Tag Archive: concepts

The need for precision as relative to a problem

When I wrote my Logik der Forschung I thought that the quest for the meanings of words was about to end. I was an optimist: it was gaining momentum. The task of philosophy was more and more widely described as concerned with meaning, and this meant, mainly, the meanings of words. And nobody seriously questioned the implicitly accepted dogma that the meaning of a statement, at least in its most explicit and unambiguous formulation, depends on (or is a function of) that of its words. This is true equally of the British language analysts and of those who follow Carnap in upholding the view that the task of philosophy is the “explication of concepts”, that is, making concepts precise. Yet there simply is no such thing as an “explication”, or an “explicated” or “precise” concept.

However, the problem still remains: what should we do in order to make our meaning clearer, if greater clarity is needed, or to make it more precise, if greater precision is needed? In the light of my exhortation the main answer to this question is: any move to increase clarity or precision must be ad hoc or “piecemeal”. If because of lack of clarity a misunderstanding arises, do not try to lay new and more solid foundations on which to build a more precise “conceptual framework”, but reformulate your formulations ad hoc, with a view to avoiding those misunderstandings which have arisen or which you can foresee. And always remember that it is impossible to speak in such a way that you cannot be misunderstood: there will always be some who misunderstand you. If greater precision is needed, it is needed because the problem to be solved demands it. Simply try your best to solve your problems and do not try in advance to make your concepts or formulations more precise in the fond hope that this will provide you with an arsenal for future use in tackling problems which have not yet arisen. [30]

Why there can be no precise concepts

[T]he quest for precision, in words or concepts or meanings, is a wild-goose chase. There simply is no such thing as a precise concept (say, in Frege’s sense), though concepts like “price of this kettle” and “thirty pence” are usually precise enough for the problem context in which they are used. (But note the fact that “thirty pence” is, as a social or economic concept, highly variable: it had a different significance a few years ago from what it has today.)

Frege’s opinion is different; for he writes: “A definition of a concept … must determine unambiguously of any object whether or not it falls under the concept … Using a metaphor, we may say: the concept must have a sharp boundary.” But it is clear that for this kind of absolute precision to be demanded of a defined concept, it must be demanded of the defining concepts, and ultimately of our undefined, or primitive, terms. Yet this is impossible. For either our undefined or primitive terms have a traditional meaning (which is never very precise) or they are introduced by so­-called “implicit definitions”—that is, through the way they are used in the context of a theory. This last way of introducing them—if they have to be “introduced”—seems to be the best. But it makes the meaning of the concepts depend on that of the theory, and most theories can be interpreted in more than one way. As a result. implicitly defined concepts, and thus all concepts which are defined explicitly with their help, become not merely “vague” but systematically ambiguous. And the various systematically ambiguous interpretations (such as the points and straight lines of projective geometry) may be completely distinct.

This should be sufficient to establish the fact that “unambiguous” concepts, or concepts with “sharp boundary lines”, do not exist. [28-9]