Franklin

Fixing Frege / John P. Burgess.

Author/Creator:
Burgess, John P. author.
Publication:
Princeton, NJ : Princeton University Press, [2018]
Format/Description:
Book
1 online resource
Series:
Princeton Monographs in Philosophy
Contained In:
De Gruyter University Press Library.
Status/Location:
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Details

Subjects:
Logic, Symbolic and mathematical.
Language:
In English.
System Details:
Mode of access: Internet via World Wide Web.
text file PDF
Summary:
The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.
Contents:
Frontmatter
Contents
Acknowledgments
CHAPTER 1. Frege, Russell, and After
CHAPTER 2. Predicative Theories
CHAPTER 3. Impredicative Theories
Tables
Notes
References
Index
Notes:
Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)
Contributor:
De Gruyter.
ISBN:
9780691187068
OCLC:
1076409736
Publisher Number:
10.1515/9780691187068 doi
Access Restriction:
Restricted for use by site license.