Finitistic Arithmetic and Classical Logic

Philosophia Mathematica 22 (2):167-197 (2014)

Mihai Ganea
University of Toronto, St. George Campus
It can be argued that only the equational theories of some sub-elementary function algebras are finitistic or intuitive according to a certain interpretation of Hilbert's conception of intuition. The purpose of this paper is to investigate the relation of those restricted forms of equational reasoning to classical quantifier logic in arithmetic. The conclusion reached is that Edward Nelson's ‘predicative arithmetic’ program, which makes essential use of classical quantifier logic, cannot be justified finitistically and thus requires a different philosophical foundation, possibly as a restricted form of logicism
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DOI 10.1093/philmat/nkt042
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Fact, Fiction and Forecast.Nelson Goodman & Andrew G. Van Melsen - 1955 - Philosophy and Phenomenological Research 16 (2):271-273.
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