Informal versus formal mathematics

Synthese 154 (3):401-415 (2007)
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Abstract

We discuss Kunen’s algorithmic implementation of a proof for the Paris–Harrington theorem, and the author’s and da Costa’s proposed “exotic” formulation for the P =  NP hypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and intuitive or informal mathematics.

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10.1007/s11229-006-9126-9

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Representation and Invariance of Scientific Structures.Patrick Suppes - 2002 - CSLI Publications (distributed by Chicago University Press).
Systems of logic based on ordinals..Alan Turing - 1939 - London,: Printed by C.F. Hodgson & son.
Mathematical logic.Stephen Cole Kleene - 1967 - Mineola, N.Y.: Dover Publications.
The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.

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