Finitistic Arithmetic and Classical Logic

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

Authors
Mihai Ganea
University of Toronto, St. George Campus
Abstract
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
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,796
Through your library

References found in this work BETA

Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Fact, Fiction and Forecast.Nelson Goodman & Andrew G. Van Melsen - 1955 - Philosophy and Phenomenological Research 16 (2):271-273.
Fixing Frege.John P. Burgess - 2006 - Tijdschrift Voor Filosofie 68 (3):665-665.

View all 38 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 55:127-41.
Numerical Abstraction Via the Frege Quantifier.G. Aldo Antonelli - 2010 - Notre Dame Journal of Formal Logic 51 (2):161-179.

Analytics

Added to PP index
2014-03-30

Total views
21 ( #391,274 of 2,244,031 )

Recent downloads (6 months)
9 ( #158,843 of 2,244,031 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature