Brief Overview of Key Parts and Key Notions in Kripke's book

1. The sceptical paradox: According to Kripke, in Wittgenstein's rule following considerations in Philosophical Investigations (roughly, PI ยงยง143-242) there is a sceptical paradox which purports to show "all language, all concept formation, to be impossible, indeed unintelligible." (K, p. 62). Wittgenstein, a la Hume, is supposed to give a sceptical solution to his sceptical paradox, and this solution "contains the argument against 'private language'; for allegedly, the solution will not admit such a language" (K, p. 60). More specifically, "the sceptical solution does not allow us to speak of a single individual, considered by him/herself and in isolation, as ever meaning anything." (K, pp. 68-9).

The alleged paradox begins with a sceptical inquiry about my right to claim that my past usage of '+' (i.e., my past usage of the plus sign) was used to denote the function plus rather than the function quus. The definition of quus is: x quus y = x + y, if x, y < 57; otherwise, x quus y = 5. (Kripke uses an encircled plus sign to represent the quus sign. I can't reproduce that sign here so I'll just use 'quus'). Basically, the problem is that on all of the problems that I have done so far, the plus and quus functions demand the same answers. So, whether I know it or not, my past responses to computations have been in accord with plus just as much as they have been in accord with quus. Thus, there seems to be no reason at all to prefer the claim that I've been plussing to the claim that I've been quussing, given my hypothetical past history. After all, the two functions are identical over the cases that I am allowed to appeal to so far.
Given this setup, Kripke boldly asks: "Who is to say that [quus] is not the function I previously meant by '+'?" The sceptic claims that no one can legitimately claim that quus is not the function I previously meant by '+', given the hypothetical situation he proposes, because no one can find a fact that shows that I meant plus rather than quus. More specifically, the sceptic challenges those of us who disagree with him to produce a fact that shows that I meant plus rather than quus. Also, the sceptic requires that the fact in question "must, in some sense, show how I am justified in giving the answer '125' to '68 + 57'" (rather than '5'). (K, p. 11). (I have always seen the second form of the challenge, as Kripke calls it, viz., the requirement that the fact show how I am justified in answering '125' rather than '5', as simply a way of clarifying the task at hand. After all, challenging someone to produce a fact that I meant plus rather than quus is not the most obvious challenge in the world, for a variety of reasons. Since it's clear that if I such a fact could be produced, it would justify my saying '125' rather than '5', the second form of the challenge does not impose a new task on us. Rather, it clarifies the task to be performed).
Now for the key step. Supposing that we cannot produce such a fact (N.B., not only does no Quinean, like myself, need convincing of this, but Kripke also provides persuasive arguments for this conclusion), how does any of this lead to the impossibility or nonsensicalness of meaning or language? Kripke's answer is as follows (Quineans can legitimately balk at the answer however!):

Of course, ultimately, if the sceptic is right, the concepts of meaning and of intending one function rather than another will make no sense. For the sceptic holds that no fact about my past history -- nothing that was ever in my mind, or in my external behavior -- establishes that I meant plus rather than quus. . . . But if this is correct, there can of course be no fact about which function I meant, and if there can be no fact about which particular function I meant in the past, there can be none in the present either. (K, p. 13).

Such, in a hurry, is Kripke's sceptical paradox and its language/meaning-threatening corollary.

The sceptical solution: First, a word about sceptical, as opposed to straight, solutions to sceptical paradoxes or problems. The locus classicus for sceptical solutions is of course Hume's Enquiry. His solution is a sceptical solution to his sceptical problem because it accepts the legitimacy or the upshot of the sceptical doubts concerning reason or the understanding. More specifically, Hume's sceptical doubts purport to show that neither reason nor the understanding are what we use to assure ourselves about future "matters of fact", nor do we use them to draw our "causal conclusions", e.g., bread will always nourish us. A straight solution to this problem would consist of showing that Hume's sceptical doubts are faulty and that in fact reason or the understanding is the source of our assurance or our causal conclusions. Hume proposes however, that custom or habit is the source of such assurance and conclusions. As such, Hume has accounted for our assurance and our conclusions without having to go back on any of his earlier sceptical doubts about reason or the understanding. As such, he has provided a sceptical solution to the sceptical doubts. (For the record, contra Kripke, a sceptical solution does not require that one acknowledge or accept the "unanswerability" of the sceptical doubts. See K, p. 66. It requires only that the sceptical solution not go back on, not contravene, anything claimed in the sceptical doubts. There may very well be a straight solution to Hume's problem but Hume provides a solution that does not go back on his sceptical doubts).
Now, what of KW's sceptical solution?  Here, unfortunately, it's difficult to provide a mere exposition, i.e., it's difficult to set out what I regard as the sceptical solution without leaning on a bit of interpretation. The problem is that one must interpret the sceptical challenge in order to make sense of KW's sceptical solution, or so I contend. I say this because if we take KW's sceptical challenge as showing the impossibility of all language (see K, p. 13 and p. 62) then a fortiori, a sceptical solution to the challenge begins by accepting the impossibility of all language. One can only wonder where we could go from here?! A better line is to see KW as accepting only the sceptic's case against the existence of "meaning facts", i.e., seeing this as the "unanswerable" part of KW's story. KW can then avoid the impossibility of language by rejecting the need for such a fact. On this view, KW never accepts the sceptic's argument for the impossibility of language. He always recognizes that the sceptic's argument is flawed because of its bogus assumption that we need a "meaning fact" in order to have substantive rule following and language.
Thus, we don't need "meaning facts" to justify our answers or our attributions of meaning. All we need are "conditions that legitimate the assertion" of such sentences. According to Kripke, we can turn our backs on the alleged need for "meaning facts" by switching from a truth-conditional account of meaning (roughly, for Kripke, the view Wittgenstein embraced in TLP) to a view of meaning and language based on assertion-conditions or justification-conditions (roughly, for Kripke, the view Wittgenstein accepts in PI).

The argument against private language: KW's case against private language is alleged to be a corollary of his sceptical solution. According to Kripke, once we make the shift from a truth conditional account of language to an assertion conditions account, we are able to give substance to talk of meaning and rule following, so long as we are talking about members of a community rather than "individuals considered in isolation" (ICIs). More specifically, KW contends that the assertion conditions for attributing correct or incorrect rule following to an ICI are "simply that [his/her] own authority is unconditionally to be accepted", a situation which is obviously at odds with our usual concept of following a rule. (K, pp. 88-89). According to KW, it is only in a community setting that there can be substantive assertion conditions for the attribution of correct or incorrect rule following. Such is KW's case for the impossibility of private language.

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Last modified September 8, 2011
JAH, Professor
Dept. of Philosophy