure iff it contains no primitive names. The underlying logic treats the sentential connectives (‘∼’, ‘&’, ‘∨’, ‘→’, ‘≡’) in classical fashion and subjects λ-abstracts to the familiar principles of λ-conversion. Identity is also treated classically: subject to the usual restrictions on free variables, every instance of α t = β t → (φ ≡ φ(β //α )) is an axiom. However, in light of L’s syntactic treatment of definite descriptions as terms, ‘∀’ will be so restricted as to ensure a free logic for such terms (‘∃’ being defined as usual via ‘∀’). In other words, where τ is a term containing no definite descriptions save those whose non-emptiness is assured by our axioms, φ(τ /α ) may be inferred from (∀α)φ ; but the conditional ψ(τ /β ) → φ(τ /α ) may be inferred from (∀α)φ for any term τ substitutable for both α and β, provided that the formula ψ is atomic. This departure from Russell as regards the treatment of definite descriptions is purely for technical convenience, and nothing essential to the results obtained below depends upon it. To the foregoing apparatus, we add the axiom scheme (Ax. 1), which formalizes the plausible (albeit metaphysically optional) thesis that if F and G are the indeed one and the same n-ary relation, then F cannot require its jth term to be identical with an object a while G requires its jth term to be identical with a distinct object b:4 (Ax. 1)
t
If φ and ψ are formulas, α1t1 , . . . , αj j , . . . , αntn are variables, θ tj and τ tj t
are terms distinct from each of α1t1 , . . . , αj j , . . . , αntn and foreign to both φ and ψ, then every instance of the following is an axiom (1 ≤ j ≤ n): t
[λα1t1 . . . αj j . . . αntn : αj = θ & φ] t
= [λα1t1 . . . αj j . . . αntn : αj = τ & ψ] → θ = τ . 3.2.2 Some Primitive Vocabulary and Axioms of MRTJ Since Russell never undertakes an axiomatic presentation of his multiple relation theory, it is not clear what primitives or axioms he would have favored for its articulation. For the purposes of our reconstruction, we shall assume that MRTJ is formulated in the language LMRTJ obtained by adding to L the four families of primitive predicates specified in (Pr1)-(Pr4): (Pr1)
the (n+2)-ary predicates Bel ,i,,i>,t1 ,...,tn > (n ≥ 0);
(Pr2)
the binary predicates Determines<<,i,,i>,> (n ≥ 0);
(Pr3)
the unary predicates LogicalForm<<,i,,i>> (n ≥ 0); and
(Pr4)
for each pure formula φ whose free variables (if any) are α1t1 , . . . , αkk and each variable δi foreign to φ, the quaternary predicate
t
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α . . . α δ/φ 1 k
of type <, i, , i>, which is counted as syntactically simple (hence as not containing occurrences of t α1t1 , . . . , αkk ).
The new terms of the sort α1 · · · αk δ/φ mentioned in (Pr4) serve as LMRTJ ’s official names for particular logical forms. The reason for including the seemingly redundant variable δ i will emerge later when we consider wholly general judgments. The informal interpretation of these special names (and their alphabetical variants) may be conveyed by the following sample glosses: • • • •
Read ‘G xi d i /G(x)’ as ‘the logical form of a (first-order) unary predication’. Read ‘G xi d i /∼G(x)’ as ‘the logical form of the negation of a (first-order) unary predication’. Read ‘F x1 i x2 i G y1 i y2 i d i /F(x1 , x2 ) ∨ G(y1 , y2 )’ as ‘the logical form of the disjunction of two (possibly unrelated, first-order) unary predications’. Read ‘d i /(∀xi )(x = x)’ as ‘the logical form of the (first-order) universal quantification of a predication of self-identity’.
A full axiomatic development of MRTJ will not be undertaken here. For our purposes it will suffice to concentrate upon certain key axiom schemes that might plausibly be proposed to govern the vocabulary introduced in (Pr1)-(Pr4). Let us begin with the connections between belief relations and logical forms. Since belief is supposed to essentially involve a relation to a logical form, [I] is an obvious candidate for axiomatic status: [I] Bel ,i,,i>,t1 ,...,tn > (α i , ρ <,i,,i> , β1t1 , . . . , βntn ) LogicalForm(ρ).
→
(Axioms peculiar to MRTJ will be indexed with bracketed roman numerals; logical axioms and the additional axioms of and + will be numbered as (Ax. 1), (Ax.2), etc.) The intuitive logic of de re belief ascriptions might be expected to supply more candidates for axiomhood. For example, although we presumably do not want MRTJ to rule out someone’s having two implicitly contradictory beliefs regarding the same object—say, one under the logical form G xi d i /G(x) and the other under G xi d i /∼G(x)—we might well be averse to the prospect of someone’s having an explicitly contradictory belief about an object under the logical form G xi d i /G(x) & ∼G(x). For the sake of argument, then, let us legislate this aversion into the axiom scheme [II]: [II] ∼Bel ,i,,i>,t1 ,...,tn > (α0i , α1t1 . . . αntn δ i /φ & ∼φ, β1t1 , . . . , βntn ). Notoriously, people’s beliefs are not closed under logical consequence, but we might at least expect some of their beliefs to respect the simple valid inferences that
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characterize the logical constants. Thus, e.g., a ‘conjunctive’ de re belief should be accompanied by de re beliefs matching the ‘conjuncts’ (though not always conversely). An appropriate axiom scheme for this kind of conjunctive belief would thus be [III]: [III]
Bel ,i,,i>,t1 ,...,tn > (α0 , α1 . . . αn δ/φ & ψ, β1 , . . . , βn ) → {Bel ,i,,i>,tg1 ,...,tgn > (α0 , αg1 . . . αgn δ/φ, βg1 , . . . , βgn ) & {Bel ,i,,i>,tj1 ,...,tjn > (α0 , αj1 . . . αjn δ/ψ, βj1 , . . . , βjn )},
where (i) αg1 , . . . , αgn are those of the variables α1 , . . . , αn free in φ, and βg1 , . . . , βgn are the corresponding terms from among β1 , . . . , βn ; (ii) αj1 , . . . , αjn are those of the variables α1 , . . . , αn free in ψ, and βj1 , . . . , βjn are the corresponding terms from among β1 , . . . , βn . Again, under the assumptions (i) and (ii), we might lay down [IV], which (roughly speaking) requires that when objects are believed to satisfy neither of two conditions, they should be separately believed not to satisfy each of those conditions: [IV]
Bel ,i,,i>,t1 ,...,tn > (α0 , α1 . . . αn δ/ ∼(φ ∨ ψ), β1 , . . . , βn ) → {Bel ,i,,i>,tg1 ,...,tgn > (α0 , αg1 . . . αgn δ/ ∼φ, βg1 , . . . , βgn ) & Bel ,i,,i>,tj1 ,...,tjn > (α0 , αj1 . . . αjn δ/ ∼ψ, βj1 , . . . , βjn )}.
