17

15.14 Is the Millian Assumption the Problem? If these considerations are correct, then the problem of finitude looks to remain with us, even if we take into account all the naturalistic facts that have been thought remotely relevant to the fixation of meaning. It is time now to wonder whether our problem would be alleviated if we substituted a Fregean picture for the essentially Millian one with which we have been working. Suppose that instead of claiming that I refer to addition directly, we claim that what happens is that I first grasp some sense PLUS, and that this determines Addition as the function that I refer to by ‘+’. What do we mean by the sense PLUS? A pair of conditions characterizes this sense. First, it is that sense that determines the plus function as its referent. Second, the sense PLUS is different from the sense PLUS, if it is possible for a thinker rationally to believe that x PLUS y = m but disbelieve that x PLUS y does not = m. On this standard Fregean way of doing things, the function plus is part of what individuates the sense PLUS. If there is a problem getting naturalistic facts to determine the plus function directly, there is going to be as much of a problem getting them to (p.356) determine PLUS rather than QUUS, where PLUS and QUUS are the same sorts of primitive senses, except that one determines addition as its referent and the other determines quaddition as its referent. Notice, what I have said is that, it is stipulatively true of the sense PLUS that it is whatever sense picks out the plus function, as well as the stuff about its role in rational belief. That is a stipulation about the sense PLUS. (Sense Individuation): If x means PLUS, then x is true of this (the plus) infinite set of triples and not any other set. By itself, though, this seems to do nothing to help us with our problem. For, as Kripke points out, we now appear to be able to restate the problem in terms of grasp of senses: how can it be a determinate fact that I grasp the primitive sense PLUS rather than the primitive sense QUUS, which differs from PLUS only in that one refers to Addition and the other to Quaddition? It’s not as though there is some other intrinsic feature by which one can tell them apart—some special quale that attaches to having the PLUS concept rather than the QUUS concept. Rather, the only basis for distinguishing between them is just that they are presumed to fix different extensions and to behave differently in rational belief. So it looks as though the route through Fregean senses is powerless to help us as well.16 15.16 Conclusion This concludes my argument for the claim that if it is only naturalistic facts that determine what we mean by our arithmetical concepts, then it is indeterminate what we mean. The question arises whether similar considerations apply in the case of non-mathematical, empirical concepts, like ‘dog’ or ‘green’. This is a very large question that I cannot take on in this chapter, havingalready exceeded the space allotted to me. There are two things that I would like to emphasize. First, even if it turned out that the problem of naturalistic indeterminacy does not arise for empirical general terms, it would still be very significant that it arises for formal notions, notions that one might intuitively have thought would be least likely to be afflicted with a problem of indeterminacy. The second point is that the question of finitude does not disappear as we look at non-mathematical concepts. Someone might very well think otherwise, maintaining that the extensions of ‘dog’ or ‘green’ are not, or anyway need not be, infinitary: unlike the infinite set of triples to which ‘+’ might be said to apply, there is only a finite number of dogs or green things. (p.357) But I think this would be a mistake. What naturalism needs to explain are expressions’ extension properties; and in the relevant sense, every term, including ‘dog’ and ‘green’, has an infinitary extension property. Even if the actual world contains only a finite number of dogs, the semantical property of the word ‘dog’ that needs explaining is not merely the fact that it applies to all the dogs in the actual world, but also that it applies to all the dogs in all possible worlds; and to nothing else. And that is an infinitary fact about it. Indeed, in the relevant sense, even a definite description like ‘my actual headache at time t’, which might intuitively be thought to refer uniquely only to one mental particular or state, has an infinitary extension property: for what’s true of it is that it applies uniquely to this unique mental item and not to any of these other infinite number of things (other headaches, all the non-headaches). Both the positive and the negative fact about its extension need to be reconstructed naturalistically, if naturalism is to be vindicated. At any rate, I hope to have shown that, at least for the class of cases made famous by Kripke, the basic elements of his argument can be used to show that there is a serious worry how determinate meaning could arise on a purely naturalistic basis.17 References Bibliography references: Blackburn, Simon. 1984. ‘The Individual Strikes Back’. Synthese 58: 281–301. Boghossian, Paul. 1989. ‘The Rule-Following Considerations’. Mind 98: 507–49. Reprinted in his Content and Justification: Philosophical Papers, pp. 9–50. Oxford: Oxford University Press. Boghossian, Paul. 2005. ‘Is Meaning Normative?’ In Philosophy—Science—Scientific Philosophy , edited by Christian Nimtz and Ansgar Beckermann, pp. 205–18. Paderborn: Mentis. Burge, Tyler. 1979. ‘Individualism and the Mental’. Midwest Studies in Philosophy 4: 73–121. Chalmers, David. 1996. The Conscious Mind: In Search of a Fundamental Theory. Oxford: Oxford University Press. Dretske, Fred. 1981. Knowledge and the Flow of Information. Center for the Study of Language and Information Publications (CSLI). Dummett, Michael. 1959. ‘Wittgenstein’s Philosophy of Mathematics’. The Philosophical Review 68: 324–48. Fodor, Jerry. 1987. Psychosemantics: The Problem of Meaning in the Philosophy of Mind. Cambridge, MA: MIT Press.Fodor, Jerry. 1992. A Theory of Content: And Other Essays. Cambridge, MA: MIT Press. Guardo, Andrea. 