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.
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Produktdetaljer
ISBN
9780691187068
Publisert
2018
Utgiver
Vendor
Princeton University Press
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter