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Geometry, philosophical issues in

DOI: 10.4324/9780415249126-Y068-1
Version: v1,  Published online: 1998
Retrieved May 19, 2024, from

Article Summary

The least abstract form of mathematics, geometry has, from the earliest Hellenic times, been accorded a curious position straddling empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of land surveying and measuring, from the prominence of visual aids (figures and constructions) in geometric proofs and, in the twentieth century, from Einstein’s General Theory of Relativity, which holds that the geometry of spacetime is dependent upon physical quantities. On the other hand, very early on, the symmetry and perfect regularity of certain geometric figures were taken as representative of a higher knowledge than that afforded by sense experience. And its concern with figures and constructions, rather than with number and calculation, rendered geometry amenable to axiomatic formulation and syllogistic deduction, establishing a paradigm of demonstrative knowledge which endured for two millennia. While the progress of mathematics has surmounted traditional distinctions between geometry and the mathematics of number, leaving only a heuristic role for geometric intuition, geometric thinking remains a vital component of mathematical cognition.

Citing this article:
Ryckman, T.A.. Geometry, philosophical issues in, 1998, doi:10.4324/9780415249126-Y068-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2024 Routledge.

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