Putnam on Ontology

Putnam on Ontology Matti Eklund Cornell University ([email protected]) [Forthcoming in Maria Uxia Rivas Monroy, Concepcion Martinez Vidal and Celeste Cancela (eds.), Following Putnam's Trail: On Realism and Other Issues, Rodopi. (Proceedings from conference on Hilary Putnam’s pragmatism in Santiago de Compostela, Spain, May 2004.]

I. Introduction In this paper, I will discuss, and to some extent criticize, Hilary Putnam’s views on ontology, recently summarized and defended in his Ethics without Ontology (2004). I will start out with a critical discussion of Putnam’s thesis of conceptual relativity. Then I will turn to what is the main issue in the book: the criticism of the focus on ontological matters in philosophical discussions of mathematics and ethics.

II. Conceptual relativity In many writings from the 1980s and onwards, Putnam has defended a view he calls the thesis of conceptual relativity. Here is a statement of the view from his most recent book (2004). Putnam considers the specific case of the existence of mereological sums, but what he says about this is supposed to generalize. (How far is an issue that I will return to later.) ...to ask whether mereological sums really exist would be stupid. It is, in my view, a matter of convention whether we say mereological sums exist or not....How can the question whether something exists be a matter of convention? The answer, I suggest, is this: what logicians call “the existential quantifier,” the symbol “(x),” and its ordinary language counterparts, the expressions “there are,” “there exist” and “there exists a,” “some,” etc., do not have a single absolutely precise use but a whole family of uses.1

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Putnam (2004), p. 37.

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To my mind, the thesis is somewhat obscure. I will later turn to what exactly the thesis comes to. But let me first give an argument to the effect that, however exactly we should conceive of the thesis, it cannot be true while saying something significant. The idea behind the thesis of conceptual relativity is that ‘exists’ and what we may call other ontological expressions of English (‘there are’, ‘object’, ‘some’,…) are somehow indeterminate in meaning. This would appear to mean that there are two possible languages English1 and English2 we could speak, with the ontological expressions of English being relatively precisified in one way in English1 and in another way in English2.2 To stick with the example Putnam employs, we can imagine that in English1 “there are mereological sums” comes out true, and in English2 “there are mereological sums” comes out false. I think we can reduce this claim to absurdity. Here goes. In English1 there can be a singular term ‘t’, purporting to refer to some mereological sum, such that there are some true atomic sentences of the form “F(t)” of English1. Now, what should be said about the sentence “F(t)” of English1 in English2 (or in English, for that matter)? It seems clear that the correct thing to say is that it is true. (Indeed, I just said in English that it is true.) But for an atomic sentence, of any language, to be true, the singular terms in that sentence must refer.3 This is a fact we can surely give expression to in English and in English2. So we can conclude in English and in English2 that ‘t’ refers. But for ‘t’ to refer, there must be a referent for ‘t’. In English2 we can conclude that ‘t’ refers. This, in conjunction with the fact that the referent of ‘t’, if any, is a mereological sum contradicts the supposition that in English2 “there are mereological sums” is not true. Hence the thesis of conceptual relativity is false. In his recent (2004), Putnam himself brings up objections similar in spirit to the ones I have pressed. Specifically, he considers an objection against his position that takes the form of a dilemma: either (say) the seemingly contradictory statements of someone (Putnam’s “Polish Logician”) who says “there are mereological sums” and someone (Putnam’s “Carnap”) who says “there are no mereological sums” really contradict each other or they do not. If the statements are genuinely contradictory there is no way in which their respective statements can be jointly true, and if the statements are not genuinely contradictory then the case can simply be described as one

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Where the ‘relatively’ is included to ward off the objection that it may be in principle impossible completely to precisify the ontological expressions. Expression e′ relatively precisifies expression e only if e′ is more precise than e is. (E.g. every precisification of e′ is a precisification of e but not vice versa.) 3 This may be argued to be an overgeneralization. Some theorists would hold that although Vulcan does not exist, “Vulcan=Vulcan” and “Vulcan is a planet” are true sentences. Roughly, on these views, when the referent of ‘t’ does not exist, ‘t’ can still occur in some true atomic sentences: namely those that ascribe certain essential or core properties to the referent of ‘t’. Even if this is correct, the argument in the main text is not impugned: just focus on atomic sentences not belonging to this special class.

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where is using the quantifier less inclusively. (The second horn can be seen as the one I have been focusing on.) Putnam’s response to the dilemma is confusing. First, he outlines the different senses in which Carnap and the Polish logician mean the same or different things by the words in their respective ontological vocabularies.4 There may well be different ways of talking about sameness of meaning, and disentangling what different things such talk can amount to might well be useful. But here it is not immediately relevant: for the potential problem is that whatever we say about whether they mean the same, the example fails to support the thesis of conceptual relativity. Later Putnam does turn explicitly to the question of whether Carnap and the Polish logician contradict each other, and says that they do not – but fails to address the question of why this does not just impale him on the second horn of the dilemma.5 In several places in (2004), Putnam simply makes fun of opposition to his thesis of conceptual relativity. For instance, he says, “once we assume that there is, somehow fixed in advance, a single “real,” and single “literal” sense of “exist”—and, by the way, a single “literal” sense of “identity”—one which is cast in marble, and cannot be either contracted or expanded without defiling the statue of the god, we are already wandering in Cloud Cuckoo Land”.6 One aspect of the fun-making is quite obviously misconceived. Putnam talks as if his opponent assumed that the string ‘exist’ independently of its use had a single literal sense, and of course that is not right. But what the opponent of the thesis of conceptual relativity (when this thesis is formulated as a semantic indeterminacy thesis – and we will later see that this way of conceiving of the thesis may not be all that happy) wants to claim is rather that given its use, the sense of ‘exist’ is uniquely determined. A less polemical point of Putnam’s would be that all, or virtually all, words of our language are somehow semantically indeterminate, as he claims that ontological expressions like ‘exist’ are, and so the opponent of conceptual relativity unmotivatedly claims that ontological expressions are special. What my above argument can be taken to show is that ontological expressions really are special. Here is a general reflection about this. In another part of his critical discussion of ontology, Putnam defends what he calls pragmatic pluralism, the recognition that it is no accident that in everyday language we employ many different kinds of discourses, discourses subject to different standards and possessing different sorts of applications, with different logical and grammatical features—different “language games” in