Similarly, we might stipulate [V], which says (again roughly) that believing objects to satisfy some condition rules out believing that condition to be unsatisfied: [V] Bel ,i,,i>,t1 ,...,tn > (α0 , α1 . . . αn δ/φ, β1 , . . . , βn ) → ∼Bel ,i,,i>> (α0 , δ/ ∼(∃α1 ) . . . (∃αn )φ). No doubt numerous other principles of this ilk could be justified for beliefs of other basic logical forms, but having a complete list of them is not important for present purposes. As for the nature of logical forms themselves, we may lay down at least this much at the outset. A logical form f is a relational entity that determines a particular ontological structure Rf , the latter being a (possibly unexemplified) formal relation between ordinary properties, relations, and individuals. The chief constraint on the identity of the structure Rf derives from the role that a logical form is supposed to play vis-`a-vis the conditions for someone’s believing truly/falsely under it: viz., a case of believing under f is a case of believing truly/falsely under f iff the entities believed-about are/are not related by Rf . Accordingly, the logical form f must be distinct from the determined structure Rf . For in a case of believing falsely
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under f , the entities believed-about are of course not related by Rf . Yet even if Rf is not exemplified by anything at all, f must still be the logical form under which the subject believes, where this naturally suggests that f (itself a relational entity) must somehow be ‘exemplified in the belief’. By this we do not mean that there is an extra entity, ‘the belief’, which is a relatum of f , but merely that any case of believing ‘under’ f must involve f ’s actually relating some items. (As it stands, MRTJ offers no account of f ’s relata; in our proposed reduction, we shall identify them with certain mental representations.) In sum, whether or not the structure it determines relates anything on the side of the world, the logical form under which one believes must relate certain things on the side of the believer, fixing (in a way that Russell never explains) the distinctive way that the believer is related to the entities believed-about. Now for technical reasons that will emerge in due course, we have chosen to speak of the ontological structures in question at one remove, by way of correlated relations with an extra argument-place. Thus, e.g., the structure determined by the logical form G xi d i/G(x) of a first-order unary predication is taken to be the corresponding ternary formal relation [λG xi d i : G(x)] instead of the binary formal relation [λG xi : G(x)]. Generalizing, we have the axiom scheme [VI]: [VI]
Determines (α1t1 . . . αntn δ i /φ, [λα1t1 . . . αntn δ i: φ]).
(Since ‘Determines’ requires arguments of different types, the very idea of a logical form being identical to the corresponding structure cannot be mooted in LMRTJ .) We shall leave unsettled the question whether a given structure can be determined by more than one logical form. But we shall adopt axiom scheme [VII], which disallows the possibility of the same logical form determining two distinct structures: [VII] (Determines(α1t1 . . . αntn δ i /φ, y ) & Determines(α1t1 . . . αntn δ i /φ, z )) → y = z. What motivates [VII] is the intuitive notion of ‘determining’at work here, according to which the logical form of a belief about e1 , . . . , en somehow encodes a unique ontological structure that e1 , . . . , en must exemplify for that belief to be true. Two beliefs about the same entities e1 , . . . , en under the same logical form must ipso facto have identical truth conditions. Indeed, it would seem that from the standpoint of their role in a multiple relation theory of judgment, logical forms just are the determiners of unique ontological structures. Accordingly, let us add the axiom scheme [VIII]: [VIII]
(∀x<,i,,i> ){LogicalForm(x) ≡ (∃!y )Determines(x, y)}.
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Given the foregoing, (T1) is a theorem scheme: (T1)
LogicalForm(α1t1 . . . αntn δ i /φ).
MRTJ, of course, treats all belief ascriptions as wholly transparent. Some (e.g., Salmon (1986) and Soames (1987a, 1987b, 2002)) have argued on Russell’s behalf that so-called attitudinal opacity is an illusion—not a syntactic/semantic datum but merely a pragmatic phenomenon—hence that there are no real substitutionfailures in attitudinal contexts to contend with in the first place. Be that as it may, MRTJ does at least have a way of handling apparent substitution-failures involving definite descriptions, despite treating them syntactically as terms. Consider, e.g., the inference from (3a-b) to (3c): (3)
a. George IV believes that Scott = the author of Waverly. b. The author of Waverly = the author of Marmion. ∴ c. George IV believes that Scott = the author of Marmion.
Because it can make fine-grained distinctions of logical form, MRTJ can in principle formalize this inference in any of the four ways (4)-(7): (4)
a. Bel ,i,,i>,i,i> (GeorgeIV , xi yi d i/x = y, Scott, (ιyi )AuthorOf (y, Waverly)). b. (ιyi )AuthorOf (y, Waverly) = (ιyi )AuthorOf (y, Marmion). ∴ c. Bel ,i,,i>,i,i> (GeorgeIV , xi yi d i/x = y, Scott, (ιyi )AuthorOf (y, Marmion)).
(5)
a. Bel ,i>,i,,i>,i,> (GeorgeIV , xi F d i/x = (ιz i )Fz, Scott, [λyi : AuthorOf (y, Waverly)]). b. (ιxi )AuthorOf (x, Waverly) = (ιxi )AuthorOf (x, Marmion). ∴ c. Bel ,i>,i,,i>,i,> (GeorgeIV , xi F d i/x = (ιz i )Fz, Scott, [λyi : AuthorOf (y, Marmion)]).
(6)
a. Bel ,i>,i,,i>,i,> (GeorgeIV , xi F d i/x = (ιz i )Fz, Scott, [λyi : AuthorOf (y, Waverly)]). b. (ιxi )AuthorOf (x, Waverly) = (ιxi )AuthorOf (x, Marmion). ∴ c. Bel ,i,,i>,i,i> (GeorgeIV , xi yi d i/x = y, Scott, (ιxi )AuthorOf (y, Marmion)).
(7)
a. Bel ,i,,i>,i,i> (GeorgeIV , xi yi d i/x = y, Scott, (ιxi )AuthorOf (y, Waverly)). b. (ιxi )AuthorOf (x, Waverly) = (ιxi )AuthorOf (x, Marmion). ∴ c. Bel ,i>,i,,i>,i,> (GeorgeIV , xi F d i/x = (ιz i )Fz, Scott, [λyi : AuthorOf (y, Marmion)]).
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Now (4), which is univocal with respect to ‘Bel’ and the logical form assignment in premises and conclusion, not only is a plausible analysis of the transparent reading of (3) but also is formally valid, being an instance of the Substitutivity of Identity. This leaves (5)-(7) as candidates for representing the wholly or partly opaque readings of (3) on which it is invalid. Each of (5)-(7) either equivocates on ‘Bel’ and the logical form assignment or changes the subject by making the statements about properties instead of (or in addition to) individuals. None of (5)-(7) is valid solely in virtue of our logical axioms, although this leaves it open that a deeper understanding of what it is to have a belief ‘under’ a logical form might lead us to accept one of them. (5), which involves no equivocation, looks promising as a rendering of the fully opaque construal of (3) and is intuitively invalid. Here the intuition is that if George IV thinks of Scott as uniquely authoring Waverly, then the mere fact that Scott uniquely authored both Waverly and Marmion offers no assurance that George IV also thinks of Scott as uniquely authoring Marmion. (7) likewise seems invalid. The fact that the two novels had the same author and that George IV has an identity-belief that happens to be about Scott and the author of Waverly is insufficient grounds for concluding that George IV thinks of Scott as the author of Marmion (or ‘as’ of any other kind, for that matter). The intuitive status of (6) is less clear and will be left to our reduction to settle.
3.2.3 Truth in MRTJ Where f is a logical form, let us call the ontological structure it determines the value of f and introduce for it the following abbreviatory notation: (Df.1) Where ρ is a term of type <, i,, i>: |ρ| =def . (ιγ )Determines(ρ, γ ). We have seen that the value | f | of a logical form f is intuitively connected with the truth conditions for beliefs under f . Can this intuitive connection be made explicit in MRTJ itself? As regards the truth-values of ‘belief facts’, it is easy to define typed counterparts of ‘truly believes’ and ‘falsely believes’. The basic idea is simple: one bears the multiple relation of truly/falsely believing to such-and-such items under a given logical form f iff (i) one bears to those items under f the multiple relation of believing and (ii) the value of f does/does not relate those items (in the indicated order). Formally, this amounts to taking (Df.2) and (Df.3) as definition schemes: (Df.2) TrBel ,i,,i>,t1 ,...,tn > =def . [λα i ρ <,i,,i> β1t1 . . . βntn : Bel ,i,,i>,t1 ,...,tn > (α, ρ, β1 , . . . , βn ) & |ρ|(β1 , . . . ,βn , α)].5
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(Df.3) FlsBel ,i,,i>,t1 ,...,tn > =def . [λα i ρ <,i,,i> β1t1 . . . βntn : Bel ,i,,i>,t1 ,...,tn > (α, ρ, β1 , . . . , βn ) & ∼|ρ|(β1 , . . . , βn , α)]. Thus, e.g., (8) will be paraphrased in MRTJ by (9), which is provably equivalent in MRTJ to (10): (8)
Othello truly believes that Desdemona loves Cassio.
