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Skepticism about Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox

  • Scott Soames (a1)


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1 In discussing ‘Kripke's Wittgenstein’ I have in mind the philosophical position presented by Kripke, Saul in chapters 2 and 3 of Wittgenstein On Rules and Private Language, (Cambridge, MA: Harvard University Press 1982). Kripke presents this position both as an interpretation of the leading ideas of Wittgenstein's Philosophical Investigations and as a philosophical point of view of independent interest. My discussion of the position will be concerned only with its content and merits, not its origin. The question of whether the position outlined by Kripke is an accurate interpretation of Wittgenstein is not directly relevant to my discussion.

2 Stating the skeptic's argument is not just a matter of uttering the words, but rather involves taking up genuine propositional attitudes toward the contents expressed by those words.

3 The advantage of this way of formulating the problem is that it allows us to take the meanings of the words we use in stating the argument for granted while the argument is being given and evaluated. Hence we do not have to rely on the meanings of certain words in stating the argument while at the same time questioning what those words mean.

4 Kripke introduces this sense of metalinguistic correctness on 8.

5 The skeptic's challenge is made graphic by his suggestion that perhaps in the past I used ‘+’ to denote not the addition function but the quaddition function, where the latter differs from the former in assigning the value 5 to all pairs of arguments greater than any arguments I had explicitly used in calculations. It is assumed, for the sake of discussion, that 68 and 57 are such a pair.

6 Kripke's skeptic raises a challenge about content-bearing (i.e. intentional) facts. The challenge is to locate non-content-bearing (i.e. nonintentional) facts that determine the content-bearing ones. In attempting to meet this challenge, the nonintentional facts that one is allowed to appeal to are not restricted to behavioural facts, publicly observable facts, or even physical facts. Mental images, representations, feelings, and sensations can all be appealed to, provided that their ‘interpretations,’ or contents, (if any) are not taken for granted, but are themselves given a thoroughly non-intentional explanation.

In certain cases, it is quite plausible to suppose that factors such as linguistic rules or representations really do play a role in determining the meanings of some expressions. A case in point is'+’ itself. However in this, as in other cases, the role is dependent upon a prior explanation of the contents of the relevant rules, algorithms, images, or representations.

7 Kripke, 26

8 Both the error and the finitude objections can be generalized to cover dispositional analyses of other terms. In this connection, it is important to note that the finitude objection to the dispositional analysis of'+’ is just one instance of a more general objection. The objection is that a term may apply to certain objects even in cases in which those objects are, for one reason or another, epistemically inaccessible to us, and hence are not objects about which we have any normal dispositions. In the case of'+’ the infinity of natural numbers ensures that at some point they will get too big for us to consider. In the case of other words the reasons for epistemic inaccessibility may be quite different.

9 One possible response to these objections would be to give up the dispositional analysis for'+,’ while retaining it for simpler notions like ‘successor,’ in terms of which'+’ could then be defined. Certainly, there is less room for error in applying the successor function than in applying the addition function. However, some room for error may remain, and, in any case, the finitude objection still seems to apply. Another possibility, considered by Kripke, is to reformulate the analysis so as to appeal to idealized dispositions- dispositions to answer questions ‘What is n + m?', not in just any circumstances, but in certain idealized circumstances, in which one scrupulously ‘checks’ one's work, and in which one's mental capacities have somehow been enhanced to allow one to consider arbitrarily large numbers. Kripke's criticism of this response is telling. In order for the analysis to be non-circular, one must not characterize the idealized dispositions in a way that presupposes in advance what we mean by'+.’ For example, they cannot be characterized as dispositions to answer the relevant questions when we have been provided with sufficient mental capacities to allow us to correctly add any two numbers. However, if our characterization of the ideal dispositions is non-circular, then we will have little reason to be confident that they will in fact determine the desired function. It is also worth noting that the finitude and error objections cannot be overcome by appealing to the dispositions of the entire linguistic community of which the speaker is a part. These dispositions are just as subject to the objections as are the dispositions of an individual.

