Unreal Nature

April 22, 2012

The Surest Path

Filed under: Uncategorized — unrealnature @ 8:23 am

… fertility is the result not of exactness but of seeing new problems where none have been seen before, and of finding new ways of solving them.

This is from Unended Quest: An Intellectual Autobiography by Karl Popper (2002: 1974):

Never let yourself be goaded into taking seriously problems about words and their meanings. What must be taken seriously are questions of fact, and assertions about facts: theories and hypotheses; the problems they solve; and the problems they raise.

… this exhortation cannot be very far from an articulation of the feelings I harboured when I first became conscious of the trap set by worries or quarrels about words and their meanings. This, I still think, is the surest path to intellectual perdition: the abandonment of real problems for the sake of verbal problems.

… The problem of universals is even today treated as if it were a problem of words or of language usages; or of similarities in situations; and how they are matched by similarities in our linguistic symbolism. It seemed to me quite obvious, however, that it was much more general; that it was fundamentally a problem of reacting similarly, to biologically similar situations. Since all (or almost all) reactions have, biologically, an anticipatory value, we are led to the problem of anticipation or expectation, and so to that of adaptation to regularities.

… I might perhaps state my position as follows. Every increase in clarity is of intellectual value in itself; an increase in precision or exactness has only a pragmatic value as a means to some definite end — where the end is usually an increase in testability or criticizability demanded by the problem situation (which for example may demand that we distinguish between two competing theories which lead to predictions that can be distinguished only if we increase the precision of our measurements).

It will be clear that these views differ greatly from those implicitly held by many contemporary philosophers of science. Their attitude towards precision dates, I think, from the days when mathematics and physics were regarded as the Exact Sciences. Scientists, and also scientifically inclined philosophers, were greatly impressed. They felt it to be almost a duty to live up to, or to emulate, this “exactness,” perhaps hoping that fertility would emerge from exactness as a kind of by-product. But fertility is the result not of exactness but of seeing new problems where none have been seen before, and of finding new ways of solving them.

… To put the idea first in a way which is merely intuitive, and perhaps a bit woolly, it is its logical relation to the prevailing problem situation which makes a theory interesting: its relation to preceding and competing theories: its power to solve existing problems, and to suggest new ones. In other words, the meaning or significance of a theory in this sense depends on very comprehensive contexts, although of course the significance of these contexts in their turn depends on the various theories, problems, and problem situations of which they are composed.

[ … ]

… One further result is, quite simply, the realization that the 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 first 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. Thus we need not be surprised at a remark like that by Clifford A Truesdell about the laws of thermodynamics: “Every physicist knows exactly what the first and the second law mean but … no two physicists agree about them.”

… 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. They may never arise; the evolution of the theory may bypass all your efforts. The intellectual weapons which will be needed at a later date may be very different from those which anyone has in store.



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