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Resolving the paradoxes

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0021
Subject:
Philosophy, Logic/Philosophy of Mathematics

The discussion of Wittgenstein's account of quantification in Chapter 20 left unaddressed what sort of theory of types it commits us to. To answer this question we need to look in more detail at the ... More


The Logic of Principia Mathematica

Peter Hylton

in Russell, Idealism, and the Emergence of Analytic Philosophy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240181
eISBN:
9780191597763
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824018X.003.0010
Subject:
Philosophy, History of Philosophy

Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact ... More


Unity

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

Merely taking the symbolic turn — to conceive of a proposition as symbolizing what it expresses, rather than being identical with it — is not yet to go very far towards uncovering the structure of ... More


A Brief Guide to Type Theory

Graeme Forbes

in Attitude Problems: An Essay On Linguistic Intensionality

Published in print:
2006
Published Online:
October 2011
ISBN:
9780199274949
eISBN:
9780191699801
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199274949.003.0002
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

The organizing principles of the simple theory of types are: (i) sentence-meanings are truth-values; (ii) the meaning of a name is its referent; and (iii) the meanings of other basic constituents of ... More


Quotients of a theory of presheaf type

Olivia Caramello

in Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

Published in print:
2017
Published Online:
March 2018
ISBN:
9780198758914
eISBN:
9780191818752
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198758914.003.0010
Subject:
Mathematics, Geometry / Topology, Pure Mathematics

In this chapter the quotients of a given theory of presheaf type are investigated by means of Grothendieck topologies that can be naturally attached to them, establishing a ‘semantic’ representation ... More


Theories of presheaf type: general criteria

Olivia Caramello

in Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

Published in print:
2017
Published Online:
March 2018
ISBN:
9780198758914
eISBN:
9780191818752
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198758914.003.0008
Subject:
Mathematics, Geometry / Topology, Pure Mathematics

This chapter carries out a systematic investigation of the class of geometric theories of presheaf type (i.e. classified by a presheaf topos), by using in particular the results on flat functors ... More


Examples of theories of presheaf type

Olivia Caramello

in Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

Published in print:
2017
Published Online:
March 2018
ISBN:
9780198758914
eISBN:
9780191818752
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198758914.003.0011
Subject:
Mathematics, Geometry / Topology, Pure Mathematics

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of ... More


The Limits of Representation

José L. Zalabardo

in Representation and Reality in Wittgenstein's Tractatus

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198743941
eISBN:
9780191803949
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198743941.003.0006
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Wittgenstein’s account of propositional representation imposes limits on what propositions can represent. This chapter explores Wittgenstein’s applications of this result. It considers first ... More


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