These considerations constitute serious obstacles to the dispositional analysis. I do not maintain that they rule out all possible reformulations. Perhaps there are reformulations of the analysis that are capable of avoiding the error and finitude objections. Even if this is so, the normativity arguments will remain, and will, I suspect, require appeal to some factors over and above dispositions. See below.

10 A relevant passage is the following:

To a good extent this reply (the dispositional analysis] immediately ought to appear to be misdirected, off target. For the skeptic created an air of puzzlement as to my justification for responding ‘125’ rather than ‘5’ to the addition problem as queried. He thinks my response is no better than a stab in the dark. Does the suggested reply advance matters? How does it justify my choice of ‘125'? What it says is: “'125’ is the response you are disposed to give, and (perhaps the reply adds) it would also have been your response in the past.” Well and good, I know that ‘125’ is the response I am disposed to give (I am actually giving it!), and maybe it is helpful to be told – as a matter of brute fact– that I would have given the same response in the past. How does any of this indicate that– now or in the past– ‘125’ was an answer justified in terms of instructions I gave myself, rather than a mere jack-in-the-box unjustified and arbitrary response? (23)

The emphasis here on justification echoes the way in which Kripke initially sets up the skeptical problem.

In the discussion below, the challenge posed by the skeptic takes two forms. First, he questions whether there is a fact that I meant plus, not quus, that will answer his skeptical challenge. Second, he questions whether I have any reason to be so confident that now I should answer ‘125’ rather than ‘5.’ The two forms of the challenge are related. I am confident that I should answer ‘125’ because I am confident that this answer also accords with what I meant. Neither the accuracy of my computation nor of my memory is under dispute. So it ought to be agreed that if I meant plus, then unless I wish to change my usage, I am justified in answering (indeed compelled to answer) ‘125’ not ‘5.’ An answer to the skeptic must satisfy two conditions. First, it must give an account of what fact it is (about my mental state) that constitutes my meaning plus, not quus. But further, there is a condition that any putative candidate for such a fact must satisfy. It must, in some sense, show how I am justified in giving the answer ‘125’ to ‘68 +57.’ (11)

11 I am here taking the meanings of the other symbols–the numerals and identity sign as given. This simplification does not affect the point at hand.

12 On page 11 Kripke insists “Neither the accuracy of my computation nor of my memory is under dispute. So it ought to be agreed that if I meant plus, then unless I wish to change my usage, I am justified in answering … ‘125,’ and not ‘5. ‘“Similarly, on page 13, in explaining why he sets up the paradox as a metalinguistic problem about the past use of an expression, Kripke says that when this is not done, “some listeners hear it as a skeptical problem about arithmetic: “How do I know that 68 +57 is 125?” (Why not answer this question with a mathematical proof?) At least at this stage, skepticism about arithmetic should not be taken to be in question: we may assume, if we wish, that 68 + 57 is 125.” I take these passages to indicate that in Kripke's formulation of the paradox, my present (true) belief that 68 +57= 125 can be appealed to (without further justification) in attempting to meet the skeptic's demand that I show how I am justified in thinking that ‘125’ is the answer required by my past understanding of the term.

13 Is it necessary, in order for the Normativity Requirement (NE) to play its proper role in the skeptic's argument, for the meaning-determining fact that F to provide the basis for an a priori, demonstrative inference to the relevant conclusion, or would it be enough for the fact that F to provide the basis for any sort of inference to the conclusion? Although the point is arguable, there are reasons for opting for the stronger interpretation. First, Kripke's skeptic seems to be looking for nonintentional facts that both metaphysically necessitate and epistemologically demonstrate the relevant meaning facts. Nonintentional facts that have meaning facts as a priori consequences would, presumably, do this; whereas nonintentional facts which provide only the basis for an empirical inference to the meaning facts presumably would not. Second, when we cast our net wider, and include nonintentional facts other than the dispositional facts presently under consideration, the skeptic's claim that meaning facts are not a priori consequences of any such set of facts remains plausible, whereas a corresponding claim, to the effect that meaning facts cannot be inferred from nonintentional facts, even by an empirical inference to the best explanation, say, is not nearly so plausible.

