Wittgenstein on Rules and Private Language
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Wittgenstein (second from right), Summer 1920
Wittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever following rules in our use of language. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date" (p. 60). He argues that Wittgenstein does not reject the argument that leads to the rule-following paradox, but accepts it and offers a 'skeptical solution' to alleviate the paradox's destructive effects.
While most commentators accept that the Philosophical Investigations contains the rule-following paradox as Kripke presents it, few have concurred in attributing Kripke's skeptical solution to Wittgenstein. Kripke expresses doubts in Wittgenstein on Rules and Private Language as to whether Wittgenstein would endorse his interpretation of the Philosophical Investigations. He says that the work should not be read as an attempt to give an accurate statement of Wittgenstein's views, but rather as an account of Wittgenstein's argument "as it struck Kripke, as it presented a problem for him" (p. 5). The portmanteau "Kripkenstein" has been coined as a nickname for a fictional person who holds the views expressed by Kripke's reading of the Philosophical Investigations; in this way, it is convenient to speak of Kripke's own views, Wittgenstein's views (as generally understood), and Kripkenstein's views. Wittgenstein scholar David G. Stern considers the book to be the most influential and widely discussed work on Wittgenstein since the 1980s.
The rule-following paradox
In PI 201a Wittgenstein explicitly states the rule-following paradox: "This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule". Kripke gives a mathematical example to illustrate the reasoning that leads to this conclusion. Suppose that you have never added numbers greater than 50 before. Further, suppose that you are asked to perform the computation '68 + 57'. Our natural inclination is that you will apply the addition function as you have before, and calculate that the correct answer is '125'. But now imagine that a bizarre skeptic comes along and argues:
- That there is no fact about your past usage of the addition function that determines '125' as the right answer.
- That nothing justifies you in giving this answer rather than another.
After all, the skeptic reasons, by hypothesis you have never added numbers greater than 50 before. It is perfectly consistent with your previous use of 'plus' that you actually meant it to mean the 'quus' function, defined as:
The skeptic argues that there is no fact about you that determines that you ought to answer '125' rather than '5'. Your past usage of the addition function is susceptible to an infinite number of different quus-like interpretations. It appears that every new application of 'plus', rather than being governed by a strict, unambiguous rule, is actually a leap in the dark.
The obvious objection to this procedure is that the addition function is not defined by a number of examples, but by a general rule or algorithm. But then the algorithm itself will contain terms that are susceptible to different and incompatible interpretations, and the skeptical problem simply resurfaces at a higher level. In short, rules for interpreting rules provide no help, because they themselves can be interpreted in different ways. Or, as Wittgenstein himself puts it, "any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning" (PI 198a).
Similar skeptical reasoning can be applied to any word of any human language. The power of Kripke's example is that in mathematics the rules for the use of expressions appear to be defined clearly for an infinite number of cases. Kripke doesn't question the validity in mathematics of the '+' function, but rather the meta-linguistic usage of 'plus': what fact can we point to that shows that 'plus' refers to the mathematical function '+'.
The skeptical solution
Kripke, following David Hume, distinguishes between two types of solution to skeptical paradoxes. Straight solutions dissolve paradoxes by rejecting one (or more) of the premises that lead to them. Skeptical solutions accept the truth of the paradox, but argue that it does not undermine our ordinary beliefs and practices in the way it seems to. Because Kripke thinks that Wittgenstein endorses the skeptical paradox, he is committed to the view that Wittgenstein offers a skeptical, and not a straight, solution. 
The rule-following paradox threatens our ordinary beliefs and practices concerning meaning because it implies that there is no such thing as meaning something by an expression or sentence. John McDowell explains this as follows. We are inclined to think of meaning in contractual terms: that is, that meanings commit or oblige us to use words in a certain way. When you grasp the meaning of the word "dog", for example, you know that you ought to use that word to refer to dogs, and not cats. Now, if there cannot be rules governing the uses of words, as the rule-following paradox apparently shows, this intuitive notion of meaning is utterly undermined.