(9)
TrBel ,i,i,i>,i,,i>,,i,i> (Othello, F xi yi d i /F(x, y), Loves, Desdemona, Cassio).
(10)
Bel ,i,i,i>,i,,i>,,i,i> (Othello, F xi yi d i /F(x, y), Loves, Desdemona, Cassio) & Loves(Desdemona, Cassio).
Clearly, however, the definition schemes (Df.2) and (Df.3) will not supply what Russell wanted of MRTJ, viz. (stratified) notions of truth and falsehood for beliefs that will serve in place of the traditional notions of propositional truth and falsehood that he jettisoned along with the propositions themselves. The obvious problem is that infinitely many truths and falsehoods may go unbelieved, so that there will not be enough surrogate ‘belief facts’ to go around (hence not enough real cases of believing-truly or believing-falsely for (Df.2) and (Df.3) to take up the slack). However, even where there is no fact that someone believes, say, that Rab, there is still the corresponding relation between a thinker x and a logical form f that consists in (i) x’s bearing the appropriate multiple relation to R, a,b under f and (ii) f ’s being such-and-such a logical form h. Taking h to be F y1i y2i d i /F(y1 , y2 ), this relation between thinker and logical form would be the complex relation Bh:R,a,b defined by (Df.4): (Df.4)
Bh:R,a,b =def . [λxi f ,i,i,i>,i,,i>,,i,i> : f = F y1i y2i d i /F(y1 , y2 ) & Bel ,i,i,i>,i,,i>,,i,i> (x, f , R , a, b)].
In sentences of the sort ‘The belief that a bears R to b is true’, we can now think of (11) as paraphraseable by (12), to which the relation Bh:R,a,b is assigned as referent: (11)
the belief that a bears R to b
(12)
beliefs under the logical form of a binary predication involving R, a,b respectively.
In general, then, for any logical form g <,i,,i> and entities e1 , . . . , en of respective types t1 , . . . , tn , we will have as a belief-surrogate the complex relation
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Bg:e1 ,...,en defined by (Df.5): (Df.5)
Bg:e1 ,...,en =def . [λxi f <,i,,i> : f = g & Bel ,i,,i>,t1 ,...,tn > (x, f , e1 , . . . , en )].
To complete the picture, we need a suitable family of typed truth-predicates for such belief-surrogates. What immediately suggests itself is an appeal to the notion of the value of the logical form relating the objects of the belief. Tailored to fit (Df.5), a suitable definition scheme would be (Df.6): (Df.6)
For any term ρ of type <, i, , i> and terms α1t1 , . . . , αntn : True<,i,,i>>> (Bρ:α1 ,...,αn ) =def . (∃β i )|ρ|(α1 , . . . , αn , β),
with ‘False<>> ’being defined as ‘∼True<>> ’. In other words, a belief-surrogate Bg:e1 ,...,en is ‘true’ just in case the value of g actually relates e1 , . . . , en to some object w. Trivially, we will have as theorems all instances of the corresponding truth scheme (T2), and from the instance of (T2) for the particular belief-surrogate Bh:R,a,b discussed above, theorem (T3) will follow: (T2) True(Bα1 ...αn δ/φ:β1 ,...,βn ) ≡ (∃γ i )([λα1t1 . . . αntn δ i:φ](β1 , . . . , βn , γ )). (T3)
True(Bh:R,a,b ) ≡ R(a, b).
Using this apparatus, we can translate a vernacularism like (13) by its perspicuous counterpart (14), which, however unwieldy, will at least have the virtue of being demonstrably equivalent to (15): (13) The belief that Desdemona loves Cassio is true. [i.e.: Beliefs under the logical form of a binary predication involving loving, Desdemona, and Cassio respectively are true.] (14) True,i,i,i>,i,,i>> ([λxi f <<,i,i,i>,i,,i> : f = F y1i y2i d i /F(y1 , y2 ) & Bel ,i,i,i>,i,,i>,,i,i> (x, f , Loves, Desdemona, Cassio)]). (15)
Loves(Desdemona,Cassio).
These results, together with the fact that MRTJ treats the logical complexity of a belief’s content as a function of its logical form, ensure that the foregoing account of truth for belief-surrogates applies not just to the ‘atomic’ ones but to the ‘molecular’ ones as well.
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3.3 THE THEORY Our concern is to vindicate MRTJ, not the various doctrines entangled with Russell’s own versions of the multiple relation theory (e.g., his Principle of Acquaintance and his sense-datum phenomenalism). In particular, we carry no brief for his curious view that the mind somehow directly arranges the (non-mental) objects of judgment in accordance with a certain logical form. Instead, we look for vindication in the direction of a representational theory of mind (RTM) according to which what gets manipulated in thought are not the nonmental objects of thought per se but mental representations of those objects. Specifically, we shall consider a formal theory that embraces RTM in the specific form of the so-called Language of Thought Hypothesis (LOT), which we understand to be the conjunction of the following five theses:6 (i) thinking is a matter of tokening sequences of mental representations, which constitute the domain of relevant mental processes; (ii) for each propositional attitude A there is a functionally definable psychological relation RA such that, for any agent a and thought-content p, a bears A to p if and only if there is a mental representation Mp to which a bears RA and which ‘means’ p; (iii) such mental representations (at the type level) form a language-like system— i.e., they are, in effect, the sentences of the agent a’s language of thought (a’s ‘Mentalese’)—which is ontologically and explanatorily prior to the agent’s public language(s) if any and for which an appropriate compositional syntax and semantics could in principle be provided [such a semantics treating a’s Mentalese as a univocal idiom each of whose terms makes a single, invariable semantic contribution to the truth condition of any Mentalese sentence in which it occurs]; (iv) the mental operations involved in a’s thinking are causally sensitive to the form (syntactic structure) of the sentences of a’s Mentalese. (v) for each sentence-type of an agent’s language of thought, the property of being a token of that sentence-type is, at some appropriate level, a functionally definable property. Since our aim is to use LOT in vindicating MRTJ, we shall be assuming its truth rather than directly arguing for it here.7 (However, its usefulness in unraveling the mysteries of MRTJ could be viewed as counting in favor of LOT, provided of course that one regards such mysteries as worth solving in the first place.) Ironically, Russell’s first, very brief and tentative sketch of his theory (Russell 1906/08) did involve mental representatives of objects in addition to the objects themselves; and after officially renouncing the multiple relation approach (Russell 1919) he immediately embraced a new view of belief as a relation to certain mental representations constructed from mental images standing for objects, properties,
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and relations. Perhaps what prevented Russell from exploiting his latent affinity for mental representations in the interest of his multiple relation theory of judgment was his failure to get beyond the unprofitable traditional talk of mental imagery to some version of LOT. In any event, let us see whether, availing ourselves of LOT, we can do better on behalf of MRTJ. As loyal type-theorists, we assume that languages of thought have a type-structure like that of L. Since we will both be talking in English about the extended language L of and using L in turn to talk about the syntax and semantics of Mentalese, it will be useful to adopt the following notational conventions to keep track of our hierarchy of languages. In our English metalanguage for L : – Expressions of the form φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >] are restricted variables ranging over formulas of L whose free variables (in order of first occurrence) are α1 , . . . , αk and whose bound variables (in order of first occurrence) are αk+1 , . . . , αn . –
Uppercase Greek letters are restricted metavariables that range solely over the boldfaced variables of L (see below).
