Two (or three) notions of finitism

Review of Symbolic Logic 3 (1):119-144 (2010)
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Abstract

Finitism is given an interpretation based on two ideas about strings (sequences of symbols): a replacement principle extracted from Hilberts class 2 can be justified by means of an additional finitistic choice principle, thus obtaining a second equational theory . It is unknown whether is strictly stronger than since 2 may coincide with the class of lower elementary functions

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10.1017/s1755020309990323

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Mihai Ganea
University of Toronto, St. George Campus

Citations of this work

Hilbert’s Program.Richard Zach - 2012 - In Ed Zalta (ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
Strict Finitism, Feasibility, and the Sorites.Walter Dean - 2018 - Review of Symbolic Logic 11 (2):295-346.
On the Concept of Finitism.Luca Incurvati - 2015 - Synthese 192 (8):2413-2436.
Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9):1-56.

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References found in this work

Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
Collected works.Kurt Gödel - 1986 - New York: Oxford University Press. Edited by Solomon Feferman.

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