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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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