– Sellarsian dot-quotes (Sellars 1963) are used for talking about the grammatical and inferential role of expressions of Mentalese. (For any expression σ of MRTJ, an expression of agent a’s Mentalese is a • σ • iff it plays therein the same grammatical/inferential role that σ plays in MRTJ.) The language L itself contains the following additions to the basic formalism of L: – Boldfaced Roman letters are used as restricted variables of type ranging over Mentalese expression-kinds (construed as type properties, so that to token an expression-kind is literally to exemplify it). – Where α is a term designating an agent a, M α designates a’s language of thought, i α is a name for the M a -type of individuals, and t α (with or without subscripts) is a variable ranging over M a -types (where the identity of the agent a is obvious, the superscripts will be omitted).8 – The vergules ‘«’ and ‘»’ are used to form structural-descriptive names of complex Mentalese expression-kinds. Thus, e.g., where ‘∧ ’ signifies concatenation of Mentalese tokens, the expression «(S1 &S2 )» is a type name for the property of being an individual x such that x = y1 ∧ y2 ∧ y3 ∧ y4 ∧ y5 for some individuals y1 , y2 , y3 , y4 , y5 such that y1 is a • (• and y2 = S1 and y3 is a • &• and y4 = S2 and y5 is a • )• . – Boldfaced logical symbols are names for the Mentalese symbol-kinds that are their counterparts: e.g., ‘&’ names the property of being a Mentalese • &• ; ‘)’ names the property of being a Mentalese • )• ; and so on). In
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particular, boldface expressions of the sort 1 . . . k / are the Mentalese counterparts of LMRTJ ’s official names for particular logical forms. The following vocabulary (minus type indices and with the obvious interpretations or those supplied in brackets) is employed for discussing the syntax and semantics of a thinker’s Mentalese sentences and the thinker’s psychological relations to those sentences: VarType(, t, M α ); NameType(, t, M α ); TermType(, t, M α ); Sentence(, M α ); Expression(, M α ); SimpleIn(, M α ); FreeIn(, ); OccursIn(, ); (1 . . . n /1 . . . n ); DenIn(, β t , M α ) [i.e., denotes9 β t in M α ]; Distinct(1 , 2 , . . . , m ) [i.e., &1≤i =j≤m (i = j )]; SynRel(µ) [i.e., µ is a syntactic relation among Mentalese expressions]; Accepts(α, ). In axiom, theorem and definition schemes where ‘t’ is employed as a schematic letter whose replacements are particular type indices of our formalism, its primed counterpart ‘t ’ is to be understood as a schematic letter whose replacements are the boldfaced indices for the corresponding Mentalese types. (Thus, e.g., if ‘t’ is replaced by ‘’ in an instance of a scheme also containing ‘t ’, then ‘t ’ must be replaced by ‘’ in that instance.) The metalinguistic expression ‘t ’ must not be confused with the object language variable ‘t’. In the case of L ’s syntactic vocabulary, the corresponding axiom schemes of are predictable. There will be, e.g., an axiom scheme to guarantee that «[λ1 . . . m :]» will count as a term of type in M α if is a sentence and 1 , . . . , m are variables of respective types t 1 , . . . , t m in M α ; another axiom scheme to guarantee that if «[λ1 . . . m :]» is a term of type in M α with foreign to , then «1 . . . m /» is a term of type <, i,, i> in M α ; and so on. Since these axiom schemes are as uninteresting as they are predictable, there is no point to enumerating and formalizing them here. For present purposes there is no need for assumptions about the make-up or semantics of anyone’s non-logical Mentalese vocabulary. It will, however, be important to specify the denotation of ‘pure’ Mentalese λ-abstracts—i.e., terms of the sort «[λv1 . . . vk : S]» in which S contains no primitive Mentalese names of any type. So will require a corresponding semantic axiom scheme. To formulate this axiom scheme (and others to come), we introduce the useful notion of the ‘shadow’ of a pure formula. Suppose φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >] is a pure formula of L. Then, for any distinct boldfaced letters 1 , . . . , k , k+1 , . . . , n : An expression is the shadow of φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >] under [<1 , . . . , k >; <k+1 , . . . , n >] iff: results from φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >] by first replacing α1 , . . . , αk , αk+1 , . . . , αn with 1 , . . . , k ,
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k+1 , . . . , n and then replacing any remaining non-boldfaced symbols with their boldface counterparts from L ’s special vocabulary for Mentalese. (For example: (∃v4 )(v1 (v4 ) & v2 (v3 )) would be the shadow of (∃x)(F(x) & G(y)) under [<‘v1 ’, ‘v2 ’, ‘v3 ’>; <‘v4 ’>]; and (∃v1 )(∃v2 )v2 (v1 ) would be the shadow of (∃x)(∃F)F(x) under [<>; <‘v1 ’, ‘v2 ’>].) tk+1 t Where is the shadow of the pure formula φ[<α1t1 , . . . , αkk >; <αk+1 , . . . , αntn >] under [<1 , . . . , k >; <k+1 , . . . , n >] and is a boldfaced letter foreign to , has the axiom scheme (Ax.2) for the semantic predicate ‘DenIn’ of type <; >: (Ax.2)
(Distinct(1 , . . . , n , ) & VarType(1 , t1 ,Mγ ) & . . . & VarType(n , tn ,Mγ ) & VarType(,i,Mγ ) & ∼OccursIn(, ))→ t DenIn(«[λ1 . . . k : ]», [λα1t1 . . . αkk δ i : φ[α1 , . . . , αk >; <αk+1 , . . . , αn >]], M γ ).
Thus, since ‘f(x)’ is the shadow of ‘F(x)’, under [<‘f ’,‘x’>; <>], it follows from (Ax.2) that if f,x,d are distinct variables of respective types , i and i in y’s Mentalese, (d foreign to «f (x)»), then y’s Mentalese name «[λfxd: f (x)]» denotes the type <, i, i> relation [λF xi d i : F(x)]. Given the adoption of LOT, it is natural to model the having of beliefs as the ‘acceptance’ of certain sentences of one’s Mentalese. Since, however, most of a person’s beliefs at any moment are merely tacit, the corresponding notion of acceptance must not require occurrent tokening of Mentalese sentences. Accordingly, let us gloss Accepts(x,S) as x is disposed as if x inwardly and assertively tokens S),10 where to token S—a property—is to produce something exemplifying it. will of course contain axioms characterizing this relation. The following, admittedly incomplete list of axioms (derived, with modifications, from Loar (1981: 72)) may serve to convey the flavor of what would be involved: (Ax.3.1)
(Sentence(S1 ,Mx ) & Sentence(S2 ,Mx )) → ∼Accepts(x, «S1 & ∼S 2 »).
(Ax.3.2)
(Sentence(S,Mx ) & Accepts(x, S)) → ∼Accepts(x, «∼S»).
(Ax.3.3)
(Sentence(S1 ,Mx ) & Sentence(S2 ,Mx ) & Accepts(x, «S1 & S2 »)) → Accepts(x, «S1 ») & Accepts(x, «S2 »)).
(Ax.3.4)
(Sentence(S1 ,Mx ) & Sentence(S2 ,Mx ) & Accepts(x, S1 ) & Accepts(x, S2 )) → ∼Accepts (x, «∼(S1 & S2 )»).
(Ax.3.5)
(Sentence(S1 ,Mx ) & Sentence(S2 ,Mx ) & Accepts (x, «∼(S1 ∨ S2 )»)) →(Accepts(x, «∼S1 ») & Accepts(x, «∼S2 »)).
