By Raymond L. Wilder and Mario Bunge (Auth.)
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Additional info for Mathematics As a Cultural System
As I have previously remarked, it is characteristic of science that "the farther its concepts seem to recede from external reality, the more successful do they become in the control of man's environment" (Wilder, 1959). 17 It has been my fortune to observe, practically from its beginnings,18 the growth of one of the most important fields of mathematics, viz. topology. The increasing abstraction (which I at first deplored, in my ignorance of evolutionary tendencies), which its growth early exhibited, was continually a source of amazement to me.
This process we shall call conceptual stress. The most elementary and best known example is probably the symbol %/-L Its occurrence in the solution of third-degree algebraic equations seems to have been the initial stress created by this "unreal" symbol. Additional considerations, such as the apparent fact that only by admitting it to number status could one assert that every algebraic equation of degree n, n ^ 1, has precisely n roots, ultimately forced the invention of acceptable definitions of complex numbers involving \/~-i.
The relativity of mathematical rigor It seems to be a commonly held belief, chiefly outside the mathematical community, that in the realm of mathematics can be found absolute truth. Such phrases as "mathematical truth," "mathematical certainty," are to be found within mathematical circles, to be sure, but usually with generally understood qualifications. Now it is certainly the case that according to the 27 A relatively recent case of this sort was Yoneyama, 1917-20. In this paper he studied indecomposable continua having only finitely many composants.
Mathematics As a Cultural System by Raymond L. Wilder and Mario Bunge (Auth.)