Rule Scepticism

Rule scepticism attacks the interaction between thinkers and their beliefs. In its most general form, a rule sceptic questions our tendency to assume the usual assignment of meaning to propositions as non-arbitrary and somehow meaningful itself. If left unanswered, this interpretation would not only mock the notion of objectivity, but, unlike most other forms of scepticism, would question even the mere reasonability of the subjective beliefs other sceptics are content with. Even when such vicious attacks are refuted by stopping or bypassing the postulated regress of rule-applications, it leaves us with a worrying, although vividly realistic, vagueness in the concept of meaning.

Although traditionally the problem has been formulated in terms of a language usage, in this essay I will rephrase it as “the meaning of a thought”, since this seems to be the ultimate target of rule sceptics. Consequently, I draw no distinction between a thought and its utterance; such a distinction is meaningful only when analyzing an exchange of information between people. Further, I take “meaning” to be a characteristic of a rule-application; specifically, a property of an instantiation of a generic concept. The other use of the word as a mapping between an empirical sample space and a set of symbols or propositions that does not imply any generalization (for example, an assignment of names to the members of a set of objects), can hardly be challenged by a rule sceptic. The “coloured square” example, and, indeed, most of the language game from the first 100 or so sections of Wittgensten's Philosophical Investigations is deliberately finite and hence perfectly well-defined, provided that only self-identity of the said squares is investigated, that is, no correspondence is drawn between the squares in the example and an abstract concept of their colours.

Although a precise definition of the concept of “meaning” would have to be self-applicable and possibly circular, I believe that the general consensus is to regard “meaning” simply as some desirable property of a proposition or a thought, such that its posession serves as a common criteria for the proposition's acceptance or rejection. That is, I am more concerned with the question of whether some proposition has a meaning, rather than the more specific question of what that meaning, if anything, is.

Rule scepticism bases its claims on the problems of interpretation of a thought and of the language used to express it. Rule sceptics allege that all thoughts are intrinsically ambiguous in that either no magic relation exists between them and their postulated meanings, or, alternatively, that the relation is not unique. When I say “this thing is a fine example of the concept of a cup of coffee,” probably expressing this as a less pretentious “this is a cup of coffee,” I apply a presumably well-defined, if ambiguous, rule describing the concept of a cup of coffee. Even if I am unsure how to classify a café laté served in a shoe, I still presume to be capable of producing an infinite number of different cups or coffee in support of my intelligence claim, or know a good cup of coffee when I see one. A rule sceptic, however, postulates that, whatever process has been applied in order to arrive at the above classification, despite my past successes in the area nothing seems to guard me against a systematic error intrinsic to that process, such as my bias against cappuccino. However, one could interpret such tendency as a complete lack of understanding of the concept of a cup of coffee, and hence deny me the knowledge that I would like to claim.

While we may discard the subject of a cup of coffee as subjective, most people are more reluctant to give the same treatment to “the important concepts” such as truth (or addition.) And because rule scepticism does not rely on vagueness or ambiguity of the attacked concept, it is by no means restricted to the subjective ones.

In Wittgenstein on Rules and Private Language, Kripke discusses one such case. He proposes that, because our understanding of addition has only been tested on a finite number of cases (i.e., the additions we have actually performed), there may be an alternative mathematical function - say, quus - with behaviour sufficiently different to make it clearly distinct from the conventional addition. If the differences only appear in test cases other than any actually applied, one may start to worry as to whether their original understanding of addition has been sufficient to justify their knowledge claim for any of the cases.

There are few obvious answers to the sceptic's worry, most focusing on the details on the rule underlying the concept. A mathematician would object to Kripke's empirical definition of addition, saying that it rather represents some abstract entity with a set of properties such as the Peano Axioms that we can “somehow” relate to. This answer is of course unsatisfactory, as the problem may be reapplied to whatever concepts are logically prior to the original one. I will return to this treatment later. One could also meet the sceptic's challenge by defining understanding of addition as an understanding of some algorithm and its application. However, unless we can formulate a clear description of that alorithm, I fail to see how this affects the problem, short of renaming some of the concepts involved.

As another obvious challenge to his experiment, one that attempts to describe the above-mentioned algorithm, Kripke describes addition in terms of marble-counting. This, clearly doomed, approach suggests an interpretation of rule scepticism that Kripke ignored. Specifically, both the challenge and Kripke's exposition of the regress worry it is prone to, clearly assume that the counting rule - meaningful or not - differs from addition. Surely, when one counts marbles and applies the counting rule, while, summing numbers on a grocery bill is an exercise of addition, suggesting that the two are indeed different. However, the distinction becomes blurred, when a boy picks a marble from a basket (say in a toy shop), saying “10 cents”, picks another two and says “30 cents”, and so on. Should we say that our boy is applying counting to marbles? Or is he rather summing the prices? Or both? It is easy to contrive examples demonstrating the vagueness of the distinction between the two concepts.

Perhaps no meaningful distinction can be made between counting and adding. Perhaps most of our rules are like that.

Patryk Zadarnowski, Sydney 1998