Classical arithmetic is quite unnatural

Logic and Logical Philosophy 11:231-249 (2003)

Authors
Jean Paul Van Bendegem
Vrije Universiteit Brussel
Abstract
It is a generally accepted idea that strict finitism is a rather marginal view within the community of philosophers of mathematics. If one therefore wants to defend such a position (as the present author does), then it is useful to search for as many different arguments as possible in support of strict finitism. Sometimes, as will be the case in this paper, the argument consists of, what one might call, a “rearrangement” of known materials. The novelty lies precisely in the rearrangement, hence on the formal-axiomatic level most of the results presented here are not new. In fact, the basic results are inspired by and based on Mycielski (1981)
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DOI 10.12775/LLP.2003.012
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References found in this work BETA

A General Characterization of Adaptive Logics.Diderik Batens - 2001 - Logique Et Analyse 173 (175):45-68.
On Some Paradoxes of the Infinite.Victor Allis & Teunis Koetsier - 1991 - British Journal for the Philosophy of Science 42 (2):187-194.
Analysis Without Actual Infinity.Jan Mycielski - 1981 - Journal of Symbolic Logic 46 (3):625-633.
Ross' Paradox is an Impossible Super-Task.Jean Paul van Bendegem - 1994 - British Journal for the Philosophy of Science 45 (2):743-748.

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Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
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