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Conclusion

Alan Weir

in Truth Through Proof: A Formalist Foundation for Mathematics

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199541492
eISBN:
9780191594915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541492.003.0010
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not ... More


Knowledge by Agreement: The Programme of Communitarian Epistemology

Martin Kusch

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.001.0001
Subject:
Philosophy, Metaphysics/Epistemology

Knowledge by Agreement defends the ideas that knowledge is a social status (like money, or marriage), and that knowledge is primarily the possession of groups rather than individuals. ... More


Proof Set in Concrete

Alan Weir

in Truth Through Proof: A Formalist Foundation for Mathematics

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199541492
eISBN:
9780191594915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541492.003.0007
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete ... More


Avoiding Strict Finitism

Neil Tennant

in The Taming of the True

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199251605
eISBN:
9780191698057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251605.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter shows how to find an acceptable reading of knowability-in-principle in order to avoid visiting upon oneself and one's opposition the overly restrictive consequence that only the ... More


Quantification and Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0004
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. ... More


From Truth-Functional Logic to a Logic of Equations

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0005
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying ... More


Strict Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print:
2008
Published Online:
September 2011
ISBN:
9780199550470
eISBN:
9780191701559
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199550470.003.0008
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a ... More


Social Constructivism

Ilkka Niiniluoto

in Critical Scientific Realism

Published in print:
2002
Published Online:
November 2003
ISBN:
9780199251612
eISBN:
9780191598098
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251614.003.0009
Subject:
Philosophy, Philosophy of Science

Philosophers of science should take seriously the fact, emphasized already by Peirce and Popper, that scientific knowledge is a product of the scientific community. The ontological and ... More


Meaning Finitism

Martin Kusch

in Knowledge by Agreement: The Programme of Communitarian Epistemology

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.003.0016
Subject:
Philosophy, Metaphysics/Epistemology

Meaning finitism is a communitarian theory of what it is to master a language. It makes community consensus central in the constitution of normativity. Finitism says that terms have no fixed ... More


Truth

Martin Kusch

in Knowledge by Agreement: The Programme of Communitarian Epistemology

Published in print:
2002
Published Online:
January 2005
ISBN:
9780199251223
eISBN:
9780191601767
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251223.003.0017
Subject:
Philosophy, Metaphysics/Epistemology

Applies finitism to ’true’ and ’false’. Applying finitism to truth leads to radical and surprising consequences. If ’true’ does not have a fixed extension, then it is simply incoherent to speak of, ... More


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