Wittgenstein on Rules, by Saul A. Kripke on rule-checking 'community'
Each person who claims to follow a rule is checked for deviance by a community. Maths + community = ‘proof’. Robinson Crusoe, isolated, cannot have followed rules.
Saul A. Kripke wrote:
Chapter 3
The 'Private Language' Argument
… [The] central sections of [Wittgenstein’s] Philosophical Investigations - have been the primary concern of this essay. We have not yet looked at the solution of the problem, but the astute reader already will have guessed that Wittgenstein finds a useful role in our lives for a 'language game' that licenses, under certain conditions, assertions that someone ‘means such-and-such' and that his present application of a word 'accords' with what he 'meant' in the past. It turns out that this role, and these conditions, involve reference to a community. They are inapplicable to a single person considered in isolation. Thus, as we have said, Wittgenstein rejects ‘private language' as early as [section] §202. …
… Do I not, in elementary mathematics, grasp rules such as that for addition, which determine all future applications? Is it not in the very nature of such rules that, once I have grasped one, I have no future choice in its application? Is not any questioning of these assertions a questioning of mathematical proof itself? And is not the grasping of a mathematical rule the solitary achievement of each mathematician independent of any interaction with a wider community? True, others may have taught me the concept of addition, but they acted only as heuristic aids to an achievement — the 'grasping of the concept' of addition that puts me in a special relation to the addition function.
Platonists have compared the grasping of a concept to a special sense, analogous to our ordinary sensory apparatus but percipient of higher entities. But the picture does not require a special Platonic theory of mathematical objects. It depends on the observation — apparently obvious on any view — that in grasping a mathematical rule I have achieved something that depends only on my own inner state, and that is immune to Cartesian doubt about the entire external material world.
[MGH: The Stanford Encyclopedia of Philosophy entry on Platonism in the Philosophy of Mathematics explains the Platonic theory of maths: “Just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.”]
Now another case that seems to be an obvious counterexample to Wittgenstein's conclusion is that of a sensation, or mental image. Surely I can identify these after I have felt them, and any participation in a community is irrelevant! Because these two cases, mathematics and inner experience, seem so obviously to be counterexamples to Wittgenstein's view of rules, Wittgenstein treats each in detail. The latter case is treated in the sections following §243. The former case is treated in remarks that Wittgenstein never prepared for publication, but which are excerpted in Remarks on the Foundations ofMathematics and elsewhere. He thinks that only if we overcome our strong inclination to ignore his general conclusions about rules can we see these two areas rightly. For this reason, the conclusions about rules are of crucial importance both to the philosophy of mathematics and to the philosophy of mind. …
… If our considerations so far are correct, the answer is that, if one person is considered in isolation, the notion of a rule as guiding the person who adopts it can have no substantive content. There are, we have seen, no truth conditions or facts in virtue of which it can be the case that he accords with his past intentions or not. As long as we regard him as following a rule 'privately', so that we pay attention to his justification conditions alone, all we can say is that he is licensed to follow the rule as it strikes him. This is why Wittgenstein says,
“To think one is obeying a rule is not to obey a rule. Hence it is not possible to obey a rule 'privately'; otherwise thinking one was obeying a rule would be the same thing as obeying it.” (§202)
The situation is very different if we widen our gaze from consideration of the rule follower alone and allow ourselves to consider him as interacting with a wider community. Others will then have justification conditions for attributing correct or incorrect rule following to the subject, and these will not be simply that the subject's own authority is unconditionally to be accepted. …
… Sometimes [fictitious] Smith, by substituting some alternative interpretation for [fictitious] Jones’s word 'plus', will be able to bring Jones’s responses in line with his own. More often, he will be unable to do so and will be inclined to judge that Jones is not really following any rule at all. In all this, Smith's inclinations are regarded as just as primitive as Jones's. In no way does Smith test directly whether Jones may have in his head some rule agreeing with the one in Smith's head. Rather the point is that if, in enough concrete cases, Jones's inclinations agree with Smith's, Smith will judge that Jones is indeed following the rule for addition.
Of course if we were reduced to a babble of disagreement, with Smith and Jones asserting of each other that they are following the rule wrongly, while others disagreed with both and with each other, there would be little point to the practice just described. In fact, our actual community is (roughly) uniform in its practices with respect to addition. Any individual who claims to have mastered the concept of addition will be judged by the community to have done so if his particular responses agree with those of the community in enough cases, especially the simple ones (and if his ‘wrong' answers are not often bizarrely wrong, as in '5' for ’68 + 57', but seem to agree with ours in procedure, even when he makes a 'computational mistake').
An individual who passes such tests is admitted into the community as an adder; an individual who passes such tests in enough other cases is admitted as a normal speaker of the language and member of the community. Those who deviate are corrected and told (usually as children) that they have not grasped the concept of addition. One who is an incorrigible deviant in enough respects simply cannot participate in the life of the community and in communication.
Now Wittgenstein's general picture of language, as sketched above, requires for an account of a type of utterance not merely that we say under what conditions an utterance of that type can be made, but also what role and utility in our lives can be ascribed to the practice of making this type of utterance under such conditions. We say of someone else that he follows a certain rule when his responses agree with our own and deny it when they do not; but what is the utility of this practice? The utility is evident and can be brought out by considering again a man who buys something at the grocer’s. The customer, when he deals with the grocer and asks for five apples, expects the grocer to count as he does, not according to some bizarre non-standard rule; and so, if his dealings with the grocer involve a computation, such as ’68 + 57', he expects the grocer's responses to agree with his own. Indeed, he may entrust the computation to the grocer. Of course the grocer may make mistakes in addition; he may even make dishonest computations. But as long as the customer attributes to him a grasp of the concept of addition, he expects that at least the grocer will not behave bizarrely, as he would if he were to follow a quus-like rule; and one can even expect that, in many cases, he will come up with the same answer the customer would have given himself.
[MGH: ‘Quus’ is explained in Chapter 2 where Krieke imagines a ‘bizarre’ or ‘frenzied’ substitute for the ‘plus’ function. The Index entry for ‘quus’ refers readers to ‘plus’.]
When we pronounce that a child has mastered the rule of addition, we mean that we can entrust him to react as we do in interactions such as that just mentioned between the grocer and the customer. Our entire lives depend on countless such interactions, and on the ‘game' of attributing to others the mastery of certain concepts or rules, thereby showing that we expect them to behave as we do.
This expectation is not infallibly fulfilled. It places a substantive restriction on the behavior of each individual, and is not compatible with just any behavior he may choose. A deviant individual whose responses do not accord with those of the community in enough cases will not be judged, by the community, to be following its rules; he may even be judged to be a madman, following no coherent rule at all. When the community denies of someone that he is following certain rules, it excludes him from various transactions such as the one between the grocer and the customer. It indicates that it cannot rely on his behavior in such transactions. …
… The set of responses in which we agree, and the way they interweave with our activities, is our form of life. Beings who agreed in consistently giving bizarre quus-like responses would share in another form of life. By definition, such another form of life would be bizarre and incomprehensible to us.
“If a lion could talk, we could not understand him” (Wittgenstein p. 223).)
However, if we can imagine the abstract possibility of another form of life (and no apriori argument would seem to exclude it), the members of a community sharing such a quus-like form of life could play the game of attributing rules and concepts to each other as we do. Someone would be said, in such a community, to follow a rule, as long as he agrees in his responses with the (quus-like) responses produced by the members of that community. Wittgenstein stresses the importance of agreement, and of a shared form of life, for his solution to his sceptical problem in the concluding paragraphs of the central section of Philosophical Investigations (§§240-2) …
… A sceptical problem is posed, and a sceptical solution to that problem is given. The solution turns on the idea that each person who claims to be following a rule can be checked by others. Others in the community can check whether the putative rule follower is or is not giving particular responses that they endorse, that agree with their own. The way they check this is, in general, a primitive part of the language game. …
… What is really denied is what might be called the 'private model' of rule following, that the notion of a person following a given rule is to be analyzed simply in terms of facts about the rule follower and the rule follower alone, without reference to his membership in a wider community. (In the same way, what Hume denies is the private model of causation: that whether one event causes another is a matter of the relation between these two events alone, without reference to their subsumption under larger event types.) The impossibility of a private language in the sense just defined does indeed follow from the incorrectness of the private model for language and rules, since the rule following in a 'private language' could only be analyzed by a private model, but the incorrectness of the private model is more basic, since it applies to all rules. I take all this to be the point of §202 [in Philosophical Investigations].
Does this mean that Robinson Crusoe, isolated on an island, cannot be said to follow any rules, no matter what he does? I do not see that this follows. What does follow is that if we think of Crusoe as following rules, we are taking him into our community and applying our criteria for rule following to him. The falsity of the private model need not mean that a physically isolated individual cannot be said to follow rules; rather that an individual, considered in isolation (whether or not he is physically isolated), cannot be said to do so. Remember that Wittgenstein's theory is one of assertability conditions. Our community can assert of any individual that he follows a rule if he passes the tests for rule following applied to any member of the community. …
… One must bear firmly in mind that Wittgenstein has no theory of truth conditions — necessary and sufficient conditions — for the correctness of one response rather than another to a new addition problem. Rather he simply points out that each of us automatically calculates new addition problems (without feeling the need to check wIth the community whether our procedure is proper); that the community feels entitled to correct a deviant calculation; that in practice such deviation is rare, and so on. Wittgenstein thinks that these observations about sufficient conditions for justified assertion are enough to illuminate the role and utility in our lives of assertion about meaning and determination of new answers. What follows from these assertability conditions is not that the answer everyone gives to an addition problem is, by definition, the correct one, but rather the platitude that, if everyone agrees upon a certain answer, then no one will feel justified in calling the answer wrong.
The Source:
Saul A. Kripke, Wittgenstein on Rules and Private Language: An Elementary Exposition, Harvard University Press 1982
[MGH: A book about this book is forthcoming: C. Verheggen (ed.), Kripke's "Wittgenstein on Rules and Private Language" at 40, Cambridge, including a chapter by Arif Ahmed. The book’s Wikipedia page (below) does not mention ‘community’.]
Evolutions of social order from the earliest humans to the present day and future machine age.