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(Ax.3.6)
(NameType(a,t,Mx ) & NameType(b,t,Mx ) & Sentence(S,Mx ) & Accepts(x, S) & Accepts(x, «a = b»)) → Accepts(x, S(a //b ))11
(Ax.3.7)
(Sentence(S,Mx ) & Accepts(x, S) → ∼(∃v)(∃a)(∃t){VarType(v,t,Mx ) & NameType(a,t,Mx ) & ∼OccursIn(v, S) & OccursIn(a, S) & Accepts(x, «∼(∃v)S(v /a )»)}.
A comprehensive list of axioms for ‘Accepts’, supplemented with principles relating acceptance to other psychological relations to Mentalese sentences, might even provide the basis for a functional definition of ‘Accepts’. But since it is controversial exactly what such a list should contain, we shall content ourselves here with the foregoing sample. The question now is how the resources of could be pressed into the service of vindicating MRTJ. 3.4 THE BRIDGE PRINCIPLES AND REDUCTION OF MRTJ TO + The reducing theory + is the extension of obtained by adding appropriate definition and axiom schemes to serve as bridge principles connecting the primitive vocabulary (Pr1)-(Pr4) of LMRTJ to that of L . Let us begin with the crucial definit tion scheme that allows the predicates α1t1 . . . αkk δ i /φ —and hence MRTJ’s talk of logical forms—to be understood purely in terms of the vocabulary of L . tk+1 t Where is the shadow of the pure formula φ[<α1t1 , . . . , αkk >; <αk+1 , . . . αntn >] under [<1 , . . . , k >; <k+1 , . . . , n >] and is a boldfaced letter foreign to , we take (Df.7) as a definition scheme of + : t
(Df.7) α1t1 . . . αkk δ i /φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >] =def t [λxyi zd i : x = [λα1t1 . . . αkk δ i : φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >]] & (∃w){NameType(w, , My ) & DenIn(w, x, My ) & [λrsi u: (∃1 ) . . . (∃n )(∃) (Distinct(1 , . . . , n , ) & VarType(1 , t1 ,Ms ) & . . . & VarType(n , tn ,Ms ) & VarType(, i,Ms ) & ∼OccursIn (, «») & r = «[1 . . . k :]») & u = «1 . . . k /»)]wyz}].12 The import of this complicated definition scheme is best appreciated by way of a simple example. Since ‘f (x)’ is the shadow of the pure formula ‘F (xi )’ under [<‘f’,‘x’>; <>], we have the definition (16) as an instance of (Df.7): (16)
F xi d i /F(x) = def . [λv<,i,i> yi zd i : v = [λF xi d i : F(x)] & (∃w){NameType(w, <, i, i>,My ) & DenIn(w, v, My ) & [λrsi u: (∃f )(∃x)(∃d)(Distinct(f , x, d) & VarType(f , ,Ms ) &
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VarType(x, i,Ms ) & VarType(d,i,Ms ) & ∼OccursIn(d, «f (x)») & r = «[λfxd: f (x)]») & u = «fxd/f(x)»)]wyz}]. From (16) we learn that what MRTJ calls ‘F xi d i /F(x)’—alias ‘the logical form of a (first-order) unary predication’—may be identified with a certain complex relation R between a structure v, person y, expression z of My , and arbitrary individual d . In effect, Rvyzd obtains just in case: (a) v is the structure [λF xi d i : F(x)]; (b) for some distinct variables f,x,d of respective My -types ,i,i the term «[λfxd: f (x)]» denotes the structure v in My ; and (c) z is the corresponding term «fxd/f (x)» of My . According to MRTJ, F xi d i/F(x) determines the ontological structure [λF xi d i : F(x)]. But by (16), F xi d i/F(x) ‘contains’ [λF xi d i : F(x)] in the sense of being a relation that requires its first term to be that very structure. This suggests a general definition of determining via ‘containing’, which is spelled out in (Df.8) with the aid of the predicate ‘SynRel’ that expresses the higher-order property of being a syntactic relation among expressions of a person’s Mentalese: (Df.8) Determines<<,i,,i>,i>,> =def [λF <,i,,i> G : (∃K <,i,> ){SynRel<<,i,>>(K) & F = [λx yi zd i : x = G & (∃w){NameType(w, , My ) & DenIn(w, x, My ) & Kwyz}]}]. For present purposes, it is not important exactly how ‘SynRel’ is ultimately characterized. All we need assume here is that it has been so axiomatized in + as to yield as a theorem any formula in which ‘SynRel’ is applied to an instance of the schematic λ-term used in (Df.7); in other words, we shall assume that (T4) is a theorem scheme: (T4) SynRel([λrsi u: (∃1 ) . . . (∃n )(∃)(Distinct(1 , . . . , n , ) & VarType(1 , t 1 , Ms ) & . . . & VarType(n , tn , Ms ) & VarType(, i, M s ) & ∼OccursIn(, ) & r = «[λ1 . . . k : ]») & u = «1 . . . k /»)]). (T4) ensures that instances of this schematic λ-term count as expressing a ‘syntactic condition’ on expressions of a person’s Mentalese. Courtesy of (Ax. 1) and the definitions (Df.7) and (Df.8), the axiom scheme [VII] of MRTJ is now a theorem scheme of + .13 With ‘Determines’ defined, we can now equate what MRTJ calls ‘being a logical form of a given type <, i, , i>’ with being a certain relation of type <, i, , i> that determines relations of the corresponding lower type
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. This is recorded in (Df.9): (Df.9)
LogicalForm<<,i,,i>> =def . [λx<,i,,i> : (∃y )Determines(x, y)].
In light of (Ax. 1), (Df.8), and (Df.9), MRTJ’s axiom schemes [VIII] and [VI] are theorem schemes of + . Having embraced LOT, we shall naturally wish to speak not only about a logical form determining a structure but also about its being a logical form of something— viz., someone’s Mentalese sentence. While it would be possible to define a relation FormOf that would apply to any Mentalese sentence, our project here requires only a more restricted version that applies to ‘pure’ Mentalese sentences, i.e. those all of whose simple terms are variables. Accordingly, we schematically define FormOf as the following complex relation: (Df.10) FormOf<<,i,,i>,,i> =def . [λf <,i,,i> Sxi : LogicalForm(f ) & Sentence(S, M x ) & (∃v1 ) . . . (∃vk )(∃d) {(Distinct(v1 , . . . , vk , d) & VarType(v1 , t1 , M x ) & . . . & VarType(vk , tk , M x ) & VarType(d, i, M x ) & (∀v0 )(FreeIn(v0 , S) ≡ (v0 = v1 ∨ . . . ∨ v0 = vk ))& ∼OccursIn(d, S) & (∀r)(∀t x ) ((NameType(r, t, M x ) & SimpleIn(r, M x )) → ∼OccursIn(r, S)) & f (|f |, x, «v1 . . . vk d/S», x)}]. In other words, FormOf is that relation between a logical form f , sentence S, and agent x consisting in S’s being a pure sentence of M x containing free variables v1 , . . . , vk such that, for some M x -type i variable d foreign to S, f relates its value to x and to the corresponding term «v1 . . . vk d/S» of M x . (Df.10) enables us to prove every instance of the important scheme (T5), in tk+1 t which is the shadow of the pure formula φ[<α1t1 , . . . , αkk >; <αk+1 , . . . , αntn >] under [<1 , . . . , k >; <k+1 , . . . , n >]: (T5)
(Distinct(1 , . . . , n ) & VarType(1 , t1 , M γ ) & . . . & t VarType(n , tn , M γ )) → FormOf(α1t1 . . . αkk δ i /φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >], «», γ i ).