A different question about the normativity requirement is whether, as it is currently stated, it is too weak. Perhaps, in addition to being required to have meaning facts as a priori consequences, meaning-determining facts should also be required to be readily accessible to the speaker- so that the speaker is in a position to draw the relevant conclusions from those facts. I have no objection to this strengthening of the requirement; all the philosophical points I want to make regarding (NE) would hold for this strengthening of (NE). My reason for preferring the weaker version in the text is that it leads to a conclusion of greater generality. I am indebted to George Wilson for a discussion of this point.

14 The point here is a general one, and applies to versions of the rule-following paradox involving all sorts of different words. For example, consider a word like ‘fossil,’ which applies to concrete physical objects. Given some object o, the normative prescription regarding whether one should apply ‘fossil’ to o depends on (i) the meaning of the word ‘fossil,’ (ii) the nonlinguistic facts about the nature of o–i.e. whether or not it is a fossil and (iii) the general presumption that one should apply a term to an object only if doing so would involve speaking the truth. As Michael Thau has emphasized to me, examples like this highlight the need for (ii) over and above (i) particularly clearly.

There is, however, another issue involving facts like (ii) that is worth mentioning, even though I don't have sufficient space here to go into detail. Suppose I apply the word ‘fossil’ to a certain object o, and then I am challenged by a skeptic to justify this new application of the word. Suppose further that part of my response involves citing some fact F about my past use of the word. Imagine for the sake of argument that knowledge ofF does allow me to demonstrate that in the past I used the word to mean fossil. Still, this by itself doesn't justify my application of the word to o, even if I am now using the word with the same meaning as before, and it is granted that I ought in this case to speak the truth. To complete my justification I have to show that I am justified in thinking that o is a fossil. And how am I to do that? Perhaps the explanation of what it is for me to think that o is a fossil is simply for me to understand the word ‘fossil’ and be disposed to apply it to o on the basis of some reasonable, empirical examination of, or inquiry about, o. If so, then the justification for my thinking that o is a fossil may amount to little more than my now understanding the word ‘fossil’ and being disposed, after appropriate investigation and reflection, to apply it to o.

If this is the situation, then in some ultimate sense I may have no justification for applying the term to a new item o, other than my own confident, informed, and reflective inclination to do so, plus my status as a competent user of the term. This does seem to be an important part of what Wittgenstein was trying to show in his deployment of the rule-following paradox, and it is also present in Kripke's discussion. Moreover, there are, I think, cases in which something like this point is correct. However, this observation about justification does not undermine the response given in the text to Kripke's version of the skeptical paradox; nor does it lead to any defensible skepticism about meaning.

What it may do is point to an alternative route to one of Wittgenstein's conclusions about language – a route that does not require any fundamental, skeptical recasting of our ordinary conception of meaning. The conclusion is that, at least in some cases, the explanation of a speaker's understanding of a term T (including his ability to apply it to newly considered objects) does not involve associating T with an independently apprehended property P (and judging those objects to have P). Understanding a term, or using it to mean a certain thing, is not always like deciding to attach a new proper name to an object with which one is already familiar. See my ‘Semantic Competence,’ Philosophical Perspectives 3 (1989) 575-96, at 587-91 for a brief discussion of this idea. This idea is discussed in more detail in my, ‘Facts, Truth Conditions, and the Skeptical Solution to the Rule-Following Paradox,’ Philosophical Perspectives 12 (1998), forthcoming.

I am indebted to James Pryor and Michael Thau for helpful discussions of the material in the footnote.

15 See also Kripke's discussion in footnote 18, 24.

16 One important reason why it is difficult to be certain on this point is that it is not completely clear what apriori definitions of intentional notions are possible. For a good discussion of this issue, and an argument for the conclusion that facts about meaning (and belief) are not a priori consequences of nonintentional facts, see Byrne, AlexThe Emergent Mind, unpublished dissertation, Princeton University, 1993.

17 If the required epistemological relationship between the nonintentional truths and the claims about meaning were weakened to include empirical inferences to the best explanation, then the skeptical thesis that meaning claims are not epistemological consequences of nonintentional truths would be far more questionable. In any case, Kripke's skeptic does not argue in this way. (See note 13 above.)

18 Given an appropriately broad listing of nonintentional facts in P1

19 The strength of this thesis, as well as the more general thesis of the underdetermination of empirical theories by observational data, depends on one's conception of what it is for a class of data statements to support a theory.

For present purposes I will follow what appears to be Quine's latitudinarianism on this subject. Theories, together with auxiliary observational statements, make (entail) observational predictions. (Which statements count as observational for this purpose will not be an issue here.) A set of such observational predictions supports a theory to the extent that the theory, supplemented by true auxiliary observation statements, entails the members of the set. Two theories (appropriately supplemented with auxiliary observational statements) that entail the same members of the set, are equally well supported by the set.

20 I am assuming, in order to simplify the argument, that words are the minimal meaning bearing units, that languages contain finitely many such words, and that the translation of the infinitely many phrases and sentences of the two languages is the result of (i) the translation of the words that make them up plus (ii) combinatorial principles specifying the translations of syntactically complex expressions in terms of the translations of their parts.

21 See chapter 2 of Word and Object (Cambridge, MA: MIT Press 1960).

22 When Quine speaks of different, incompatible theories (or ‘theory formulations’) all equally supported by the same possible observational evidence, he seems to have in mind logically incompatible theories (or theory formulations). (See ‘On the Reasons for Indeterminacy of Translation,’ Journal of Philosophy 67 (1970) 178-83, at 179; and ‘On Empirically Equivalent Systems of the World,’ Erkenntnis 9 (1975) 313-28, at 322.) However, despite the obvious difference in meanings between ‘rabbit,’ ‘set of undetached rabbit parts,’ and ‘temporal stage of a rabbit’ as I use them now, the following claims are not logically incompatible: (i) the term ‘rabbit’ as I used it in the past means the same as the term ‘rabbit’ as I use it now (ii) the term ‘rabbit’ as I used it in the past means the same as the phrase ‘set of undetached rabbit parts’ as I use it now, (iii) the term ‘rabbit’ as I used it in the past means the same as the phrase ‘temporal stage of a rabbit’ as I use it now. Consequently, translation theories making these different claims need not be logically incompatible with one another.

Logical incompatibility will result if translation theories are embedded in larger background theories containing the following claims: (a) Rabbits are not sets of undetached rabbit parts & sets of undetached rabbit parts are not temporal stages of rabbits & rabbits are not temporal stages of rabbits ; (b) ‘Rabbit’ (as I use it now) refers to an object iff it is a rabbit & ‘set of undetached rabbit parts’ (as I use it now) refers to an object iff it is a set of undetached rabbit parts & ‘temporal stage of a rabbit’ (as I use it now) refers to an object iff it is a temporal stage of a rabbit; (c) if two words refer to different things then they don't mean the same; (d) if a means the same as b & a means the same as c, then b means the same as c. Let T1 be a translation theory containing statement (i), T2 be a translation theory containing statement (ii), and T3 be a translation theory containing statement (iii). The union of T1, T2, and a set containing (a)-( d) is logically inconsistent; as are corresponding unions involving the other relevant combinations. The justification for appealing to these auxiliary claims is that (a) states an obvious fact and (b)-(d) are axiomatic to any overall theory that makes significant use of the concepts of meaning and reference.

23 See Quine, Reply to Chomsky,Davidson, D. and Hintikka, J. eds., Words and Objections (Dordrecht: Reidel 1969), 303.

24 In this paper I will assume, without argument, that Quine's behaviourism about language is false. It is noteworthy, however, that the appeal of the indeterminacy thesis, and the challenge posed by it, have been strongly felt by many philosophers who have not been prepared to accept behaviourism independently. My task here is to diagnose the source of that appeal, and defuse the challenge felt by those philosophers.

25 It is important not to confuse what is a genuine pretheoretic conviction- namely that we do know what our words, and those of our neighbors, mean - with what is not such a conviction - namely that we arrive at this knowledge by deriving true claims about the meanings of our words, and those of our neighbors, as a priori consequences of purely physical truths. Whereas the former claim is clearly true, the latter is almost certainly false.

26 Quine's doctrines of Physicalism, the Indeterminacy of Translation and the Inscrutability of Reference entail that claims of the sort, Person P's word w refers to rabbits (as opposed to sets of undetached rabbit parts, etc.), are not determined by the totality of physical facts and so do not express genuine truths; ditto for any open formula P's word w refers to x relative to an assignment of an object as value of the variable ‘x.’ Given Quine's usual understanding of the existential quantifier, one can conclude from this that ∃x P's word w refers to x never expresses a genuine truth. Supposing that it is nevertheless meaningful, we may conclude that ∼∃x P's word w refers to x will always be true; in effect, no one's words ever refer to anything. This is eliminativism about reference (as ordinarily understood). Pretty paradoxical, especially for someone who clearly is attempting to use words to refer to, and make claims about, things.

Quine nowhere explicitly acknowledges such starkly paradoxical consequences of his views. The closest he comes is in the essay ‘Ontological Relativity; in Quine, Ontological Relativity (New York and London: Columbia University Press 1969), 2668, at 47-51. There he notes the paradoxical consequences of applying the Indeterminacy and Inscrutability doctrines to our (present) selves, and attempts (unsuccessfully) to avoid these consequences by invoking his mysterious doctrine of reference relative to a coordinate system (48) and “acquiescing in our mother tongue” (49). Unfortunately, space limitations prevent me from providing a thorough discussion of these passages here.

27 This result could be avoided if it could be shown that there are genuinely apriori semantic definitions of ‘gene’ and ‘DNA’ from which, together with the set of purely physical truths, the theoretical identification of genes with DNA can be derived. Since I am not certain whether this is possible in principle, I am not certain that the case of genetics provides a genuine counterexample to the strong epistemological version of physicalism. By the same token, I am not certain that no genuinely a priori semantic definitions of notions like meaning and reference exist from which, together with all physical truths, claims about meaning and reference can be derived.

28 This conception of determination is closely related to familiar conceptions of theoretical reduction, which are used by Friedman, Michael in ‘Physicalism and the Indeterminacy of Translation,Noûs 9 (1975) 353-73, to characterize Quine's theses of Physicalism and the Indeterminacy of Translation. There Friedman recognizes two kinds of reduction, strong and weak. Strong reduction is reduction in the classical sense. A theory T2 is classically reducible to a theory T1 iff the theorems of T2 are logical consequences of T1 together with a set D containing a ‘definition’ for each primitive predicate of T2. A ‘definition’ is a universally quantified biconditional establishing the extensional equivalence of an nplace primitive predicate of T2 with a corresponding formula of arbitrary complexity of the language of T1.

The same point can be expressed in another way by noting that the ‘definitions’ appealed to in a reduction can be taken as establishing a mapping D from primitive predicates of T2 onto coextensive open formulas of T1 Given this, we may define the notion of an n-place (primitive) predicate P of T2 being satisfied by an n-tuple in an arbitrary model M relative to a mapping D as consisting in the image of P under D being satisfied by that n-tuple in M. Classical (strong) reduction obtains when there is a mapping D such that every model of T1 is a model-relative-to D of T2. (See Friedman 357-8.)

Weak reduction is just like strong reduction except that the mapping D associates each primitive predicate of T2 with a set of corresponding open formulas of the language of T1 The set of formulas D associates with each primitive predicate P must be coextensive with P – i.e., as a matter of fact an n-tuple will satisfy P iff it satisfies at least one formula in the image of P under D. The notion of an n-place (primitive) predicate P of T2 being satisfied by an n-tuple in an arbitrary model M relative to such a mapping D is then defined as consisting in there being at least one member of the set of formulas associated with P by D being satisfied by that n-tuple in M. As before, reduction obtains when there is a mapping D of this sort such that every model of T1 is a model-relative-to D of T2 (Weak reduction differs from strong reduction only in cases in which the sets associated with the primitive predicates of T2 are infinite.)

Friedman's stated reason (358) for allowing weak reduction to count as a genuine type of theoretical reduction is to make room for positions such as functionalist theories of mind which identify each token of a mental type with a particular physical realization, while recognizing arbitrarily many different ways in which the given type might be physically realized. Note, however, the modal notion here. Its use in characterizing the relevant functionalist theories points up a modest puzzle having to do with Friedman's position. Reduction, as he officially characterizes it, does not require the ‘definitional’ mapping D to pair the predicates of T2 with formulas, or sets of formulas, that are intensionally equivalent to them in any sense. In particular D is not required to produce pairs that are extensionally equivalent in arbitrary counterfactual, or apriori imaginable, circumstances. Because of this the different merely possible, or merely imaginable, ways in which a mental type might be physically realized are, strictly speaking, irrelevant to the existence of ‘definitional’ mappings D satisfying Friedman's stated conditions for reduction. Since, as far as I know, physicalist functionalists never maintain that there actually exist infinitely many physically different kinds of realizations of a given mental type, they presumably ought to be reasonably confident in asserting the strong reducibility (in Friedman's official sense) of their theories to physics. Why then is there a need for the notion of weak reducibility? Does Friedman's use of the notion reflect an implicit desire to require the ‘definitional’ mappings in genuine reductions to provide more than actual coextensiveness? Do they also have to provide coextensiveness in all counterfactual (or in all apriori imaginable) situations as well? If so, then couldn't we define the determination relations needed to evaluate Quine's theses directly in terms of necessary, or a priori, consequence, as above?

Putting these and other subsidiary issues aside, I would like to acknowledge the essential correctness of some of Friedman's central points. In particular, he makes a plausible case for interpreting Quine's thesis of the Indeterminacy of Translation as the doctrine that theories of translation are not reducible (in either his strong or his weak sense) to the set of physical truths. He then argues for the correct (but understated) conclusion that Quine has given no compelling argument for the Indeterminacy Thesis, understood in this way.

29 In this discussion I ignore certain practical complications such as the fact that some speakers speak more than one language, the fact that words of the language may be ambiguous, and the possibility that sometimes there may be no translation of a word in one language onto a word or phrase of the other language. Although these are real factors in translation, they are peripheral to Quine's philosophical claims about translation.

30 On this interpretation Friedman's relation of weak reduction, strengthened by the requirement that the mapping from predicates in T2 to sets of formulas of the language of T 1 produce pairs that are necessarily coextensive (in the sense of note 28), should count as a genuine instance of determination in the sense presently under consideration.

31 The ideas in this paper date back to seminars I gave in the summer of 1988 at the University of Washington, and in the fall of 1988 at Princeton University. These ideas were refined and elaborated in my fall semester seminar of 1993 at Princeton. An early versmn of the first section of this paper, on Kripke's account of the rule-following paradox, was presented in june of 1995 at the lnstituto de Investigaciones Filosoficas de Ia Universidad Nacional Autonoma de Mexico. Later versions of the paper were presented at the Department of Philosophy, Wayne State University on October 13, 1995, the Chapel Hill Philosophy Colloquium on October 29, 1995, the Division of Humanities at the California Institute of Technology on November 3, 1995, the lnstituto de investigaciones Filosoficas de la Unversidad Nacional Autonoma de Mexico on january 26 and 29, 1996, the Department of Philosophy at Rutgers University on March 7, 1996, the Department of Philosophy at Reed College on March 20, 1996, and the Department of Philosophy at the University of California at Berkeley on April 25, 1996. It was also presented at my fall semester seminar in 1996 at Princeton. I would like to thank the participants at all those presentations, and seminars, for their comments. In addition, I would like to thank james Pryor, Michael Thau and George Wilson for reading and commenting on earlier drafts of the paper.

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Skepticism about Meaning: Indeterminacy, Normativity, and the Rule-Following Paradox

  • Scott Soames (a1)


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