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Putnam (2004), pp. 40-5. Putnam (2004), pp. 45-7. 6 Putnam (2004), p. 84f. 5

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Wittgenstein’s sense—no accident because it is an illusion that there could be just one sort of language game which could be sufficient for the description of all of reality!7 I do not think this is entirely clear. But I think we can anyway see that even if the claim is correct, there can be expressions which occur in different discourses and whose meanings are invariant across discourses: the logical expressions. Getting back to the main topic, even if the vast majority of our expressions are somehow semantically indeterminate, the logical expressions very arguably constitute an exception to the rule. And, and this is the point, those who oppose Putnam’s thesis of conceptual relativity often already for independent reasons want to assimilate ontological expressions to logical expressions: the existential and universal quantifiers are standardly taken to be part of logic. Incidentally, there are independent reasons for concern with how Putnam in (2004) conceives of the thesis of conceptual relativity. As stated, it is clearly a kind of semantic indeterminacy thesis (that ontological expressions “do not have a single absolutely precise use”).8 But there are reasons to be skeptical of the idea that this is a happy characterization of what Putnam is after. First, Putnam’s thesis of conceptual relativity is quite clearly meant as a metaphysical thesis: but how can the truth of a metaphysical claim turn on (something as shallow as) the semantic indeterminacy of some words we actually employ? Second, in order for the extension of any predicate to include some thing a under any acceptable assignment, a must exist. So, under the supposition, for reductio, that ontological expressions have different semantic values under different acceptable assignments, it turns out that the most generous assignment is the correct one. Reductio. It is perhaps instructive to compare Putnam’s earlier, more metaphysical sounding characterizations of the view. Thus, in (1981) he says, “‘Objects’ do not exist independently of conceptual schemes”. Not that there is not a trivializing reading also of this claim. The just quoted claim occurs just after the passage “In an internalist view also, signs do not intrinsically correspond to objects, independently of how those signs are employed and by whom. But a sign that is actually employed in a particular way by a particular community of users can correspond

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Putnam (2004), p. 22. There are several slightly different things Putnam’s formulation might come to: he might be saying that ontological expressions are ambiguous, or that they are polysemic, or that they are context-sensitive, or that they are semantically indeterminate, or he might be suggest a hybrid of some or all of these claims, or he might be suggesting something slightly different altogether. For my purposes, the differences between these possibilities do not really matter. For simplicity, I will lump all these possibilities together under the heading ‘semantic indeterminacy’. 8

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to particular objects within the conceptual scheme of those users”.9 Putnam’s characterization of his view certainly sounds radical: objects are somehow conceptual scheme-dependent. But in light of the clarificatory remarks, does it amount to anything more than a truism? On any reasonable view, the meaning of a sign depends on how it is employed. The notion of a conceptual scheme is notoriously slippery, but absent a characterization of the notion that determines a different reading, it is natural, on any view, to hold that it is only given a particular use, within a particular “conceptual scheme”, that signs refer to the objects they refer to, and in particular that it is only within a particular conceptual scheme that “exist” and “object” mean what they do. Both in his (2001b) reply to an article by Jennifer Case and in his (2004), Putnam makes remarks supposed to ward off misunderstandings of the thesis of conceptual relativity, and to clarify just what the thesis comes to. First, he distinguishes conceptual relativity from what he calls conceptual pluralism. Conceptual pluralism, as Putnam explains it, is what is at issue when “‘the contents’ of a room” may be described “very differently by using first the vocabulary of fundamental physical theory and then again the vocabulary of tables and chairs and lamps and so on”.10 This is not a matter of conceptual relativity, Putnam rightly remarks, for the two descriptions can rather unproblematically be true together. This distinction strikes me as useful. (Indeed, the upshot of my criticism of the thesis of conceptual relativity can be said to be that every case that Putnam takes to be a case of conceptual relativity is really just an instance of conceptual pluralism.). But another supposed clarification that Putnam offers is more problematic. He says, The most common misunderstandings [of the notion of conceptual relativity] are (1) that by a “conceptual scheme” I meant any body of thought and talk at all, including our ordinary talk of tables and chairs; and (2) that by “conceptual relativity” I meant a doctrine which implies that every conceptual scheme in this sense, every body of thought and talk, has an alternative which is incompatible with it (sometimes my critics miss the qualifier – “at face value”) but equally true. According to these misunderstandings of the notion, “there is a computer on this desk” is true or false depending on what “conceptual scheme” one happens to pick. But the problem with this is that, as things stand right now (I happen to be typing these words into a computer on the desk in front of me), if anyone were to use those wordt [sic] to make a false statement, then either (s)he would be talking about a different desk or a different time and 9

Putnam (1981), p. 52; Putnam’s emphasis. Putnam (2004), p. 48.

