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Is (Determinate) Meaning a Naturalistic Phenomenon? 15.1 Introduction When philosophers worry about the relation between the mental and the physical, they typically have in mind the problem of consciousness: how could phenomenal states emerge from the comings and goings of purely naturalistic—that is, purely physical/functional—things and states? How could there be something that it’s like to be a certain kind of physical thing, no matter how complex? With some notable exceptions, philosophers haven’t worried as much about how we might account for the intentional on such a naturalistic basis. Or, if they have worried about it, they have usually been quite optimistic that the intentional can be shown to be a purely naturalistic phenomenon (see Fodor (1987) , Dretske (1981) , and Stalnaker (1984) for example). Chalmers (1996 : 24) nicely sums up philosophers’ attitudes when he says: ‘These problems [posed by intentional states] are all serious, but they have the character of puzzles rather than mysteries’. Well, perhaps nothing is quite as much of a mystery as consciousness. However, I am inclined to think that we have tended to underestimate just how mysterious intentionality is, especially when it is viewed from a naturalistic standpoint. In this chapter, I revisit the question whether facts about intentional content can be understood in purely naturalistic terms, a question that I first discussed in detail in Boghossian (1989) . In that paper, I argued that Saul Kripke’s Wittgenstein-inspired discussion of following a rule was, pace Kripke’s intention, best understood as showing that facts about intentional content resist naturalistic reduction.1 (p.332) The message of this chapter is the same, although there are several respects in which it differs from, and, I hope, improves upon, the earlier paper. First, it argues for a somewhat weaker conclusion—not that facts about intentional content cannot be naturalistically reduced, but, rather, that either they cannot be reduced or that they are indeterminate. Second, it uses bits of Kripke’s discussion that neither he nor I emphasized previously and that, in any case, have been widely rejected as ineffective. And, finally, it takes into account important distinctions that were missing both from Kripke’s original discussion and from mine. 15.2 Comparison with Kripke’s Argument For ease of exposition, I will pretend that we think in a language of thought, so that when we think that snow is white we are thinking a sentence S whose meaning is that snow is white. In fact, for greater simplicity, I will assume that we think in English. Like Kripke, I will focus on the case of addition, leaving until later the question how, if at all, the argument might extend to non-mathematical cases. It will prove useful, before proceeding any further, to compare the argument I will be pursuing to Kripke’s. Kripke’s argument has been nicely summarized by Soames. He represents it as follows (1997: 232): 1. P1 If in the past there was a fact about what I meant by ‘+’, in particular, if there was a fact that I meant addition by ‘+’, then, either 1. (i) this fact was determined by nonintentional facts of such and such kinds—facts about my past calculations using ‘+’, the rules or algorithms I followed in doing calculations involving ‘+’, my past dispositions to respond to questions ‘What is n+m?’, the totality of my past dispositions to verbal behavior involving ‘+’, etc.or 2. (ii) the fact that I meant addition by ‘+’ was a primitive fact, not determined by nonintentional facts. 2. P2 Nonintentional facts of type (i) did not determine that I meant addition (or anything else) by ‘+’. 3. P3 What I meant by ‘+’ was not a primitive fact. 4. C1 Thus, in the past there was no fact that I meant addition (or anything else) by ‘+’. 5. C2 By parity of reasoning, there never was a fact about what I, or anyone else, meant by any word; ditto for the present. Soames goes on to expresses puzzlement as to how Kripke’s argument could hope to succeed. Kripke’s conclusion—that there is no fact that anyone has ever meant (p.333) anything by his or her words— looks to be more than hugely implausible. It looks to be self-refuting. So we have plenty of reason to think that there must be something wrong with the argument that seems to lead up to it. And, indeed, according to Soames, it is quite clear where Kripke’s argument goes wrong: it suffers from equivocating between a priori and a posteriori notions of determination. Soames thinks that if we construe ‘determination’ as a priori determination, we can concede the truth of P2: Kripke does provide us with good grounds for denying that the naturalistic facts a priori determine the meaning facts. For example, he does provide us with good grounds for denying that meaning facts can be analyzed in terms of naturalistic facts. But on that construal of determination, Soames maintains, there is no reason to believe P3. For Kripke has provided us with no reason to think that, if meaning facts exist, they could not be conceptually primitive, non-analyzable facts. On the other hand, if we work with the notion of mere necessary determination, which does not entail apriority, or analyzability, then while P3 may look plausible, P2 doesn’t: Kripke has provided us with no reason to deny that naturalistic facts determine the meaning facts in some a posteriori way. Hence, Soames concludes, Kripke’s argument suffers from equivocation and its abhorrent conclusion is blocked.2 Now, I agree with Soames that Kripke’s argument, as he actually pursues it, fails to make enough distinctions—not only between a priori and a posteriori forms of determination, but also, and not unrelatedly, between concepts (modes of presentation) and properties, and between reductive claims and supervenience claims. Having said that, I think that Kripke’s discussion lays the foundation for a good argument, one that can accommodate all the relevant distinctions, for a somewhat weaker conclusion than the one Kripke pursues—namely: (Naturalistic Indeterminacy, NI) If what we mean is determined exclusively by naturalistic facts, then what we mean is indeterminate. Let me lay out the form of argument that I will use in support of (NI): A. If Naturalism is true, then the only facts relevant to fixing the meanings of our words are non-intentional facts x, y, and z. B. x, y, and z do not fix determinate meanings for our words.Therefore, C. If Naturalism is true, our terms do not have determinate meanings. (p.334) At first, I will operate with the following reading of premise A: A’: If Naturalism is true, then the only facts relevant to fixing the meanings of our terms are our dispositions to use those terms in certain ways. Later, I will argue that broadening our conception of which naturalistic facts are relevant will not help. The argument will be illustrated by example. We need to work with a term whose meaning is indefinable in terms of other words, so we can’t just read its meaning off its definition. Following Kripke, we will assume that word to be ‘+’. If you don’t like using this term for this purpose we can use another simpler concept, for example the concept successor. Anything I say about this case should work for the case of every other word that is not explicitly definable in terms of other meaningful words. Of course, if the primitives of the language have indeterminate meanings, then any word defined in terms of them will also have an indeterminate meaning. I will also assume for the moment that the meaning of a word is its referent—i.e. I will assume a Millian picture. An alternative view, of course, is that, in addition to its reference, every word expresses a meaning or sense that, in turn, determines a reference for it. It makes no difference to the effectiveness of the argument I have in mind which of these pictures we work with, but it might be easier to appreciate this once we have looked at the argument with the Millian picture in place. We take our use of ‘+’ to refer to the addition function, a two-place function that assigns a unique natural number as value to each of infinitely many pairs of natural numbers taken as its arguments. Even while we take ourselves to determinately refer to this function with an infinite domain, we have to acknowledge that there is an upper bound to the numbers whose ‘sum’ we have actually computed. Of all the numbers that we have actually employed in computing sums, there is one that is the largest. Indeed, it looks as though there is also an upper bound to those numbers whose ‘sum’ we are able to compute, at least as we are currently constituted, without idealizing our present capacities. In particular, some numbers are such that we would die before we could process which numbers they are. (We will look at idealizations of our capacities in due course.) This is a bit tricky because how long it takes to write out a particular number is, of course, a function of the numeral system being used. But we will ignore this complication and just assume that the privileged system for representing numbers is the common Arabic numeral system. Another complication is that we can use abbreviations to give very short representations of very large numbers, as in exponentiation. But even with exponentiation, there will still be a largest number that we are able to compute. And the crucial point for our purposes is that exponentiation would be a procedure that we would have to introduce by definition, using terms whose meaning had already been pinned down. (p.335) So it looks plausible to say that there are numbers that we cannot take in or process. I will call such numbers inaccessible numbers. I will call a function quus-like if it is exactly like the addition function up to some inaccessible number, but diverges from it thereafter (this is somewhat different from the definition that Kripke works with). Such a quus-like function may assign the number ‘5’ as the value of ‘m quus n =?’ for any m or n that is inaccessible. There are an infinite number of such functions and they are all perfectly good mathematical functions. My contention will be that no naturalistic fact can serve to pin down that what we mean by our symbol ‘+’ is addition rather than one of these infinitely many quus-like functions.3 15.3 Various Dispositional Accounts We are assuming, for the moment, that if Naturalism is true then the only natural facts relevant to fixing meaning are dispositional facts. We will revisit this assumption later. But let us start by focusing on those dispositional facts. How might they be relevant to fixing the meaning facts? I will work with the following menu of four options. To begin with, a dispositionalist might think that facts about meaning can be analyzed dispositionally: i.e., he might think that (Analysis): ‘S means plus by “+” ’ is synonymous with: ‘S is disposed to use “+” in way X’. Or, he might hold merely that, even if we reject a synonymy claim, we can still say a priori that the property of meaning plus by ‘+’ is identical to some dispositional property: (A Priori): The property of S’s meaning plus by ‘+’ is a priori identical to S’s being disposed to use ‘+’ in way X. More weakly still, he might think that, although this identity holds, it holds only a posteriori: (A Posteriori): The property of S’s meaning plus by ‘+’ is a posteriori identical to S’s being disposed to use ‘+’ in way X. (p.336) Finally, he might hold that meaning facts merely supervene on the dispositional facts without being identical to any of them. To say that meaning supervenes on the dispositional is to say that there can be no difference in the meaning facts without some difference in the dispositional facts. Equivalently, it is to say that fixing the dispositional facts fixes the meaning facts, but without there being any commitment either to our being able to explain a priori how the one set of facts determines the other, or to our being able to replicate the explanatory work that is done by the meaning facts in terms of the facts about dispositions: (Supervenience Dispositionalism): There can be