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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkt042
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 54,431
Through your library

References found in this work BETA

Fact, Fiction, and Forecast.Nelson Goodman - 1955 - Harvard University Press.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge: Harvard University Press.

View all 52 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Intuitionistic Choice and Restricted Classical Logic.Ulrich Kohlenbach - 2001 - Mathematical Logic Quarterly 47 (4):455-460.
An Algebraic Treatment of Quantifier-Free Systems of Arithmetic.Franco Montagna - 1996 - Archive for Mathematical Logic 35 (4):209-224.
On the Untenability of Nelson's Predicativism.St Iwan - 2000 - Erkenntnis 53 (1-2):147-154.
Hilbert's Program and the Omega-Rule.Aleksandar Ignjatović - 1994 - Journal of Symbolic Logic 59 (1):322 - 343.
Interpreting Classical Theories in Constructive Ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
A Realizability Interpretation for Classical Arithmetic.Jeremy Avigad - 2002 - Bulletin of Symbolic Logic 8 (3):439-440.
Two (or Three) Notions of Finitism.Mihai Ganea - 2010 - Review of Symbolic Logic 3 (1):119-144.
Classical Arithmetic as Part of Intuitionistic Arithmetic.Michael Potter - 1998 - Grazer Philosophische Studien 55 (1):127-41.
Numerical Abstraction Via the Frege Quantifier.G. Aldo Antonelli - 2010 - Notre Dame Journal of Formal Logic 51 (2):161-179.


Added to PP index

Total views
22 ( #460,746 of 2,374,856 )

Recent downloads (6 months)
1 ( #559,821 of 2,374,856 )

How can I increase my downloads?


My notes