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place, or (s)he would be giving at least one of those words a different meaning or reference in some other way.11 If we understand the above quoted remarks from Putnam’s (1981) to constitute a statement of the thesis of conceptual relativity – and I think I am not alone in finding it natural to regard them as such even though Putnam does not there employ the label – then what Putnam here describes as a misunderstanding cannot justly be regarded as such. For there the view is explicitly that objects, quite generally, do not exist independently of conceptual schemes. However, given Putnam’s more recent statements of the view, for example those in (2004), the remarks make more sense. For if Putnam is only talking about the semantic indeterminacy in our ontological expressions, then there is a distinction worth marking between entities that fall under ‘there exists’ under every relative precisification of the existential quantifier and (would-be) entities that do so under some but not all ways of relatively precisifying it. The latter entities can perhaps, in an intuitive sense, be seen as optional. So if, like Putnam, we focus on the actual semantic indeterminacy of the ontological expressions, there is a distinction to be drawn, of the kind Putnam here calls attention to. But there is still an oddity. This oddity serves to bring out further what is strange about focusing on semantic indeterminacy. I can best make the point by contrasting the way Putnam now appears to conceive of conceptual relativity with how Eli Hirsch views his related doctrine of “quantifier variance”. Hirsch’s statement of his view is that there are “many possible perspectives on ‘the existence of objects’, which all are adequate for describing the same facts, the same ‘way the world is’”.12 He is not focused on any actual semantic indeterminacy in our ontological expressions, but on the supposed possibility of there being significantly different sets of ontological expressions, all adequate for describing the way the world is. For Hirsch, the question is not whether “there is a computer on this desk” is true on all ways of relatively precisifying our actual ontological expressions, but rather whether there are alternatives to our actual ontological expressions, all adequate for describing the way the world is, such that if we understand “there exists” one of these ways the statement comes out true and if we understand “there exists” another way it comes out false. This alternative way of conceiving of conceptual relativity (or maybe: this alternative thesis) faces the same problems that I have earlier outlined for the thesis of conceptual relativity. But it appears preferable – and should be preferable by Putnam’s own lights – to conceive of the thesis this way than to conceive of it as a semantic indeterminacy thesis. For the way Putnam appears to conceive it, there is a significant ontological 11 12

Putnam (2001b), p. 431. Hirsch (forthcoming), p. 13.

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difference between the existence of tables and chairs and the existence of what we only talk about in what Putnam calls our “optional languages”. But this difference is grounded only in how we happen to employ ontological expressions.

III. “Objectivity requires objects” In fact, I am not sure about the significance of the thesis of conceptual relativity for Putnam’s overall argument concerning ontology in Putnam’s (2004). The main issue there is the following. Consider ethics and mathematics. Traditionally, analytic philosophers have regarded ethics and mathematics as somehow problematic, and have been more drawn toward antirealism about these areas than about science. Putnam thinks that the discussion of the realist credentials of ethics and mathematics has been overly focused on ontology. He thinks theorists often reason as follows. First, it is assumed that “if a claim is objectively true, then there have to be objects to which the claim ‘corresponds’”. (In slogan form we may say: objectivity requires objects.) Second, it is held that natural objects cannot be truth-makers for ethical claims. So ethics is objective only if there are ‘non-natural’ objects. The choice is then between denying that there are such objects (antirealism) and defending this consequence of the objectivity of ethics (a kind of platonistic realism).13 Putnam criticizes this way of thinking. I think there is something importantly right about Putnam’s criticism, but also that there are serious problems with it. I want first to stress that whatever is right or wrong about what Putnam aims to show, it is not clear that there is any need to bring in the thesis of conceptual relativity. For suppose that, as I have argued, the thesis of conceptual relativity should be rejected. Still one can hold that the above argument against the objective truth of ethical claims just gets the cart before the horse. One can hold that the question of whether there are ethical properties – whether natural or not – is to be determined by investigating the nature of ethical discourse, our practice of making ethical claims: and not vice versa. This type of claim is for instance made by theorists in the neo-Fregean tradition, most prominently in the case of mathematics.14 According to neo-Fregeans, we arrive at the conclusion that there are mathematical objects through arriving at the view that some mathematical claims are true and noting, through an investigation of the logical form of these claims, that for their truth some mathematical terms must refer. This line of argument by no means requires conceptual relativity.

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Putnam (2004), p. 52f. See Dummett (1956), (1973) and (1981); Wright (1983); and Hale and Wright (2001). Later I will discuss neo-Fregeanism further.