Thus, e.g., (‘G(v)’ being the shadow of ‘G (xi )’ under [<‘G’,‘v’>; <>]) we can prove that where G and v are free variables of respective Ma -types and i, the logical form G xi d i /G(x) is a logical form of the elementary Ma -sentence «G(v)». This is recorded in theorem (T6): (T6)
(∀ai )(∀G)(∀v){{Distinct(G, v) & VarType(G, , M a ) & VarType(v, i, Ma )} → FormOf((G xi d i/G(x), «G(v)», a)}.
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The axiom scheme (Ax.2) that + inherits from specifies the denotata of Mentalese counterparts of relational names of the form [α1 . . . αk δ:φ] . But in order to complete the connection of MRTJ’s vocabulary for logical forms with ’s vocabulary for their mental representations, we need to specify the denotata of the Mentalese counterparts of relational names of the form α1 . . . αk δ/φ . Intuitively, these Mentalese counterparts are supposed to be names of logical forms. Accordingly, we suppose that, where is the shadow of the pure formula tk+1 t φ[<α1t1 , . . . , αkk >; <αk+1 , . . . , αntn >] under [<1 , . . . , k >; <k+1 , . . . , n >] and is is a boldfaced letter foreign to , the instances of scheme (Ax.4) are axioms of + : (Ax.4)
(Distinct(1 , . . . , n , ) & VarType(1 , t1 , M γ ) & . . . & VarType(n , tn , M γ ) & VarType(, i, M γ ) & ∼OccursIn(, )) → DenIn(«1 . . . k /», α1 . . . αk δ/φ[<α1 , . . . , αk >; <αk+1 , . . . , αn >], M γ ).14
Having said in + what sort of relation MRTJ’s logical forms are and what it is for one of them to be a logical form of a (pure) Mentalese sentence, we must now specify the nature of the multiple relation of belief in which logical forms are to figure as terms. Suppose, for the sake of illustration, that F y1 i y2 i d i /F(y1 , y2 ) is the logical form invoked for ‘Desdemona loves Cassio’ and that (17) is MRTJ’s analysis of (18): (17)
Bel,i,i,i>,,i,i,i> (Othello, F y1 i y2 i d i /F(y1 , y2 ), Loves, Desdemona, Cassio).
(18)
Othello believes that Desdemona loves Cassio.15
The idea about ‘Bel’ we want to articulate in + is that the truth of (18) requires something like the following: (i) that Othello assertively tokens in his language of thought some sentence S comprising names of loving, Desdemona, and Cassio; and (ii) that these names are syntactically arranged in S in exactly the way dictated by F y1 i y2 i d i /F(y1 , y2 ) (so that S will be a relational sentence of Othello’s Mentalese whose binary predicate, first argument, and second argument are respectively the aforementioned names of loving, Desdemona, and Cassio). This would be straightforward were it not for a difficulty that arises in trying to generalize the account to cover nested beliefs. A purported vindication of MRTJ must surely take seriously the latter’s guiding idea—that belief is a multiple relation involving thinker, logical form, and the various entities thought about. If so, however, then that guiding idea should be applied across the board, to any proffered analysis of belief ascriptions in Mentalese as well as in English! (This is part of the point of the adequacy condition (C5), which bars appeal to any unanalysed Mentalese analogue of a ‘that’-clause construction.)
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Now MRTJ analyses an iterated belief ascription like (19) by something of the form (20): (19)
Iago believes that Othello believes that Desdemona loves Cassio.
(20)
Bel 1 (Iago, f1 , Bel 2 , Othello, f2 , Loves, Desdemona, Cassio).
In (20), however, there are two logical forms to contend with—f1 , which determines how Bel1 relates Iago to all the other constituents, and f2 , which determines how Iago thinks of Bel2 as relating Othello, loving, Desdemona and Cassio! In other words, logical forms must be capable of figuring among the objects of a belief as well. The difficulty facing the attempt to generalize the account to cover (20) is this: it is not enough merely that Iago should accept a Mentalese sentence whose structure is dictated by f1 and whose terms respectively denote believing, Othello, loving, Desdemona, Cassio, and a certain logical form f2 (for Othello’s belief). Rather, Iago must represent the logical form of Othello’s alleged belief in some canonical way that reveals to Iago the conditions under which Othello’s belief would be true, i.e., puts Iago in a position to appreciate those truth conditions (if he considers the matter, is smart enough, etc.). The need for such canonical representation of the logical forms of others’ beliefs is intrinsic to any view of thinking as a kind of inner speech. This is most easily seen when we pretend that the inner speech in question occurs in a natural language like English. Imagine, e.g., a situation like the following. Iago, peering through a telescope, dimly sees a man a crouched behind a bush spying on a woman b who is embracing a man c. Iago, thinking in approved multiple-relation jargon, then says to himself (21) while mentally ostending a, b, and c respectively in connection with the tokens of ‘he’, ‘her’, and ‘him’: (21)
He has a belief of the binary first-order relational sort about her and him.
But—unbeknownst to Iago—a = Othello, b = Desdemona, and c = Cassio. In such a situation, a wholly transparent construal of (19) would presumably be true, and the logical form of Othello’s alleged belief (viz., binary first-order relational predication) is recoverable from what Iago has said to himself. On the other hand, suppose Iago had instead said to himself (22): (22)
He has a belief of his favorite sort about her and him.
This is plainly not enough to make true even a wholly transparent construal of (19), precisely because the logical form of Othello’s alleged belief would no longer be recoverable from what Iago had said to himself. In light of the foregoing, we need to ensure that when a logical form v1 . . . vk δ/ψ occurs among the objects of a person’s belief, the person’s mental name for it is ‘canonical’ in the sense of being a Mentalese • v1 . . . vk δ/ψ• .
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Accordingly, we define by cases the ternary predicate ‘CNO’ (read: ‘. . . is a canonical name of . . . in . . .’s Mentalese’). For the cases in which t ∗ is a type of the sort <, i, , i>, we provide definition scheme (Df.11): ∗
∗
(Df.11) CNO<,t ,i> =def . [λwxt yi : {LogicalForm(x) & (∃r)(∃S) {Sentence(S, M y ) & (∃v1 )(∃v2 )(∃v3 )(∃d){Distinct(v1 , v2 , v3 , d) & VarType(v1 , , M y ) & VarType(v2 , i, M y ) & VarType(v3 , , M y ) & VarType(d, i, M y ) & (∀v0 ) (FreeIn(v0 , S) ≡ (v0 = v1 ∨ v0 = v2 ∨ v0 = v3 )) & ∼OccursIn(d, S) & (∀n)(∀t y )(NameType(n, t, M y ) →∼OccursIn(n, S)) & r = «[λv1 v2 v3 d: S]» & DenIn(r, |x|, M y ) & w = «v1 v2 v3 d/S»}} ∨ {∼LogicalForm(x) & DenIn(w, x, M y )}]. For types t not of the sort <, i, , i>, canonical naming may be equated with ordinary denotation, as in (Df.12), since no type t entity could be a logical form: (Df.12) CNO<,t
,i>
=def . [λwxt yi : DenIn(w, xt , M y )].
At last we are in a position to define the family of predicates Despite the proliferation of Bel-relations to which MRTJ is committed, it is nevertheless possible to capture them all in + by means of the single definition scheme (Df.13): Bel ,i,,i>,t1 ,...,tn > .
