The conventional statement that experience only tells us how men have
thought or _do_ think, while logic is concerned with norms, with how men
_should_ think, is ludicrously inept. Some sorts of thinking are shown
_by_ experience to have got nowhere, or worse than nowhere--into
systematized delusion and mistake. Others have proved in manifest
experience that they lead to fruitful and enduring discoveries. It is
precisely in experience that the different consequences of different
methods of investigation and ratiocination are convincingly shown. The
parrot-like repetition of the distinction between an empirical
description of what is and a normative account of what should be merely
neglects the most striking fact about thinking as it empirically
is--namely, its flagrant exhibition of cases of failure and
success--that is, of good thinking and bad thinking. Any one who
considers this empirical manifestation will not complain of lack of
material from which to construct a _regulative_ art. The more study that
is given to empirical records of actual thought, the more apparent
becomes the connection between the specific features of thinking which
have produced failure and success. Out of this relationship of cause and
effect as it is empirically ascertained grow the norms and regulations
of an art of thinking.
Mathematics is often cited as an example of purely normative thinking
dependent upon _a priori_ canons and supra-empirical material. But it is
hard to see how the student who approaches the matter historically can
avoid the conclusion that the status of mathematics is as empirical as
that of metallurgy. Men began with counting and measuring things just as
they began with pounding and burning them. One thing, as common speech
profoundly has it, led to another. Certain ways were successful--not
merely in the immediately practical sense, but in the sense of being
interesting, of arousing attention, of exciting attempts at improvement.
The present-day mathematical logician may present the structure of
mathematics as if it had sprung all at once from the brain of a Zeus
whose anatomy is that of pure logic. But, nevertheless, this very
structure is a product of long historic growth, in which all kinds of
experiments have been tried, in which some men have struck out in this
direction and some in that, and in which some exercises and operations
have resulted in confusion and others in triumphant clarifications and
fruitful growths; a history in which matter and methods have been
constantly selected and worked over on the basis of empirical success
and failure.
Public-domain text, read in full here on John Shaqi.
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