Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics

Abstract
Does science justify any part of mathematics and, if so, what part? These questions are related to the so-called indispensability arguments propounded, among others, by Quine and Putnam; moreover, both were led to accept significant portions of set theory on that basis. However, set theory rests on a strong form of Platonic realism which has been variously criticized as a foundation of mathematics and is at odds with scientific realism. Recent logical results show that it is possible to directly formalize almost all, if not all, scientifically applicable mathematics in a formal system that is justified simply by Peano Arithmetic (via a proof-theoretical reduction). It is argued that this substantially vitiates the indispensability arguments
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 12,095
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles
Geoffrey Hellman (1992). On the Scope and Force of Indispensability Arguments. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456 - 464.
Edward N. Zalta (2007). Reflections on Mathematics. In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Peter Schreiber (1996). Mengenlehre—Vom Himmel Cantors Zur Theoria Prima Inter Pares. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143.
Marcus Rossberg & Daniel Cohnitz (2009). Logical Consequence for Nominalists. Theoria. An International Journal for Theory, History and Foundations of Science 24 (2):147-168.
Analytics

Monthly downloads

Added to index

2010-12-22

Total downloads

14 ( #120,567 of 1,102,036 )

Recent downloads (6 months)

1 ( #306,606 of 1,102,036 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.