How effective indeed is present-day mathematics?

Athanassios Tzouvaras

DOI: http://dx.doi.org/10.12775/LLP.2006.008

Abstract


We argue that E. Wigner’s well-known claim that mathematics is unreasonably effective in physics (and not in the natural sciences in general, as the title of his article suggests) is only one side of the hill. The other side is the surprising insufficiency of present-day mathematics to capture the uniformities that arise in science outside physics. We describe roughly what the situation is in the areas of (a) everyday reasoning, (b) theory of meaning and (c) vagueness. We make also the point that mathematics, as we know it today, founded on the concept of set, need not be a conceptually final and closed system, but only a stage in a developing subject.

Keywords


effectiveness of mathematics; everyday reasoning; vagueness; meaning

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