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Putnam argues against the “objectivity requires objects” view by considering logic, which is supposed to be a counterexample. Putnam asks us to consider statements like, If all platypuses are egg-laying mammals, then it follows that anything that is not an egglaying mammal is not a platypus. This statement is objectively true, and yet there are no objects which make it true. That is the claim. But someone who thinks that the objective truth of mathematical claims requires mathematical objects will presumably rely on the fact that some true mathematical claims – say, “there is an even prime number” – require for their truth that there are mathematical objects, on grounds of their being quantified claims. This contrasts with logic. To argue that ethical claims, if true, are ontologically committing, one will have to assume either that claims of the form “a is good” or “a is right” are ontologically committing to ontological correlates for the predicates, or focus on what is required for the truth of claims like “goodness is a virtue”, or focus on quantification over things like rights. The issues here are perhaps not as straightforward as in the case of mathematics, but still it appears reasonable to hold that ethics is on the side of mathematics rather than logic here. So one reason for dissatisfaction with Putnam’s appeal to the case of logic is that apparently relevant features of the case do not unproblematically carry over to the cases of mathematics and ethics. Another reason for dissatisfaction is this. Someone generally attracted to the “objectivity requires objects” view might well be attracted to an ontology of facts, and to the view that for every true claim there is a fact that makes it true, even when the claim is not otherwise ontologically committing, and that truths can be said to describe the facts which make them true. Given this view on truthmaking, even logical truths have facts as truth-makers. Surely this view is not off the map, and nothing in Putnam’s argument militates against it. In fact, there is another puzzling feature of Putnam’s discussion. Putnam starts off the relevant chapter by discussing, in the context of Wittgenstein interpretation, whether there is a distinction between those discourses that do and those discourses that do not “describe reality”. The examples, from Wittgenstein, are ethical discourse and mathematical discourse: do these discourses describe reality? Putnam’s discussion of this issue leads him to consider the question “how there can be such a thing as a truth which is not a description of some object or objects?”.15 This in turn brings him to logic: logical truths seem to be of this kind. But somewhere in this reasoning, “describe” starts being used with a different meaning. The initial question about 15

Putnam (2004), p. 55.

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ethical and mathematical discourse is whether the apparent assertions of these discourses are genuine assertions rather than, say, avowals. The question is here framed in terms of whether the discourses are “descriptive”. Very arguably logical discourse is in this sense descriptive: at any rate nothing Putnam says in any way casts doubt on this claim. But when Putnam argues that statements of logic are not descriptions, the issue is rather whether these statements describe some objects. I have already criticized Putnam’s reasoning about logical, mathematical and ethical discourse. But if the reasoning were cogent it would primarily show something about the “objectivity requires objects” view. Putnam’s discussion suggests that it also poses difficulties for the way that realism/antirealism disputes are normally conceived, but this is misleading.

IV. Putnam and Wittgenstein As already mentioned, Putnam appeals to Wittgenstein in his discussion.16 To explain the relevant points, let me provide some background. There is a discussion in the literature of what Wittgenstein really holds about discourses like ethical discourse and mathematical discourse. Is he some sort of realist? Some sort of antirealist? Or a quietist? Here is a menu of some different possible views. Realism across the board. Wittgenstein holds that superficial features – declarative form, etc. – suffice to determine that the use of a particular class of sentences is descriptive, and this is all that’s required by a realist view. Selective antirealism. Wittgenstein is an antirealist about (e.g.) ethics and mathematics. Quietism. All we can say about declarative sentences of various discourses is that they are used in such-and-such a way. Questions about realism/antirealism cannot be raised. Motley. The realism/antirealism distinction – the distinction between genuinely assertoric or genuinely descriptive discourses and those that discourses that somehow fall short of this ideal – is too coarse-grained. Instead there is a motley of distinctions to be drawn between different discourses.17 (Notice that ‘description’ is here used in the way relevant to realism/antirealism disputes.) On Putnam’s view (which for what it is worth seems reasonable to me), the ‘motley’ interpretation is the right one. On this interpretation, the right question to ask about ethical discourse or mathematical discourse is not whether this discourse really is descriptive, but what are the salient 16 17

See Putnam (2004), especially ch. 3. For discussion of these interpretations of Wittgenstein, see e.g. Blackburn (1990) and Conant (1997).

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similarities and differences between this and paradigmatically descriptive discourses. For Putnam, this is not only how Wittgenstein is best interpreted: it is also the most reasonable view to take. What, then, are the claims of Putnam and Wittgenstein with respect to mathematical discourse? What are some salient similarities and differences between this discourse and, say, ordinary object discourse? Both in the relevant parts of Wittgenstein’s writings on mathematics – especially his lectures XXV and XXVI in (1975) – and in Putnam’s discussions I find a certain tension. Neither Putnam nor Wittgenstein properly distinguishes between the following two claims: (a) Non-existence. Mathematical terms like ‘0’, ‘1’, ‘2’ do not refer to objects; there is no special class of objects that mathematical assertions are about; mathematical assertions cannot be said to correspond to reality. (b) Non-explanation. The appearance that we somehow explain the nature of mathematical discourse by appeal to the fact that mathematical terms refer, that mathematical assertions are about mathematical objects, and that true mathematical assertions correspond to reality is illusory. In his discussion of Wittgenstein, Putnam makes the following remark: [Wittgenstein] clearly pooh-poohs the idea that talk of numbers—either ordinary numbers or the so-called “transfinite numbers”—is in any way analogous to talk about objects. If we think that way, then of course we will think that set theory has discovered...not just objects, and not just intangible objects, but an enormous—an unprecedentedly large—quantity of intangible objects. And the very vastness of the universe which set theory appears to have opened up for our intellectual gaze will then be part of its charm; but Wittgenstein thinks this reason for being charmed is a bad one. Wittgenstein believes—and I think he is right—that it does not make the slightest sense to think that in pure mathematics we are talking about objects.18 Here the focus seems clearly to be on (a). As Putnam indicates, he agrees with the view he here imputes to Wittgenstein. But what should be most important for Putnam’s purposes is (b). After all it is the thesis that objectivity requires objects that is Putnam’s main focus: and this thesis

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Putnam (2001), p. 150.

