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 Cantorian set theory

Alex Oliver and Timothy Smiley

in Plural Logic

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199570423
eISBN:
9780191755866
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570423.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter applies plural logic to set theory. Set theory may be axiomatized with full plural logic as the underlying logic and with the function sign { }—read ‘set of’—as its only nonlogical ... More


Plural Logic

Alex Oliver and Timothy Smiley

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199570423
eISBN:
9780191755866
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570423.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This book aims to be the natural point of entry to what will be a new subject for most readers. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate ... More


Cantorian set theory

Alex Oliver and Timothy Smiley

in Plural Logic: Second Edition, Revised and Enlarged

Published in print:
2016
Published Online:
February 2017
ISBN:
9780198744382
eISBN:
9780191843877
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198744382.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter applies plural logic to set theory. Set theory may be axiomatized with full plural logic as the underlying logic and with the function sign { }—read ‘set of’—as its only nonlogical ... More


Higher-level plural logic

Alex Oliver and Timothy Smiley

in Plural Logic: Second Edition, Revised and Enlarged

Published in print:
2016
Published Online:
February 2017
ISBN:
9780198744382
eISBN:
9780191843877
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198744382.003.0015
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter is conceived as meeting the challenge left by the abandoned second volume of Russell's Principles of Mathematics. An outline of higher-level plural logic is presented making use of ... More


Plural Logic: Second Edition, Revised and Enlarged

Alex Oliver and Timothy Smiley

Published in print:
2016
Published Online:
February 2017
ISBN:
9780198744382
eISBN:
9780191843877
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198744382.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII's wives’, ‘the real numbers’, ‘√—1’, ‘they’); plural predicates ... More


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