Murphy Shimamoto

How Kripke’s Wittgenstein argues that there are no meaning facts. A Summary

Kripke’s Wittgenstein On Rules and Private Language proffers a sceptical argument dragging one into the conclusion that there are no meaning facts. This paper will reproduce how the sceptic argues this point by focusing almost exclusively on the tension Kripke unearths between the finite and the infinite in the process of rule-following. I will take up the idea of the tension between the infinite and the finite as a conclusion which reaffirms the validity of the sceptic’s argument after reproducing his refutation of the internalized learning objection. In so doing, I hope to demonstrate the soundness of that argument.

Kripke says of rules that “I grasp a rule: my past intentions regarding addition determine a unique answer for indefinitely many new cases in the future.”¹ In Kripke’s understanding a rule is a normative function which guides the follower into its correct application for an infinite number of cases. For example, addition should function as a rule which guides the calculator to the correct sum for any infinite amount of numbers being added. Kripke writes “Although I myself have computed only finitely many sums in the past, the rule determines my answer for indefinitely many new sums that I have never previously considered.”² However, it is this finitude of past calculations which exposes the rule-follower to the sceptical challenge as “The sceptic doubts whether any instructions I gave myself in the past compel (or justify) the answer ‘125’ rather than ‘5’…Perhaps when I used the term ‘plus’ in the past, I always meant quus: by hypothesis I never gave myself any explicit directions that were incompatible with such a supposition.”³ The sceptic points out the fact that for any number of past calculations each example which is supposed to be an instantiation of addition can be made out to conform with an infinite number possible alternative rules as well. As Kripke indicates “there are infinitely many candidates the sceptic can propose for the role of quaddition.”⁴ Therefore, each individual past calculation which is meant to exemplify addition rule-following can plausibly be compatible with another rule. This is due to the fact that each calculation or group of calculations which are held up as instantiations of addition are finite. For example, a sum can accord with addition for each calculation put forward in the finite number of cases and, yet, simultaneously deviate from addition in cases which aren’t included in the finite sample size which has actually been calculated. Given that examples of rule-following are limited to one’s past, and this is necessarily finite, there is no way for the finite amount of cases put forward to be able to escape the sceptical doubt which considers rules that could conform exactly to the calculations performed thus far and deviate in an infinite amount of alternative calculations. Simply put “How can I justify my present application of such a rule, when a sceptic could easily interpret it so as to yield any of an indefinite number of other results. It seems that my application of it is an unjustified stab in the dark. I apply the rule blindly.”⁵ If this is the case, as Kripke’s sceptic argues, then there is no way to ground meaning in a fact of the matter. Which rule one means, i.e. which intention that normatively guides the rule-follower to a correct and unique answer, cannot be pinned down in any past calculation. And if “there was no fact about me that constituted my having meant plus rather than quus…If there was no such thing as my meaning plus rather than quus in the past, neither can there by any such thing in the present…There can be no fact as to what I meant by ‘plus’, or any other word at any time.”⁶

It should be taken into account that Kripke addresses a possible objection before his sceptic explicitly attacks dispositionalist refutations. Given that the latter is the topic of another essay question I will only deal with the former here. He addresses the obvious intuition that “I learned - and internalized instructions for - a rule which determines how addition is to be continued,” and that therefore “I proceed according to an algorithm for addition that I previously learned.”⁷ However, the sceptical response to this objection shows that this claim is ultimately defeated through its vulnerability to an infinite regress. For in addition one must count properly and thus the response that “But I applied ‘count’, like ‘plus’, to only finitely many past cases. Thus the sceptic can question my present interpretation of my past usage of ‘count’ as he did with ‘plus’…he can claim that by ‘count’ I formerly meant quount, where to ‘quount’ a heap is to count it in the ordinary sense, unless the heap was formed as the union of two heaps.”⁸ The sceptical response shows the futility of searching for “a rule for interpreting a rule.”⁹ Again, limited to a finite set of instances in the past, each case or group of cases could be made to accord to an infinite number of compatible rules. It is this infinite mutual compatibility for any finite case(s) which closes the avenue for grounding a rule in a concrete case. If we were to express this in a Kripkenstenian manner then we could say that any rule could become a ‘quule’. Thus Kripke writes “The infinitely many cases…are not in my mind for my future self to consult. To say that there is a general rule in my mind that tells me how to add in the future is only to throw the problem back on to other rules that also seem to be given only in terms of finitely many cases…It seems that the entire idea of meaning vanishes into thin air.”¹⁰

If Kripke’s demonstration that any finite case(s), because of its finitude, can be made to conform to an infinite number of rules, then one must conclude that the sceptic’s argument that there are no meaning facts is sound. This paper believes the aforementioned summation of Kripke’s argument and response to internalized learning is sufficient to substantiate that claim. However, in addition I would like to add some quick remarks which familiarise this notion in an older philosophical dialectic. Kripke points out a tension between finitude and infinitude in the case of following a rule. When expressed in these terms it should not be surprising that Kripke fails to answer his sceptic. For what one must do in order to satisfy him would have to be the reconciliation of infinity and finitude from within the finite itself. A stream of finite instances would each have to contain within themselves the same infinite, which seems to be, by definition, a logical contradiction. For if one only has access to the finite, how can one expect to find the infinite within it without presupposing that the infinite grounds the finite and that the finite is a sufficient base for finding the infinite? Kripke, in an outstandingly original way, shows the futility of the attempt to ground the infinite in the finite through the finite alone and thus his sceptical argument is sound.

Notes

¹ S. Kripke, On Rules and Private Language, p. 8.

² Ibid., p. 7.

³ Ibid., p. 13.

⁴ Ibid., p. 27.

⁵ Ibid., p. 17.

⁶ Ibid., p. 21.

⁷ Ibid., p. 15.

⁸ Ibid., p. 16.

⁹ Ibid., p. 43.

¹⁰ Ibid., p. 22.

Works Cited

Kripke, Saul A. Wittgenstein on Rules and Private Language. Blackwell, 1982.