Vagueness : preliminary to a Wittgensteinian solution to the problems

The problems of vagueness, e.g. the Sorites paradox, are a significant concern of contemporary Anglo-American philosophy of language and philosophy of logic. And the vagueness of language that gives rise to these problems was itself a significant concern of Ludwig Wittgenstein’s in his later writings. It is therefore surprising that no-one has really brought Wittgenstein’s ideas on vagueness to bear on those problems in the current debate. The following study is my attempt to do this. There is, I believe, in Wittgenstein’s Philosophical Investigations, the groundwork for an eventual blanket solution to the problems of vagueness and I have tried to write an exposition of the relevant sections of the book and to indicate how the account contained therein relates to the problems. The solution to the problems of vagueness is, as I understand it, a corollary to Wittgenstein’s conception of the nature of logic in Philosophical Investigations, and this conception forms the core of my study.
I begin, though, with an account of some of the problems themselves, and my account is in the form of an exposition of several arguments contained in the writings of Gottlob Frege. With these arguments Frege presents a case for the thesis that logic cannot hold for a language, like ours, that contains vague predicates: in such a language, he argues, one cannot make inferences, one cannot even say anything true. The moral of Frege’s arguments is that logic requires sharp concepts.
Wittgenstein’s response to the problems of vagueness is to call into question the requirement of sharp concepts. That requirement is one of a number of requirements—none of which language actually satisfies—that appear to need to be satisfied by language if it is to serve us as a vehicle for truth. And Wittgenstein thinks that all of these requirements stem from a common aetiology which is: our attempts to understand how language works as 4 a vehicle for the expression and conduction of truth. He thinks that they all form part of a mythology of truth generated by those attempts; and sets about trying to expose and understand this mythology. His understanding turns out to be twofold: on the one hand, it accounts for the psychological origin of the mythology; and on the other, it explains how the mythology has managed to survive the rigorous demands for a genuine understanding of truth in language from a serious scientific discipline like logic. It is a characteristic of the picture of language painted by the mythology that, despite appearances, language is an absolutely precise and rigidly articulated instrument: in an important sense ideal. And it is the way in which language has come to be thought to be ideal in this way that constitutes Wittgenstein’s account of the psychological origin of the mythology. The story is a history of the mythology, which sees it as the working out of an idealization of a primal, primitive, approach to understanding language by way of defending that approach against the relentless clamour, all through the progression of the history, for justification of it as the approach towards a genuine understanding. The account is psychoanalytical: logic, as we understand it, is the product of a process of sublimation in the psychoanalytical sense. But accounting for the psychology by itself it is not enough to explain how the mythology has managed to survive into our current thinking about the workings of language. What is required in addition is an account of the contribution that the mythology makes to our genuine understanding of those workings. And this comes, according to Wittgenstein, as an account of the utility of thinking of language as conforming to the ideal blueprint of the mythology; in essence, thinking of language in this way provides us with a very useful model for the use of language as a vehicle for truth: by thinking of language as the ideal we are, in effect, comparing and contrasting the use of language with this model.
That is, very briefly, Wittgenstein’s thesis. And, as I say, I think that it contains the fundamentals of a solution to the problems of vagueness: the problems arise because of a mismatch between the way that we think language is, under the influence of the mythology—we think that it must have sharply defined concepts—, and the way that it actually is.