Note on the Rule Following Paradox
August 18, 2020
Here’s a few thoughts about Wittgenstein’s private language argument, or more specifically Saul Kripke’s development of it into a generalised rule-following paradox (Kripke, 1982). This paradox emerges against the background of Wittgenstein’s later philosophy of language, at the heart of which is a pragmatic treatment of meaning. According to this treatment meaning is not (in the first instance) about the truth-conditions of propositions, but about the assertability conditions of sentences within given language-games. The central idea that, roughly, to understand a concept is to know how to use a word, provided an alternative to the then dominant representationalist understanding of meaning as picturing, replacing it with a normative understanding of meaning as rule-following.1 The impossibility of private language—a language that is used and understood by only one person—then arises from the further argument that rule-following is an essentially communal activity. While the implications for linguistic meaning in general have been elaborated by Kripke and others, it seems to me that this paradox has implications for a broader concept of meaning that touches on shared narratives, collective desire, and their conditions of possibility.
Kripke relates the paradox (Kripke, 1982, p. 7) by considering a person who is adding two numbers they have not applied the addition function to before, let’s say to 51 and 1300. The question is: how do they know what function to apply? They have applied what they take to be the ‘\(+\)’ function many times before, let’s assume only to numbers less than 1300. But since they have done so only finitely many times there are infinitely many distinct functions consistent with the previous applications. One of them is quaddition, whose output is defined as \( x + y \) for all \(y \lt 1300\), and \(0\) for \(y \ge 1300\). Previous applications of the function underdetermine the present application, since they are all consistent with both addition and quaddition. On what grounds should addition rather than quaddition be applied in this new case? It seems there is none.
One response to this apparent paradox invokes behavioural dispositions, contending that what settles the choice between addition and quaddition is whether the person applying the function has a disposition (presumably a learned one) to apply one or the other—a disposition that would account for past, present and future applications. Kripke replies that this line of thought misfires by providing an account of what function the person will apply, when what is actually at issue (i.e. what would settle the question of what they mean) is what function they should apply, given previous applications. An account based on causal dispositions fails to address the normative dimension of the paradox. A calculating machine that takes two numbers as inputs and returns their sum may be said to have a disposition that accords with adding, but this seems insufficient to establish that its function is addition, since any finite set of calculations are consistent with infinitely many distinct functions. To establish its function as addition seems to require the further possibility of subjecting its calculations to normative assessment, such that any possible output can be judged as a correct or incorrect application of addition.
Now consider the problem of self-discipline. Say you decide on Monday that you want to give up smoking. You get through the week without so much as a sniff of tobacco. But then on Friday you go for a drink with some friends, and of course now you want a cigarette. At this point there’s a conflict between two incompatible desires—a past desire to not smoke and a present desire to smoke. The present desire can always win out through an act of retroactive interpretation, for example by rewriting Monday’s desire to not smoke ever as the desire to not smoke except on Friday evenings.
This situation can be understood as a crisis of authority, namely of the authority that a maxim affirmed in the past has to hold present action accountable to it. If in general an individual has no reason to prefer a past desire to a present one, then such authority is inherently unstable, since the previous affirmation can always be reinterpreted to make past action rationally consistent with present desire. If it is the case that only an individual’s own desires can provide them with a reason to act, this will lead to a problem of cascading temporal implosion as conflicts between desires within a temporally extended individual will always be won by the desire of the present timeslice. The authority of a principle transcending desire (paradigmatically a moral principle) will be overridden first by the authority of individual desire, and then again by the moment-by-moment whims of the individual’s prominent impulse. The atomisation of agency is therefore coextensive with a kind of contraction of normative temporality, as the authority of past commitment to determine present action fades to zero.
Both Wittgenstein and Kripke hold that any solution to this paradox must make reference to a community of rule-followers, who, by holding each other to account according to their own standards of correctness, can in practice stabilise the content of the rule. The community provides a kind of public memory which determines and indexes the content of commitments across time, thereby preserving their authority over the present.
Clearly much rides on the details. Nevertheless, the leveraging of community to stabilise the content of a rule is an idea with some prima facie intuitive force. Accountability groups are common in start-up culture, for example, where group members publicly express their goals so that they can hold each other accountable to them. Insofar as this practice does work, it raises interesting questions about exactly why it works. If the individual is sovereign then the authority a community member has to hold another accountable is always conditional on that authority being granted by the same individual who is supposed to be being held to account. But if this is so then this situation does not represent an improvement on the original: if someone’s authority to hold you accountable is conditional on you choosing to grant them that authority, then you can always choose to retract it. The paradox has not been avoided by communalisation, since ultimately an individual’s recognition of a motivation to act is still conditional on that motivation being in accordance with their present desire.
It seems that the practice should only work if community members are capable of treating each other as having a kind of unconditional authority to hold each other to account, an authority which cannot be retracted by choice.2 In this case, then, that a public announcement of a goal could provide a binding reason to stick to the maxim of a past desire in the face of an incompatible present desire must be dependent on some kind of social norm that one did not choose but nonetheless acknowledges as authoritative—e.g. the fear of looking stupid, or of losing face. To end on some speculation, this suggests to me that insofar as the norm is binding its acknowledgement must be unconscious, an implicit practical attitude rather than an explicit commitment whose authority it would be possible to explicitly disavow. If to be able state a rule is to be able to choose not to be bound by it, then this implies that a rule one is unconditionally bound by must be one that cannot be spoken. If this is right, then the force of a public expression of intent derives not from the explicitly chosen accountability structure of the group, but from the implicit norms of self and status that constitute the boundary conditions of its self-representation.
References
- Kripke, S. (1982). Wittgenstein: On Rules and Private Language. Blackwell.
Notes
-
As Brandom often points out, this is what connects Wittgenstein’s project with Kant’s. ↩
-
An unconditional authority is the kind of authority one grants to a moral principle insofar as one recognises it as correct—this is not the same as having a preference to act in a way which happens to accord with the principle (it is, rather, to acknowledge that one should act in accordance with it even in the absence of such a preference—it is subjunctively robust in a way the preference is not). A similar point can be made about truth and belief. To believe (to attribute truth to) a proposition is to acknowledge its authority in a way which is not conditional on the fact that you believe it. It is interesting to consider these authority structures alongside belief-sensitive phenomena. The placebo effect, for example, is known to work even when the patient is aware that they are taking a placebo, but only if they believe in the placebo effect. ↩