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appears only to require (b). Consider for instance Putnam’s characterization of his main point on ontology in (2004): I see the attempt to provide an Ontological explanation of the objectivity of mathematics as, in effect, an attempt to provide reasons which are not part of mathematics for the truth of mathematical statements and the attempt to provide an Ontological explanation for the objectivity of ethics as a similar attempt to provide reasons which are not part of ethics for the truth of ethical statements; and I see both attempts as deeply misguided.19 Here what is at issue is, explicitly, the relevance of an ontological explanation. And if anything, the stance that Putnam here gives voice to is in tension with (a). It is in the spirit of these remarks to take the question of whether there are numbers to be one settled by criteria internal to mathematics: but clearly by these criteria there are numbers. Numbers, moreover, are objects in the sense that is at issue: they are in the range of the first-order variables.20 Recall too that Putnam defends a thesis of conceptual relativity. This conceptual relativity thesis meshes well with (b). If different things can truly be said to ‘exist’ under different conceptual schemes, then it seems natural further to say that facts about what entities there really are cannot serve to explain the nature of our practices. (I am saying this somewhat hesitantly as I have earlier raised doubts about what exactly the thesis of conceptual relativity comes to. But surely (b) is in the spirit of conceptual relativity.) It is harder to reconcile (a) with the thesis of conceptual relativity. Suppose the thesis of conceptual relativity is true. Then suppose further that it is common practice to take there to be numbers: in this sense our conceptual scheme licenses us to take numbers to exist. I would have thought that statements to the effect that numbers exist, made ‘within our conceptual scheme’, are true. Benacerraf’s problem about our lack of causal contact with would-be mathematical objects, and other problems that potentially confront the metaphysical realist about mathematics, would seem beside the point. For numbers to exist, it is, roughly, sufficient that the hypothesis that they do so is coherent, that it is not in conflict with the empirical facts (in the way the hypothesis that there are yetis is), and that numbers exist ‘according to our conceptual scheme’. Naturally, the metaphysical question of what is must be the case for numbers to exist is different from the epistemic question of what knowledge of the 19

Putnam (2004), p. 3. Compare too the following passage from Putnam (1992): “Wittgenstein is not puzzled, as many philosophers are, about how we can ‘refer’ to abstract entities....For Wittgenstein the fact is that the use of number words is simply a different use from the use of words like cow. Stop calling three an ‘object’ or an ‘abstract entity’ and look at the way number words are used, is his advice” (p. 168).

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existence of numbers requires. But it is clear that the relevant metaphysical issues are directly relevant also to the epistemology of mathematics. The same tension that can be found in Putnam can be found already in Wittgenstein. For the most part, Wittgenstein is apparently concerned to establish (b). Consider e.g., Suppose we said first, ‘Mathematical propositions can be true or false.’ The only clear thing about this would be that we affirm some mathematical propositions and deny others. If we then translate the words ‘It is true…’ by ‘A reality corresponds to…’—then to say a reality corresponds to them would say only that we affirm some mathematical propositions and deny others. We also affirm and deny propositions about physical objects.—But this is plainly not Hardy’s point. If this is all that is meant by saying that a reality corresponds to mathematical propositions, it would come to saying nothing at all, a mere truism: if we leave out the question of how corresponds, or in what sense it corresponds.21 But there are also passages where Wittgenstein appears concerned to establish (a): To say “A reality corresponds to ‘2+2=4’” is like saying “A reality corresponds to ‘two’.” It is like saying a reality corresponds to a rule, which would come to saying: “It is a useful rule, most useful—we couldn’t do without it for a thousand reasons, not just one.”22 If you have a mathematical proposition about 0, and you imagine you are talking about a realm of numbers,—I would reply that you aren’t as yet talking about a realm of anything, in the most important sense of “about”. You are only giving rules for the use of “0”.23 Compare too a passage from Wittgenstein (1964): The comparison with alchemy suggests itself. We might speak of a kind of alchemy in mathematics.

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Wittgenstein (1975), p. 239. The mathematician Hardy apparently wanted to say that mathematical statements are about mathematical objects in a a way analogous to how ordinary empirical statements are about material objects. 22 Wittgenstein (1975), p. 249. 23 Wittgenstein (1975), p. 251.

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Is it the earmark of this mathematical alchemy that mathematical propositions are regarded as statements about mathematical objects,–and so mathematics as the exploration of these objects?24 Having stressed that there is a tension in Putnam and Wittgenstein as between thesis (a) and thesis (b), I should hasten to add that I think Putnam’s considered view must be that (b) but not (a) is true. I have already indicated why this should be Putnam’s view: it fits better with his thesis of conceptual relativity. Moreover, although I find this reading somewhat strained, it may be possible to read the passage that suggest thesis (a) to say only that talk of numbers should not be understood too much on the model of talk of material objects. To return to the relevant passage in Putnam: perhaps he means to say only that even if there are vastly many abstract objects we should not this analogous to how we would think of the discovery of vastly many planets; and even if arithmetical statements are made true by numbers, we should not understand this on the model of how ordinary empirical statements are made true by ordinary objects. (I will avoid getting into Wittgenstein-interpretation, but the same remarks may apply also to his remarks. For example, when Wittgenstein stresses that mathematical propositions are not really about numbers he may not wish thereby to imply that numbers have to exist for the relevant mathematical propositions to be true.) In the next section I will return to the significance of the tension noted.

