The sceptical paradox has been brought to the fore by Kripke (1982, cf. Stegmüller 1986). His problem can be traced back, at least, to Pyrrhonian scepticism as summarized by Sextus Empiricus (circa 160-210 A.D.). Especially, Sextus's use of the concept of criterion is illustrative. He attributes two different senses to it (Sextus 1955: 17): 1. "the standard regulating belief in reality and unreality", and 2. "the standard of action by conforming to which in the conduct of life we perform some actions and abstain from others". The first sense he considers most problematical. To decide the dispute as to whether such a criterion exists, one needs an accepted criterion by which the dispute can be judged. This leads to circularity (the dispute must be first decided), to infinite regress (looking for another criterion to judge the criterion), or to dogmatism (Sextus 1955: 161 f.). Since sceptics don't want to dispose of contrasting opinions by mere assumption, they propose to suspend judgment, and to continue the investigation. In the second – practical – sense, Pyrrhonian scepticism considers appearance its criterion. Appearance, contrary to reality, is not open to question, because it lies in feeling and involuntary affection. "Adhering, then, to appearances we live in accordance with the normal rules of life, undogmatically, seeing that we cannot remain wholly inactive". (Sextus 1955: 17; for a more wide-ranging actualization of scepticism, see Hiley 1988).
Kripke's formulation of the problem is quite close to Sextus's problem with criterion 1 (the standard of belief – interpreted rather conceptually than realistically, nowadays). And his solution assumes the unproblematicality of criterion 2 (the practical standard).
1. Kripke translates Wittgenstein's paradox of the (non-) effectiveness of rules into a problem with addition. Grasping the rule for addition implies that one is able to use the same operation in new cases. But what criterion do I have to judge whether I am doing the same in circumstances that never occurred before? Here Kripke introduces a 'bizarre sceptic', who argues that the rule earlier applied while adding, was not that of addition, but that of 'quaddition': a function X quus Y that, in all earlier cases, has the same result as X plus Y; but, when applied to higher numbers than dealt with before (let's say over 57), the result is 5. This means that I would alter my earlier practice when I came to the decision that 68 + 57 equals 125 instead of 5. The sceptic could even improve his point by baptizing his own operation 'addition', while saying that my stubborn insistence that 125 is the correct answer can only be seen as an inimitable result of madness or hallucination. In terms of Sextus, there is no criterion to justify either result. Although Kripke calls this suggestion bizarre, he admits that it can't be refuted by reference to earlier (qu)addition experiences. Before I have been informed about new cases, the instructions followed may imply each of both operations. I didn't [p. 118:] know what rule I was following by using '+'. I obey a rule blindly: it does not guide in new circumstances, so that each new application is a leap in the dark.
2. Conceding that the sceptic's criticism can't be answered, Kripke tries to solve the paradox sceptically – that is by stating that, in ordinary practice, we don't need the kind of justification just shown to be untenable. Wittgenstein would hold, with the sceptic, that there is no fact as to whether I mean plus or quus. But this is no problem, since he is not interested in truth conditions, but in practical conditions of assertability or justification. The idea of necessity in following a rule has to do with custom. A single person, taken in isolation, can apply a rule as it strikes her/him; but, considered as interacting with a wider community, her/his practice has to agree sufficiently with the customs of the community – if she/he is to be seen as a participant of that community (and of communication). Asserting that we mean addition by '+', therefore, is part of a customary language game. In this form, Kripke says, this assertion sustains itself only because of the 'brute empirical fact' that we generally agree. "What has to be accepted, the given, is – so one could say – forms of life" (PI p. 226). In order to check persons that claim to be following a rule, members of a community don't need an a priori paradigm. The fostering of agreement is just a primitive part of their language game.