2012. ‘Rule-Following, Ideal Conditions and Finkish Dispositions’. Philosophical Studies 157: 195–209. (p.358) Handfield, Toby and Alexander Bird. 2008. ‘Dispositions, Rules, and Finks’. Philosophical Studies 140: 285–98. Horwich, Paul. 1995. ‘Meaning, Use and Truth: On Whether a Use-Theory of Meaning Is Precluded by the Requirement that Whatever Constitutes the Meaning of a Predicate Be Capable of Determining the Set of Things of Which the Predicate is True and to Which It Ought to Be Applied’. Mind, 104 (414), 355–68. Horwich, Paul. 2005. Reflections on Meaning. Oxford: Clarendon. Johnston, Mark. 1992. ‘How to Speak of the Colors’. Philosophical Studies 68: 221–63. Kripke, Saul. 1982. Wittgenstein on Rules and Private Language: An Elementary Exposition. Cambridge, MA: Harvard University Press. Lewis, David. 1983. ‘New Work for a Theory of Universals’. Australasian Journal of Philosophy 61: 343–77. Martin, C.B. 1994. ‘Dispositions and Conditionals’. The Philosophical Quarterly 44: 1–8. Martin, C.B. and John Heil. 1998. ‘Rules and Powers’. Noûs 32: 283–312. Millikan, Ruth. 1990. ‘Truth Rules, Hoverflies, and the Kripke–Wittgenstein Paradox’. The Philosophical Review 99: 323–53. Schiffer, Stephen. 1999. ‘The Epistemic Theory of Vagueness’. Noûs 33: 481–503. Soames, Scott. 1997. ‘Skepticism About Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox’. Canadian Journal of Philosophy 27 (suppl. 1): 211–49. Stabler, Edward. 1987. ‘Kripke on Functionalism and Automata’. Synthese 70: 1–22. Stalnaker, Robert. 1984. Inquiry. Cambridge, MA: MIT Press. Notes: (1) Naturally, I am not suggesting that Kripke would deny the anti-reductionist claim, but only that he claimed that his argument showed something stronger—not just an anti-reductionism about meaning facts, but an eliminativism about them. (2) A similar criticism of Kripke’s argument has been developed by Horwich (1995) . (3) As Kripke is well aware, there might seem to be a difficulty setting up this problem. Since it has to be set up in language, we must assume, as we are setting it up, that our current language has determinate meanings and, indeed, that we know what those meanings are. To enable the problem to get off the ground, Kripke starts by construing it as an issue about the past meanings of my terms, rather than about their current meanings. However, once the conclusion is established about one’s past meanings, it can be brought forward to cover the present as well since, in the relevant sense, no new facts will have emerged since then. If meaning was not determinate in the past, it couldn’t be determinate in the present, either. I will ignore this nicety in what follows. (4) I discuss this issue in detail in Boghossian (2005) . David Velleman was very helpful in getting me clear on this. Although Boghossian (1989) is often cited as defending a normativist view, it in fact expresses substantial skepticism about it. I explain all this in the 2005 article.(5) If we acknowledge that people can make ‘mistakes’ aren’t we conceding that meaning is a normative notion after all? No. The point is that, in the relevant sense, using a word ‘incorrectly’ (making a mistake) need not be understood as a genuinely normative notion, but simply as corresponding to using a word in application to something not in its extension. (6) Elsewhere, I have also developed at length an argument to the effect that belief holism gives us a different ground for doubting the existence of such optimality conditions. See Boghossian (1989) . (7) Since quus was defined as the function that diverges from plus over numbers greater than what a typical human adder is able to compute, one might think that it follows analytically from the existence of quus-like functions that there are inaccessible numbers. And indeed it does. The question before us therefore is: what reason does Kripke give for thinking that there are quus-like functions? (8) It might be thought that without the conditional analysis it will be hard to determine whether a possible situation is one in which a particular disposition is present or absent. But that would be a mistake. We had better be able to have fairly reliable intuitions directly about the presence or absence of dispositions, if we are to be able to check on the correctness of putative analyses of disposition talk in terms of conditionals. (9) In developing this point in a recent paper, Guardo (2012 : 203) has formulated it like this: On the one hand, there are the dispositions I would have had if I had been in ideal conditions. On the other, there are, among the dispositions I actually had, my past dispositions to give, if conditions had been ideal, certain responses to certain stimuli. I’m not sure that this is exactly the way to put it, but something in the general vicinity seems right. (10 ) It is worth noting that a problem would remain even if we allowed the dispositionalist to appeal to these hyper-idealized dispositions. For it would still be true, intuitively speaking, that I am disposed to die before answering questions involving inaccessible numbers. So now we have two conflicting dispositional ascriptions, both of which are said to be true (something that David Lewis was prepared to allow). As Handfield and Bird (2008) point out, though, we now would have to say which of the two conflicting dispositions we should take to be meaning constituting. (11 ) See Handfield and Bird (2008) (12 for a somewhat different way of presenting this idea. ) As Kripke mentions, Dummett (1959) (13 ) See Millikan (1990) raised this issue. . For a trenchant critique of teleosemantic approaches to meaning see Fodor (1992) . (14 ) Horwich (2005 : chapter 4) argues along these lines. (15 ) See Schiffer (1999) . Horwich (2005) also links the critique of epistemicism with the question of the adequacy of a dispositional account, but in a different way. His focus is not, as mine is here, on the problem of finitude. (16 ) Of course, these points echo ones that Kripke makes. (17 ) For helpful comments on the material in this paper, I am grateful to Ralf Bader, David Barnett, Ned Block, David Chalmers, Sinan Dogramaci, Hartry Field, Yu Guo, Paul Horwich, Jonathan Simon, Ted Sider, and to members of the seminar on Rule-Following at NYU, given with Paul Horwich, in 2006, and members of the Mind and Language Seminar at NYU in 2010; and to audience participants at the MidSouth Conference Keynote Address in Memphis in 2008.