(Df.13) Bel ,i,,i>,t1 ,...,tn > =def . [λxi f <,i,,i> y1t1 . . . yntn : (∃S)(∃v1 ) . . . (∃vn ){Sentence(S, M x ) & VarType(v1 , t1 , M x ) & . . . & VarType(vn , tn , M x ) & Distinct(v1 , . . . , vn ) & (∀w)(FreeIn(w, S) ≡ (w = v1 ∨ . . . ∨ w = vn ) & FormOf (f , S, x) & (∃b1 ) . . . (∃bn ) {(NameType(b1 , t1 , M x ) & . . . & NameType(bn , tn , M x ) & CNO(b1 , y1 , x) &. . . & CNO(bn , yn , x) & Accepts(x, S(bl ...bn /v1 ...vn ))}}]. (n ≥ 0) What (Df.13) tells us is that an (n+2)-ary Bel-relation of given type is that relation between an agent, a logical form, and entities y1 , . . . yn (of corresponding types) which consists in the agent’s being disposed as one who inwardly and assertively tokens the (closed) Mentalese sentence which results from uniformly substituting names b1 , . . . , bn for the free variables of an n-ary open Mentalese sentence having the given logical form, where each bi is a canonical name of yi in the agent’s Mentalese. The description of b1 , . . . , bn is couched in terms of canonical names for the sake of generality: we want MRTJ to apply to iterated belief ascriptions, its analysis of which requires logical forms to appear among the entities y1 , . . . yn . However, in cases not involving nested belief predicates—hence where none of y1 , . . . yn is a logical form—the description of b1 , . . . , bn simply amounts to the
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requirement that b1 , . . . , bn respectively denote y1 , . . . yn in agent’s Mentalese. So, in the non-nested cases, to have a belief about y1 , . . . yn under a logical form f is to accept the substitution-instance S(b1 ...bn /v1 ...vn ) of a pure sentence S of one’s Mentalese which is such that (i) f is a form of S and (ii) b1 , . . . , bn respectively denote y1 , . . . yn in one’s Mentalese. In the formulation of (Df.13) the Mentalese names b1 , . . . , bn , unlike the Mentalese variables v1 , . . . , vn they replace, are not required to be distinct from one another, for (like Russell) we are dealing with relational rather than notional belief, hence allowing that identities among the objects of a belief may not tracked by identities among their Mentalese names. The unity of the family of Bel-relations is thus more intimate than that of a group of relations that merely obey the same or similar laws: members of the family of Bel-relations are all structurally alike in the way depicted in (Df.13). It is this structural likeness, together with their incorporation of the relation Accepts, which makes them all belief relations—though of course this cannot be ‘said’ in + itself but only ‘shown’ by the definitional status of (Df.13)’s instances. Given (Df.10) and (Df.13), MRTJ’s axiom scheme [I] becomes a theorem scheme of + . Indeed, in light of (Df.7) and (Df.13), all the remaining axiom schemes of MRTJ also become theorem schemes of + : [II] via (Ax.3.1); [III] via (Ax.3.3); [IV] via (Ax.3.5); and [V] via (Ax.3.7). Furthermore, it is now possible to say what it is for a type-indexed expression of M x to be a ‘belief predicate’ (a • Bel • ) or a ‘believes-truly predicate’ (a • TrBel • ) of that Mentalese type—two notions that will loom large in the next section. To simplify the formulation, let us take ‘Vocab(v1t 1 , . . . , vnt n , di , ui , y1t 1 , . . . ynt n , S; M x )’ to say that v1 , . . . , vn , d, u, y1 , . . . yn are distinct variables of respective M x -types t 1 , . . . , t n , i, i, t 1 , . . . , t n and that S is a pure formula of M x in which the free variables are exactly v1 , . . . , vn but in which d does not occur. Now consider the schematic formula (23), in which ‘x’, ‘B’, and ‘t 1 ’, . . . ,‘t n ’ are the only free variables: (23) (∀v1 ) . . . (∀vn )(∀d)(∀u)(∀y1 ) . . . (∀yn )(∀S){Vocab(v1t 1 , . . . , vnt n , di , ui , y1t 1 , . . . ynt n , S; M x ) → Accepts(x, «(∀u)∼B,i,,i>,t 1 ,...,t n > (u, v1 . . . vn d/S & ∼S, y1 , . . . , yn )»)}. (23) attributes to x acceptance of Mentalese sentences that mimic instances of the axiom scheme [II] of MRTJ. It seems clear that, whatever the plausible axiom schemes for ‘Bel’ turn out to be in MRTJ (including ones that might be added to relate belief to desire and intention), there will be corresponding open formulas of analogous to (23) for attributing acceptance of instances of those schemes. Since ‘x’, ‘B’, and ‘t 1 ’,…,‘t n ’ are the only free variables involved, let ‘(x, B, t 1 , . . . , t n )’ denote the conjunction of all such open acceptance-attribution formulas of . Then what it is for a type-indexed expression «B,i,,i>,t 1 ,...,t n > » of M x to be an (n + 2)-ary ‘belief predicate’ of that Mentalese type can be equated with
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x’s accepting (i.e., being disposed as one who assertively tokens) all the relevant axioms. In other words, we can lay down (Df.14) as a definition scheme in + : (Df.14) BeliefPred n =def . [λbt x x: (∃t x1 ) . . . (∃t xn )(t = , i, , i>, t 1 , . . . , t n > &(∃e)(Expression(e, M x ) & b = «et » & ∼(∃d)(∃t 0 x ) (Expression(d, M x ) & e = «dt 0 »)) & (x, e, t 1 , . . . , t n )))]. (n>0) Given (Df.14), we can define in + what it is for an expression p of M x to be a ‘believes-truly predicate’ of suitable type. This is accomplished by adoption of the definition scheme (Df.15), in which t ∗ = , i, , i>, t 1 , . . . , t n >: (Df.15) TrueBeliefPred n =def . [λpt x x: (∃t x1 ) . . . (∃t xn )(∃e){t = t ∗ & Expression(e,M x ) & p = «et » & ∼(∃d)(∃t x0 ) (Expression(d, M x ) & e = «dt 0 ») & (∃b)BeliefPred n (b, t, x) & (∀b)(∀v1 ) . . . (∀vn )(∀d)(∀a)(∀y1 ) . . . (∀yn )(∀S){(BeliefPred n (b, t, x) & Vocab(v1t 1 , . . . , vnt n , di , ui , y1t 1 , . . . ynt n , S, M α )) → Accepts(x, «(∀y1 ) . . . (∀yn )([λu: p(u,v1 . . . vn d/S, y1 , .., yn )] = [λu: b(u, v1 . . . vn d/S, y1 , .., yn ) & S(y1 ,..,yn /v1 ...vn )])»)}}]. The idea (near enough) is that a ‘believes-truly’ predicate of x’s Mentalese is one for which x accepts a Mentalese analogue of (Df.2), MRTJ’s definition of ‘Trbel’ in terms of ‘Bel’. If we pretend that x thinks in regimented English, we could put the idea by saying that τ is a Mentalese ‘believes-truly’ predicate for x just in case x accepts every instance of (24): (24)
For any y1 , .., yn : being a u such that τ (u, v1 . . . vn δ/ψ, y1 , .., yn ) = being a u such that u has a belief about y1 , .., yn under v1 . . . vn δ/ψ where ψ(y1 ,..,yn /v1 ...vn ).
In particular (and continuing the ‘inner English’ pretense), it follows that if β and τ are respectively Mentalese belief and true-belief predicates for x, then x accepts every instance of (25): (25)
For any y1 , .., yn : being a u such that τ (u, v1 . . . vn δ/ψ, y1 , .., yn ) = being a u such that β(u, v1 . . . vn δ/ψ, y1 , .., yn ) where ψ(y1 ,..,yn /v1 ...vn ).