Kripke holds that other commentators on Philosophical Investigations have believed that the Private Language Argument is presented in sections occurring after §243. Kripke reacts against this view, noting that the conclusion to the argument is explicitly stated by §202, which reads “Hence it is not possible to obey a rule ‘privately’: otherwise thinking one was obeying a rule would be the same as obeying it.” Further, in this introductory section, Kripke identifies Wittgenstein’s interests in the philosophy of mind as being related to his interests in the foundations of mathematics, in that both subjects require considerations concerning rules and rule following. 
Kripke's skeptical solution is this: A language-user's following a rule correctly is not justified by any fact that obtains about the relationship between his candidate application of a rule in a particular case, and the putative rule itself (as for Hume the causal link between two events a and b is not determined by any particular fact obtaining between them taken in isolation), but rather the assertion that the rule is being followed is justified by the fact that the behaviors surrounding the candidate instance of rule-following (by the candidate rule-follower) meet the expectations of other language users. That the solution is not based on a fact about a particular instance of putative rule-following-- as it would be if it were based on some mental state of meaning, interpretation, or intention-- shows that this solution is skeptical in the sense Kripke specifies.
The "straight" Solution
In contrast to the kind of solution offered by Kripke (above) and Crispin Wright (elsewhere), John McDowell interprets Wittgenstein as correctly (by McDowell's lights) offering a "straight solution". McDowell argues that Wittgenstein does present the paradox (as Kripke argues), but he argues further that Wittgenstein rejects the paradox on the grounds that it assimilates understanding and interpretation. In order to understand something, we must have an interpretation. That is, to understand what is meant by "plus," we must first have an interpretation of what "plus" means. This leads one to either skepticism - how do you know your interpretation is the correct interpretation? - or relativity whereby our understandings, and thus interpretations, are only so determined in so far as we have used them. In this latter view, endorsed by Wittgenstein in Wright's readings, there are no facts about numerical addition that man has so far not discovered, so when we come upon such situations, we can flesh out our interpretations further. Both of these alternatives are quite unsatisfying; the latter because we want to say that the objects of our understandings are independent from us in some way: that there are facts about numbers, that have not yet been added.
McDowell writes further, in his interpretation of Wittgenstein, that to understand rule-following we should understand it as resulting from inculcation into a custom or practice. Thus, to understand addition, is simply to have been inculcated into a practice of adding.
- Stern, David G. 2006. Wittgenstein’s Philosophical Investigations: An Introduction. Cambridge University Press. p. 2
- Fitch, G. W. (2004). Saul Kripke. Montreal: McGill-Queen's University Press. ISBN 0-7735-2885-7.
- Kripke, Saul A. (2004). Wittgenstein on rules and private language : an elementary exposition (Reprinted. ed.). Oxford: Blackwell. p. 2. ISBN 0-631-13521-9.
- Kripke, Saul A. (2004). Wittgenstein on rules and private language : an elementary exposition (Reprinted. ed.). Oxford: Blackwell. p. 4. ISBN 0-631-13521-9.
- McDowell, John (March 1984). "WIttgenstein on following a Rule". Synthese 58 (4): 325–363. doi:10.1007/bf00485246.
- Kripke, Saul (1982). Wittgenstein on Rules and Private Language. Harvard University Press. ISBN 0-674-95401-7.
- Wittgenstein, Ludwig (1953/2001). Philosophical Investigations. Blackwell Publishing. ISBN 0-631-23127-7. Check date values in:
- Baker, G. P. and Hacker, P. M. S. (1986). Skepticism, Rules and Language. Blackwell Publishers. ISBN 0-631-14703-9.
- McGinn, Colin (1984). Wittgenstein on meaning: an interpretation and evaluation. Oxford: Blackwell. ISBN 0-631-15681-X.