David Corfield
Personal Knowledge

Published in 1958.

When the laws of physics thus appear as particular instances of geometric theorems, we may infer that the confidence placed in physical theory owes much to its possessing the same kind of excellence from which pure geometry and pure mathematics in general derive their interest, and for the sake of which they are cultivated.(p. 15)

We cannot truly account for our acceptance of such theories without endorsing our acknowledgement of a beauty that exhilarates and a profundity that entrances us. Yet the prevailing conception of science, based on the disjunction of subjectivity from objectivity, seeks–and must seek at all costs–to eliminate from science such passionate, personal, human appraisals of theories, or at least to minimize their function to that of a negligible by-play. For modern man has set up as the ideal of knowledge the conception of natural science as a set of statements which is ‘objective’ in the sense that its substance is entirely determined by observation, even while its presentation may be shaped by convention. This conception, stemming from a craving rooted in the very depths of our culture, would be shattered if the intuition of rationality in nature had to be acknowledged as a justifiable and indeed essential part of scientific theory. That is why scientific theory is represented as a mere economical description of facts; or as embodying a conventional policy for drawing empirical inferences; or as a working hypothesis, suited to man’s practical convenience–interpretations that all deliberately overlook the rational core of science.

That is why, also, if the existence of this rational core yet reasserts itself, its offensiveness is covered up by a set of euphemisms, a kind of decent understatement like that used in Victorian times when legs were called limbs–a bowdlerization which we may observe, for example, in the attempts to replace ‘rationality’ by ‘simplicity’. It is legitimate, of course, to regard simplicity as a mark of rationality, and to pay tribute to any theory as a triumph of simplicity. But great theories are rarely simple in the ordinary sense of the term. Both quantum mechanics and relativity are very difficult to understand; it takes only a few minutes to memorize the facts accounted for by relativity, but years of study may not suffice to master the theory and see these facts in its context. Hermann Weyl lets the cat out of the bag by saying: ‘the required simplicity is not necessarily the obvious one but we must let nature train us to recognize the true inner I simplicity.’ In other words, simplicity in science can be made equivalent to rationality only if ‘simplicity’ is used in a special sense known solely by scientists. We understand the meaning of the term ‘simple’ only by recalling the meaning of the term ‘rational’ or ‘reasonable’ or ‘such that we ought to assent to it’, which the term ‘simple’ was supposed to replace. The term ‘simplicity’ functions then merely as a disguise for another meaning than its own. It is used for smuggling an essential quality into our appreciation of a scientific theory, which a mistaken conception of objectivity forbids us openly to acknowledge.

What has just been said of ‘simplicity’ applies equally to ‘symmetry’ and ‘economy’. They are contributing elements in the excellence of a theory, but can account for its merit only if the meanings of these terms are stretched far beyond their usual scope, so as to include the much deeper qualities which make the scientists rejoice in a vision like that of relativity. They must stand for those peculiar intellectual harmonies which reveal, more profoundly and permanently than any sense-experience, the presence of objective truth.

I shall call this practice a pseudo-substitution. It is used to play down man’s real and indispensable intellectual powers for the sake of maintaining an ‘objectivist’ framework which in fact cannot account for them. It works by defining scientific merit in terms of its relatively trivial features, and making these function then in the same way as the true terms which they are supposed to replace.

Other areas of science will illustrate even more effectively these indispensable intellectual powers, and their passionate participation in the act of knowing. It is to these powers and to this participation that I am referring in the title of this book as ‘Personal Knowledge’. We shall find Personal Knowledge manifested in the appreciation of probability and of order in the exact sciences, and see it at work even more extensively in the way the descriptive sciences rely on skills and connoisseurship. At all these points the act of knowing includes an appraisal; and this personal coefficient, which shapes all factual knowledge, bridges in doing so the disjunction between subjectivity and objectivity. It implies the claim that man can transcend his own subjectivity by striving passionately to fulfil his personal obligations to universal standards.

The acceptance of different kinds of articulate systems as mental dwelling places is arrived at by a process of gradual appreciation, and all these acceptances depend to some extent on the content of relevant experiences; but the bearing of natural sciences on facts of experience is much more specifiable than that of mathematics, religion or the various arts. It is justifiable, therefore, to speak of the verification of science by experience in a sense which would not apply to other articulate systems. The process by which other systems than science are tested and finally accepted may be called, by contrast, a process of validation.

Our personal participation is in general greater in a validation than in a verification. The emotional coefficient of assertion is intensified as we pass from the sciences to the neighbouring domains of thought. But both verification and validation are everywhere an acknowledgement of a commitment: they claim the presence of something real and external to the speaker. As distict from both of these, subjective experiences can only be said to be authentic, and authenticity does not involve a commitment in the sense in which both verification and validation do. (p. 202)

A new mathematical conception may be said to have reality if its assumption leads to a wide range of new interesting ideas. (p. 116)

…while in the natural sciences the feeling of making contact with reality is an augury of as yet undreamed of future empirical confirmations of an immanent discovery, in mathematics it betokens an indeterminate range of future germinations within mathematics itself. (p. 189)

Blog post

Last revised on November 27, 2009 at 16:43:13. See the history of this page for a list of all contributions to it.