This is recorded in theorem scheme (T7), where t ∗ = , i,, i>, t 1 , . . . , t n >: (T7) (∀xi )(∀b)(∀v1 ) . . . (∀vn )(∀d)(∀u)(∀y1 ) . . . (∀yn )(∀S)(∀p) {{TrueBeliefPredn (p, t ∗ , x) & BeliefPredn (b, t ∗ , x) & Vocab(v1t 1 , . . . , vnt n ,
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di , ui , y1t 1 , . . . ynt n , S; M x )} → Accepts(x, «(∀y1 ) . . . (∀yn )([λu: p(u, v1 . . . vn d/S, y1 , .., yn )] = [λu: b(u, v1 . . . vn d/S, y1 , .., yn ) & S(y1 ,..,yn /v1 ...vn )])»)}. This completes the apparatus needed for the reduction of MRTJ to + . Assuming (as we have) the plausibility of LOT in general and of in particular, the status of this reduction as a vindication of MRTJ depends upon whether the reduced version of MRTJ satisfies the adequacy conditions (C1)-(C5) laid down in section 1. We shall now argue that these conditions have indeed been satisfied. 3.5 VINDICATION AND THE ADEQUACY CONDITIONS Since we have neither appealed to propositions nor made use of any undefined predicates of a language that take nominalized sentences of that language as arguments, condition (C5) has clearly been met. Moreover, the definition schemes (Df.7)(Df.13) provide a precise ontological account of the logical forms posited by MRTJ and reveal (via the systematic connection with the single relation Accepts> ) what is structurally common to the members of the family of differently typed belief relations in virtue of which they are belief relations; so (C2) and (C3) are satisfied. What remains to be shown is that (C1) and (C4) are met as well. Let us begin with (C1). There are two issues here: viz., (a) whether MRTJ, understood via the reduction to + , can provide analyses of ‘A believes that p’ and ‘The belief that p is true/false’ for all grammatically admissible replacements of ‘p’; and (b) whether the proffered analyses are plausible. The answer to question (a) is clearly affirmative. Since logical forms themselves can be of arbitrary truthfunctional and/or quantificational complexity, and since according to MRTJ all of a judgment’s structure derives from its logical form, it should be obvious that MRTJ is not restricted merely to atomic judgments but can provide analyses of belief ascriptions with content-clauses of any degree of complexity.16 Question (b) is not so easily settled. Even assuming, as we have, the acceptability of the general framework of LOT, we can only argue from representative examples in which the analyses of belief ascriptions provided by the reduced version of MRTJ can be seen to be plausible. Let us begin with (18), an ascription to Othello of the atomic belief that Desdemona loves Cassio. MRTJ’s analysis of (18) is (26): (26)
Bel ,i,i,i>,,i,i,i> (Othello, F xi yi d i/F(x, y), Loves, Desdemona, Cassio).
In + , (26) will be provably equivalent to (27): (27)
(∃b1 )(∃b2 )(∃b3 ){(NameType(b1 , , MOthello ) & NameType (b2 , i, MOthello ) & NameType(b3 , i, MOthello )) & DenIn (b1 , Loves, MOthello )
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& DenIn(b2 ,Desdemona,MOthello ) & DenIn(b3 ,Cassio,MOthello ) & Accepts(Othello, «b1 (b2 , b3 )»)}]. According to + , then, (18)/(26) obtains iff Othello is disposed as one who inwardly and assertively tokens in his language of thought a relational sentence whose binary predicate, first argument, and second argument respectively denote loving, Desdemona, and Cassio. Consider next (28), which (suppressing the type-indices) is analysed by MRTJ as (29): (28) A believes that either R(a1 , . . . , an ) or S(b1 , . . . , bk ). (29)
Bel(A; Fx1 . . . xn Gy1 . . . yk d i /F(x1 , . . . , xn ) ∨ G(y1 , . . . , yk ); R, a1 , . . . , an , S, b1 , . . . , bk ).
According to + , (29) obtains just in case A accepts a Mentalese sentence of the sort «R(a1 , . . . , an ) ∨ S(b1 , . . . , bk )» in which (i) the Mentalese names R and S respectively denote the relations R and S, and (ii) the Mentalese names a1 , . . . , an , b1 , . . . , bk respectively denote the individuals a1 , . . . , an , b1 , . . . , bk . No peculiar logical object is required to correspond to the disjunction sign itself, whether in English or in A’s Mentalese. The same results holds, mutatis mutandis, for belief ascriptions with content-clauses involving other connectives, quantifiers, etc. In our examples so far, the dummy variable in logical form specifications has merely been along for the ride. However, when the content-clause in a belief ascription is wholly general, this otherwise inert element finally comes into play. Thus, e.g., (30) is analyzed as (31): (30) A believes that every individual has properties. (31) Bel ,i,,i>> (A; d i /(∀vi )(∃F )F(v)). Now by (Df.7) the logical form d i /(∀vi )(∃F )F(v) is the relation [λx yi zd i : x = [λd i : (∀v)(∃F)F(v)] & (∃w){DenIn(w, x, M y ) & [λrsi u: (∃v)(∃F)(∃d)((VarType(d, i, M s ) & VarType(v, i, M s ) & VarType(F, , M s ) & r = «[λd: (∀v)(∃F)F(v)]») & u = «d/(∀v)(∃F)F(v)»}]wyz]. So (31) is ultimately equivalent to (32): (32)
(∃v)(∃F){VarType(v, i, MOthello ) & VarType(F, , MOthello ) & Accepts(Othello, «(∀v)(∃F)F(v)»)}.
A wholly general belief is thus a binary relation between a thinker and a ‘general’ logical form f , i.e., one which is a logical form for certain wholly general sentences
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of the thinker’s Mentalese; and to be so related to f is inwardly and assertively to token a sentence of that form (or at least to be disposed as if one did so). The reduced version of MRTJ easily handles iterated belief ascriptions like (33): (33)
Iago believes that Othello believes that Desdemona loves Cassio.
Where the two occurrences of ‘believes’ in (33) are translated as predicates ‘Bel t1 ’ and ‘Bel t2 ’ of appropriate (and, of course, distinct) types t1 and t2 , we have the analysis (34) of (33): (34)
Bel t1 (Iago, H t2 z i G <,i,i,i> J xi yi d i /H (z, G, J , x, y), Bel t2 , Othello,F xi yi d i /F(x, y), Loves, Desdemona, Cassio).
Skipping the derivation and stating the result less formally, (34) obtains just in case (35) does: (35)
Iago [is disposed as if he] assertively tokens a certain sentence in MIago of the form «b(o, f , l, d, c)» in which (i) b, o, f, l, d, and c are names in MIago respectively denoting Bel t2 , Othello, F xi yi d i /F(x, y), loving, Desdemona, Cassio; and (ii) f has the form «v1 v2 v3 d/v1 (v2 , v3 )» for distinct variables v1 , v2 , v3 , and v4 of respective MIago -types , i, i, and i.
By our definitions and axioms, Iago’s belief is true (i.e., Iago truly believes that Othello believes that Desdemona loves Cassio) iff, in addition to (35), (36) also obtains: (36)
[λH t2 z i G <,i,i,i> J xi yi d i : H (z, G, J , x, y)](Bel t2 , Othello, F xi yi d i /F(x, y), Loves, Desdemona, Cassio).
But (36) is equivalent to (26), which we unpacked above. So, in the end, Iago’s belief is true iff (35) obtains and Othello accepts in his language of thought a relational sentence whose binary predicate, first argument, and second argument respectively denote loving, Desdemona, and Cassio. Moreover, independently of any assumptions about what belief facts there are, we are now entitled to assert (37): (37)
The belief that Othello believes that Desdemona loves Cassio is true iff Othello believes that Desdemona loves Cassio.
For MRTJ’s translation of (37) is (38): (38)
True([λui f : f = H t2 z i G <,i,i,i> J xi yi d i /H (z, G, J , x, y) & Bel t1 (u, f , Bel t2 ,Othello, F