no difference in the meaning facts without some difference in the dispositional facts. As I previously indicated, one of the issues with Kripke’s discussion is that he did not sufficiently distinguish between supervenience and reduction, nor between various ways of understanding what it would be to give a naturalistic ‘reduction’ of meaning. For the most part, he seems to have assumed that the only sort of naturalism about meaning worth discussing was a priori conceptual reduction. This gave many philosophers an opening with which to reject his arguments, as is well illustrated by the article by Soames discussed earlier. Kripke may be right that meaning cannot be analyzed in naturalistic terms, they say. But that leaves it open that meaning properties are identical with naturalistic properties, or that they supervene upon them. And these latter theses are naturalism enough. My task in this chapter is to argue that there is a way of developing some of Kripke’s arguments in a way that undermines even the weakest non-reductive form of naturalism about meaning— Supervenience—just outlined. It will prove useful to begin with the identity claims and then turn to Supervenience only later. 15.4 The Argument from Normativity Let’s start with the question: how might we go about identifying a meaning property with a dispositional property? Kripke works with a basic version of the dispositional theory, which he formulates as follows: (Basic Dispositional Theory): Necessarily: ‘S means plus by “+” ’ is true iff: For any two numerals ‘m’ and ‘n’ denoting particular numbers m and n, S is disposed, if queried about ‘m + n’, to reply ‘p’ where ‘p’ is a numeral denoting plus (m, n). Against this basic theory, Kripke formulates three distinct arguments, which I will call respectively, the Argument from Normativity, the Argument from Error, and the Argument from Finitude. The Argument from Normativity states that the notion of meaning is an essentially normative notion: if I mean addition by ‘+’, then I ought to answer ‘125’ to the question (p.337) ‘68 + 57 = ?’ (Kripke sometimes puts the point by saying that my meaning addition by ‘+’ justifies my saying ‘125’.) However, Kripke maintains, the relation of a disposition to its exercise is descriptive, not normative; hence, meaning facts can’t be identified with dispositional facts. I think this argument is problematic in several ways. I mention it here largely to set it aside, although, as I will explain in a moment, I believe it contains an important kernel of truth. The first problem with it is that it isn’t clear that meaning really is a normative notion, in the strict sense of the term.4 Second, even if the concept of meaning were normative, the most that would show is that the concept of meaning is not the concept of a disposition; it wouldn’t necessarily show that a meaning fact is not identical to a dispositional fact. A utilitarian might hold that the property that constitutes an act’s goodness is its conducing to the greatest happiness, even as he denies that the concept of goodness is identical to the concept of conducing to the greatest happiness. The conceptual claim might court an ‘open question’ objection, but not so the property claim. Similarly, someone might hold that the concept of meaning is not identical with the concept of a disposition, even though the property that underlies a true meaning claim is a dispositional property. There is, though, an important kernel of truth that the normativist claim contains which can be brought out as follows. Although my meaning, say, DOG by ‘dog’, doesn’t, all by itself, ground an ought claim about my use of the word, it can explain why I use that word one way, rather than another. It is in part because of what I mean by ‘dog’ that I apply it to this salient beagle and not to this cat or tree. The meaning doesn’t explain the use all by itself, of course, but only in conjunction with other facts, such as facts about my perceptions, and so forth. But it does enter into the explanation. So far, this doesn’t look to pose much of a problem for the dispositionalist. Although it used to be said that a disposition to dissolve in water couldn’t explain why this particular sugar cube dissolves in water, I think that’s now generally regarded as unjustifiably restrictive. Someone’s being risk-averse can explain why he chose not to make a particular investment; and, in general, we should allow that an object’s disposition to phi can explain why on a given occasion it phi’s. The trouble is that if we look at the matter intuitively we can see that my meaning something by a worddoes not merely explain my use of that word; it also explains my disposition to use that word in a certain way. Thus, my meaning plus by ‘+’ not only explains why, on a given occasion, I say that ’68 + 57 = 125’, but also why, on that occasion, I am disposed to say it. (p.338) Suppose I am queried about this particular arithmetical problem. I look at it, find myself disposed to say ‘125’, but, for whatever reason, don’t come out and say it. The fact that I was so disposed would itself be explained in part by the fact that I mean plus by ‘+’. However, it looks as though the dispositionalist cannot make sense of this for the simple, but incontestable, reason that something cannot explain itself. Notice that this consideration applies not only to a priori versions of identity dispositionalism, but also to its a posteriori versions. If water is H2O then whatever we can explain by appeal to something’s being water we should also be able to explain by appeal to its being H2O. Of course, we might be able to explain more through H2O than we can with water: science gives us deeper and more comprehensive explanations than we can give in ordinary life. But we should at least be able to replicate some of the genuine ordinary explanations that we are able to give. And this, I have claimed, we won’t be able to do in the case of a dispositional view of meaning. Let us call this the Argument from Explanation, in contrast with Kripke’s Argument from Normativity.