V. Allies? Throughout the book, Putnam writes as if he is pretty much alone in criticizing the emphasis on ontology in mainstream analytic philosophy. This is for several reasons unfortunate. First, it is far from accurate. Second, a discussion of how Putnam’s conception of the issues here relates to those conceptions that are broadly in the same camp as Putnam’s would have helped clarify just what the view amounts to. I will focus on three types of conceptions that are broadly in the same camp as that of Putnam: the neo-Fregean view of Michael Dummett, Crispin Wright and Bob Hale; the conception of realism/antirealism issues defended by Crispin Wright in (1992) and (2003) (which although related to Wright’s neo-Fregeanism is a somewhat separate idea); and Simon Blackburn’s quasi-realism. Of these theorists, neither Wright nor Dummett is ever mentioned in Putnam’s (2004); and Blackburn is brought up only to be criticized, and an unsuspecting reader might get the impression from the criticism that Blackburn’s views on the relevant issues are 24

Wittgenstein (1964), IV, §16. This passage is quoted in Putnam (2001), p. 150f.

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radically different from Putnam’s. (While Putnam has elsewhere compared his view on the nature of truth – specifically on the possibility of unknowable truths – with those of Wright and Dummett, he has never directly addressed the relation between his metaontological views and the aspects of Wright’s and Dummett’s metaontological views that I will focus on.) Consider first the neo-Fregean view of Michael Dummett (see especially the early 1956 but also 1973 and 1981) and of Crispin Wright and Bob Hale (see Wright (1983) and Hale and Wright (2001)). Here is Dummett (1956) justifying the claim that mathematical objects exist: If a word functions as a proper name, then it is a proper name. If we have fixed the sense of sentences in which it occurs, then we have done all there is to be done towards fixing the sense of the word. If its syntactic function is that of a proper name, then we have fixed the sense, and with it the reference, of a proper name. If we can find a true statement of identity in which the identity sign stands between the name and a phrase of the form ‘the x such that Fx’, then we can determine whether the name has a reference by finding out, in the ordinary way, the truth-value of the corresponding sentence of the form ‘There is one and only one x such that Fx’. There is no further philosophical question whether the name—i.e., every name of that kind—really stands for something or not.25 Dummett is very much concerned to defend the existence of mathematical objects. Here there is a clear difference between Dummett and Putnam. But there is a deeper similarity. Dummett argues that mathematical objects exist because some mathematical terms refer; and the referring mathematical terms refer because they occur in true mathematical sentences, and we arrive at whether these sentences are true “in the ordinary way”. In (2004), Putnam emphasizes Kreisel’s point that “the question is not the existence of mathematical objects but the objectivity of mathematics”.26 Putnam does not acknowledge Dummett in this connection – but it is arguably very much via Dummett that this remark of Kreisel’s is as well-known as it is. Dummett famously calls it “Kreisel’s dictum”.27 Turn now to a second type of view which is similar in spirit to that of Putnam. In (1992) – and in later works like the articles collected in (2003) – Crispin Wright outlines and defends an original conception of realism/antirealism disputes. Standard alternatives for the would-be antirealist about, say, ethics is to opt either for non-factualism (which denies that ethical

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Dummett (1956), p. 40f. Compare Wright (1983), pp. 13-4. Putnam (2004), p. 67. 27 See especially Dummett (1973), p. 228. 26

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statements are truth-evaluable) and a so-called Mackie-style error theory (which holds that no ethical properties are exemplified and hence that no – atomic – ethical sentences are true). But Wright thinks there are devastating problems for both these antirealist paradigms. There is no denying that ethical statements are truth-evaluable, and that some atomic ethical sentences are true. But this does not mean that the realist wins. Nor does it mean that the quietist wins. Ethical discourse, and even discourses like comic discourse, are like, say, ordinary scientific discourse in that the sentences made are truth-evaluable and some atomic sentences are true. But there are differences – differences relevant to the issue of realism – with respect to what the truth of sentences belonging to these different discourses consists in, or involves. We can ask the following questions about the sentences of a particular discourse: (1) Can their truth be evidencetranscendent? (2) Is their truth response-dependent? (3) Is it apriori that there is a guarantee that all differences of opinion about the truth-values of these sentences can be traced to cognitive shortcoming (like that at least one of the disputants believes what she does on the basis of erroneous information, or that the conditions are unsuitable, or one of the disputants’ cognitive system is malfunctioning)? (4) Is there something else that can be explained by the facts to which true sentences of the discourse can be said to correspond, besides the truth of the sentences? These questions all correspond to different ‘marks of realism’, to use Wright’s label. A discourse can possess some of these marks of realism without possessing them all.28 This is somewhat akin to what Wittgenstein, under the ‘motley’ interpretation, holds. There is a sense in which statements of all discourses can be said to have a descriptive and assertoric function. But within the realm of such statements there are many potentially crosscutting realism-relevant distinctions that can be made. And on Wright’s view, the realismrelevant questions do not turn on ontology in the way that Putnam finds objectionable. Given that error theory is not an option for Wright, it is never the existence of the requisite objects that is the issue. The ‘motley’ view that theorists like Putnam ascribe to Wittgenstein is often held to be in tension with the view that discourses can be usefully distinguished into the ones that realism is true of and the ones that antirealism is true of (and Putnam clearly holds that there is a tension there). But Wright’s view suggests that reconciliation may be possible. It may be that although it is too simplified to employ a black and white realism/antirealism distinction, the motley of ways in which discourses may differ from each other may include a number of realism-relevant ways.

28

This is a very quick summary of some very delicate issues. See Wright (1996) for Wright’s own summary of his position.

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A discourse may possess all or only some marks of realism. This does not mean that questions about realism and antirealism are somehow rendered moot. Next, Blackburn. In Putnam’s discussion, Blackburn is mentioned only as one of the all too scientistic enemies of the kind of views Putnam espouses.29 But it is far from clear that Blackburn’s quasi-realism is all that different from the kind of view favored by Putnam. Here is how Blackburn explains his quasi-realism as applied to the case of modal discourse: The aim is to see these propositions as constructions that stand at a needed point in our cognitive lives – they are the objects to be discussed, rejected, or improved upon when the habits, dispositions or attitudes need discussion, rejection, or improvement. Their truth corresponds to correctness in these mental states, by whichever standards they have to meet.30 Blackburn does not deny that the propositions belonging to modal discourse can be true and false. He is only opposing a realist construal of modal discourse in that he thinks that, in a certain way, the truth-values of modal propositions are tied to our responses. I think there are some deep unclarities with respect to just how to understand Blackburn’s position. But given as quasirealism about a particular discourse does not involve denying that statements made within the discourse are true and false, the position appears compatible with much of what Putnam says. Specifically, note that on Blackburn’s view on modal discourse, we do not explain the truth of modal propositions by appeal to the entities which they somehow describe or correspond to: rather we turn to their role in our cognitive lives. Blackburn accordingly agrees with Putnam that the truth of statement of a particular discourse is not always to be explained by appeal to objects to which the statements correspond, or which the statements are about.31 I do not mean to assert that there are not any differences between Putnam’s view and the different views I have walked through here. Some differences are obvious: Putnam believes in conceptual relativity and the others do not. But there seems to be a convergence in opinion about the “objectivity requires objects” view. Maybe there are differences, even apart from differences over conceptual relativity. The point is just that these views are sufficiently similar that there is some cause for concern regarding just what the differences are, when the merely rhetorical differences have been subtracted. And even to the extent that there are clear, genuine differences 29

Putnam (2004), p. 83f. Blackburn (1987), p. 636. 31 Although Blackburn often focuses on special cases like moral and modal discourse – and hence gives the impression that he holds there to be a sharp divide between such cases and ‘ordinary’ descriptive discourse, a view Putnam would surely reject – he does also have global aspirations for his quasi-realist view. See e.g. Blackburn (1993), introduction and essay 1. 30

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it is not clear just what arguments favor Putnam’ view over one of these alternative views. It is here that the discussion in the previous section, concerning the tension between (a) and (b), is relevant. Once it is clear that it is (b) and not (a) that Putnam wants to defend – if this really is the case – then the question of how exactly Putnam’s criticism of the “objectivity requires objects” view differs from the views of Dummett, Wright and Blackburn becomes all the more pressing. By contrast, to the extent that Putnam really seeks to defend something like (a), there is a clearcut difference.

VI. Pragmatism In this section, let me briefly relate the preceding discussion to pragmatism. Putnam likes to relate his stands on the ontological issues discussed here to his affinities with the classic American pragmatists. How accurate is this? Through his defense of ‘pluralism’ and ‘humanism’, William James is sometimes taken to have defended something similar to Putnam’s thesis of conceptual relativity, and Putnam himself stresses his debt to James, especially in (1987).32 But consider what exactly James says in the passages that underlie the attribution of this metaontological view to him. First, reflect on the well-known passage “Common sense is better for one sphere of life, science for another, philosophic criticism for a third; but whether either be truer absolutely, Heaven only knows”.33 This does not justify ascribing to James anything like a thesis of conceptual relativity. Rather, he only expresses a kind of (principled) agnosticism about what is ‘truer’, together with a lack of concern regarding this issue. Or consider another well-known passage from James: We carve out groups of stars in the heavens, and call them constellations, and the stars patiently suffer us to do so, – though if they knew what we were doing, some of them might feel much surprised at the partners we had given them. We name the same constellation diversely, as Charles’s Wain, the Great Bear, or the Dipper. None of the names will be false, and one will be as true as another, for all are applicable. In all these cases we humanly make an addition to some sensible reality, and that reality tolerates the addition. All the additions ‘agree’ with reality; they fit in, while they

32

See e.g. Pihlström (1996) pp. 64-88 and Thayer (1968), pp. 352-57. Putnam stresses his debt to James repeatedly in the sections leading up to the argument for ontological pluralism in Putnam (1987). 33 James (1907/46), p. 190.

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build it out. No one of them is false. Which may be treated as the more true, depends altogether on the human use of it…. What shall we call a thing anyhow? It seems quite arbitrary, for we carve out everything, just as we carve out constellations, to suit our human purposes.34 There are two ways of reading this passage. On one way of reading it, James here espouses conceptual relativity. Different, and incompatible, ways of conceptually carving up reality into objects are all equally acceptable. On another way of reading the passage, however, James holds that all names are applicable – that they all refer – without saying anything about this being relative to conceptual schemes, in any interesting sense. On now to my second remark about pragmatism. Here I can be briefer. Consider theses (a) and (b), about non-existence and non-explanation, respectively. I have earlier criticized Putnam for running the theses together. Now let me just add that the one of these theses with the better pragmatist credentials is (b), concerning the (supposed) futility of ontological explanations.

