The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine.
The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences observation, comparison, classification, trial, and generalisation are essential in both cases. But when I think of Shoolbred’s on the one hand and, say, the ornithological collections of the British Museum upon the other, I feel as though it would take me less trouble to master the second than the first. Why should the botanist, geologist or other-ist give himself such airs over the draper’s assistant? Is it because he names his plants or specimens with Latin names and divides them into genera and species, whereas the draper does not formulate his classifications, or at any rate only uses his mother tongue when he does? Yet how like the sub-divisions of textile life are to those of the animal and vegetable kingdoms! A few great families-cotton, linen, hempen, woollen, silk, mohair, alpaca-into what an infinite variety of genera and species do not these great families subdivide themselves? And does it take less labour, with less intelligence, to master all these and to acquire familiarity with their various habits, habitats and prices than it does to master the details of any other great branch of science? I do not know.
The term probability, as its etymology indicates, originates in practical and legal considerations of probing and proving. After astronomers began to use it in correcting their observations, it spread to other physical sciences and the prestige which it thus acquired has given it vogue in the social field. The concept of average was developed in the Rhodian laws as to the distribution of losses in maritime risks. It is therefore not anomalous to find similar transformations in the history of such fundamental concepts of statistics as average and probability.
Originally a strict anthropomorphic conception, it was gradually depersonalized or dehumanized in the natural sciences and then taken over by the social sciences in an effort to eliminate final causes or purposes from the study of human affairs. The same is true of the concept of law of nature. It was taken over into physics, developed there, and in the 18th century brought back as a foreign-born kind for the adoration of the social sciences. The Greek aitia or the Latin causa was originally a purely legal term. It is interesting to note how many fundamental terms which the social sciences are trying to adopt from physics have as a matter of historical fact originated in the social field.
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