Authors
William W. Tait
University of Chicago
Abstract
There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, the discussion in §§58-60 of the G r u n d l a g e n defends a conception of mathematical existence, to be found in Cantor (1883) and later in the writings of Dedekind and Hilbert, by basing it upon considerations about meaning which have general application, outside mathematics.2..
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
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: 65,811
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.

Add more references

Citations of this work BETA

Structure in Mathematics and Logic: A Categorical Perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
II—W Hat is the N Ormative R Ole of L Ogic&Quest.Peter Milne - 2009 - Aristotelian Society Supplementary Volume 83 (1):269-298.
Dedekind and Cassirer on Mathematical Concept Formation†.Audrey Yap - 2017 - Philosophia Mathematica 25 (3):369-389.

View all 16 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
125 ( #88,507 of 2,463,160 )

Recent downloads (6 months)
4 ( #179,109 of 2,463,160 )

How can I increase my downloads?

Downloads

My notes