In lieu of an abstract, here is a brief excerpt of the content:

243 V Scientific Method and the Significance of Mathematics for Linguistics Section 1. Mistaken Presumptions about What “Scientific Method” Requires This chapter shows the indispensability of informal rules to mathematical practice and scientific method and development. The requirement of conformity to mechanically applicable rules arises only in certain specialized contexts. The deceptive plausibility of arguments that such mechanically applicable rules are necessary leads us into a trap, “up the garden path” as it were; this chapter shows the pits, dumps, and general chaos at the end of this garden path. (a) My approach contrasted with its rivals For many modern philosophers and psycholinguists it is the received “common sense” that in order to know the sense of an utterance, we need first to identify the words and their langue-meanings in their order, the intonation, and the context of utterance, envisaged as the elements and features of the total utterance which identify its lexical meaning. Then, second, we need to use the knowledge of these elements and features to work out or “calculate” the sense of the whole in an “effective” or reliable way—a view only plausible because “work out” and “effective” are ordinarily such vague terms. Without such “effective” access ,it is argued that the speaker could never rely on being understood correctly. However, many cognitive scientists and AI theorists take a methodolog- 244   Words and Their Dynamism ical view involving a third supposition—namely, that the only way in which a method of “working out” the senses of whole sentences could be effective is by its being mechanically applicable. They require a mechanical procedure which, in the case of each sentence, would yield a proof that such and such were the sense of the sentence concerned, since, if one follows Church and Gödel, such a mechanical procedure is necessary and sufficient for “effectiveness ”.1 In sum, ordinary security in communication within a short finite time requires a mechanically applicable procedure in applying linguistic rules. This third requirement is much more demanding than that the process be finite, since tasks may be accomplishable in a finite number of steps without these steps following according to a mechanically applicable rule.2 But I showed in chapter I that in speech we express the sense we intend and that the primary role of words and other sentence factors is as senseexpressors , so that in speaking we know the sense or meaning of what is said with the directness with which in doing something intentionally we know what we are intending to do, rather than knowing it indirectly by external observation . Hence the idea that we know the meaning or sense of what is said in an utterance by first identifying the langue-meanings of words and other contributory sense-identifiers, and then calculating the resultant sense of the whole utterance, is far-fetched—besides which such calculation is impossible . The primary exercise of the capacity to swim is in actual swimming, not in the capacity to explain how to swim, distinguish particular strokes, or describe particular muscle movements. Likewise the understanding of the langue-meaning of words has its primary exercise in the understanding of parole —that is, in the understanding of the word in use as a functioning part of utterances—along with its companion words expressing the sense of the whole utterance, not in the capacity to identify the langue-meanings of words and then calculate utterance meaning. Thus understanding plays an indispensable part, both in enabling us to speak in a way which is meaningful to ourselves and in enabling others to understand the same thing as we do from what we say, here performing a task beyond the power of calculation or the mechanical processing of relevant information . 1. Alonzo Church, Introduction to Mathematical Logic (Princeton, N.J.: Princeton University Press, 1956), 52–53. The requirements of effectiveness he lays down are explained in section 4(a) of this chapter. 2. This chapter provides many examples of such finite serial processes—e.g., proofs which are finite but not discoverable by mechanical process, and not of one mechanically specifiable form. Each time, for instance, given a particular axiomatization of natural arithmetic, we prove something by Gödelian reasoning (informal in the sense of not being according to this axiomatization, but arising by reflection upon it, taking the consistency of natural arithmetic as evident), we have produced a proof which is “along particular lines”, but not along mechanically specifiable lines. More generally, the search for a...

Share