How effective indeed is present-day mathematics?

Logic and Logical Philosophy 15 (2):131-153 (2006)

Abstract
We argue that E. Wigner’s well-known claim that mathematics is unreasonably effective in physics 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 everyday reasoning, theory of meaning and 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 vagueness  meaning  effectiveness of mathematics  everyday reasoning
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DOI 10.12775/LLP.2006.008
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On Sense and Reference.Gottlob Frege - 2010 - In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge. pp. 36--56.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Non-Well-Founded Sets.Peter Aczel - 1988 - Csli Lecture Notes.

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