VII. Concluding remarks Let me conclude by briefly stressing some of the main points. I started out by criticizing Putnam’s thesis of conceptual relativity. However, as I went on to note, even if this thesis is rejected, it is not clear that this impugns Putnam’s main aim in the discussion of ontology in (2004): to, so to speak, dethrone ontology. About this my verdict is more equivocal. I criticized Putnam for not properly distinguishing between, for example, the view that there are mathematical objects and the view that we can usefully explain the nature of mathematical discourse by appealing to what mathematical objects there are. Putnam criticizes both views. I am more sympathetic to the criticism of the latter view (although I have not here provided any substantive arguments for why we ought to be sympathetic to this criticism). REFERENCES Benacerraf, Paul: 1973, “Mathematical Truth”, Journal of Philosophy 70: 661-79. Blackburn, Simon: 1986, “Morals and Modals”, in Graham MacDonald and Crispin Wright (eds.), Fact, Science and Morality, Oxford University Press, Oxford. Reprinted in Jaegwon Kim and Ernest Sosa, Metaphysics: An Anthology, Blackwell, Oxford, 1999. Page references are to Kim and Sosa (1999).

34

James (1907/46), pp. 252-3.

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Blackburn, Simon: 1990, “Wittgenstein’s Irrealism”, in J. Brandt and R. Haller (eds.), Wittgenstein: Towards a Re-evaluation, Holder-Pickler-Tempsky, Vienna, pp. 13-26. Blackburn, Simon: 1993, Essays in Quasi-Realism, Oxford University Press, Oxford. Conant, James: 1997, “On Wittgenstein’s Philosophy of Mathematics”, Proceedings of the Aristotelian Society 97: 195-222. Dummett, Michael: 1956, “Nominalism”, Philosophical Review 65: 491-505. Reprinted in Dummett (1978), pp. 38-49. Dummett, Michael: 1973, Frege: Philosophy of Language, Duckworth, London. Dummett, Michael: 1973a, “The Philosophical Basis of Intuitionistic Logic” in H. E. Rose and J. C Shepherdson (eds.), Logic Colloquium ’73, North Holland, Amsterdam, 1975, pp. 5-40. Reprinted in Dummett (1978), pp. 215-47. Dummett, Michael: 1978, Truth and Other Enigmas, Harvard University Press, Cambridge, Mass. Dummett, Michael: 1981, The Interpretation of Frege’s Philosophy, Harvard University Press, Cambridge, Mass. Hale, Bob and Crispin Wright: 2001, The Reason’s Proper Study, Clarendon Press, Oxford. Hirsch, Eli: forthcoming, “Sosa’s Existential Relativism”, in J. Greco (ed.), Sosa and his Critics, Blackwell, Oxford. James, William: 1907/46, Pragmatism: A New Name for Some Old Ways of Thinking, Longmans, Green and Co., New York. Lovibond, Sabina: Realism and Imagination in Ethics, University of Minnesota Press, Minneapolis. Price, Huw: 2004, “Immodesty Without Mirrors – Making Sense of Wittgenstein's Linguistic Pluralism”, in Max Kölbel and Bernhard Weiss (eds.), Wittgenstein’s Lasting Significance, Routledge, London, pp. 179-205. Putnam, Hilary: 1981, Reason, Truth and History, Cambridge University Press, Cambridge. Putnam, Hilary: 1987, The Many Faces of Realism, Open Court, La Salle. Putnam, Hilary: 1987a, “Truth and Convention: On Davidson’s Refutation of Conceptual Relativism”, Dialectica 41: 69-77. Reprinted in Realism with a Human Face, Harvard University Press, Cambridge, Mass., 1990, pp. 96-104. Putnam, Hilary: 1992, Renewing Philosophy, Harvard University Press, Cambridge, Mass. Putnam, Hilary: 1994, “The Question of Realism”, in Words and Life, Harvard University Press, Cambridge, Mass., pp. 295-312.

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Putnam, Hilary: 2001, “Was Wittgenstein Really an Anti-Realist about Mathematics?”, in Timothy McCarthy and Sean C. Stidd (eds.), Wittgenstein in America, Oxford University Press, Oxford, pp. 140-194. Putnam, Hilary: 2001b, “Reply to Jennifer Case”, Revue Internationale de Philosophie 55: 431-8. Putnam, Hilary: 2004, Ethics Without Ontology, Harvard University Press, Cambridge, Mass. Wittgenstein, Ludwig: 1964, Remarks on the Foundations of Mathematics, Basil Blackwell, Oxford. Wittgenstein, Ludwig: 1975, Lectures on the Foundations of Mathematics: Cambridge, 1939, edited by Cora Diamond, The University of Chicago Press, Chicago and London. Wright, Crispin: 1983, Frege’s Conception of Numbers as Objects, Aberdeen University Press, Aberdeen. Wright, Crispin: 1992, Truth and Objectivity, Harvard University Press, Cambridge, MA. Wright, Crispin: 1996, “Précis of Truth and Objectivity”, Philosophy and Phenomenological Research 56: 863-8. Reprinted in Wright (2003), pp. 3-10. Wright, Crispin: 2003, Saving the Differences: Essays on Themes from Truth and Objectivity, Harvard University Press, Cambridge, Massachusetts.

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