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Works of Music: An Essay in Ontology

Julian Dodd

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199284375
eISBN:
9780191713743
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199284375.001.0001
Subject:
Philosophy, Aesthetics

This book gives a sustained defence of the simple view of the ontological nature of works of pure, instrumental music. The simple view is the conjunction of two theses: the type/token theory and ... More


TOWARD A MINIMALIST FOUNDATION FOR CONSTRUCTIVE MATHEMATICS

Maria Emilia Maietti and Giovanni Sambin

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The two main views in modern constructive mathematics usually associated with constructive type theory and topos theory are compatible with the classical view, but they are incompatible with each ... More


From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Laura Crosilla and Peter Schuster (eds)

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Constructive mathematics is a vital area of research which has gained special attention in recent years due to the distinctive presence of computational content in its theorems. This characteristic ... More


INTERACTIVE PROGRAMS AND WEAKLY FINAL COALGEBRAS IN DEPENDENT TYPE THEORY

Peter Hancock and Anton Setzer

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0007
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter considers the representation of interactive programs in dependent type theory and bases it on the monadic I/O used in Haskell. Two versions are described: in the first the interface with ... More


INTRODUCTION

Laura Crosilla and Peter Schuster

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This introductory chapter sets the stage for the following chapters. It first discusses the issue of foundational systems for constructive mathematical practice, and expresses the desire for a closer ... More


The Contradiction (ii): A Simple Solution

David Bostock

in Russell's Logical Atomism

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199651443
eISBN:
9780191741197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651443.003.0004
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Seeking for a solution to his ‘contradiction’, Russell came to think that he could set aside classes in favour of propositional functions. In fact his first attempt in this direction, i.e. the ... More


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


Introduction

Julian Dodd

in Works of Music: An Essay in Ontology

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199284375
eISBN:
9780191713743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199284375.003.0001
Subject:
Philosophy, Aesthetics

This chapter both introduces the simple view in the ontology of music and explains its scope. In essence, the simple view consists of an answer to two questions: the categorial question and the ... More


Problems

David Bostock

in Russell's Logical Atomism

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199651443
eISBN:
9780191741197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651443.003.0006
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Russell’s attempt to obey the Vicious Circle Principle must lead to the conclusion that there are only countably many propositional functions, but this conflicts with his axiom of reducibility. So we ... 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


Logic

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/9780199541492.003.0009
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Gappy semantics is used to model indeterminacy with ‘upwards falsity-preservation’ emphasized as much as downwards truth-preservation. This two-way idea is generalized to multiple premiss/multiple ... More


The Contradiction (iii): A Ramified Solution

David Bostock

in Russell's Logical Atomism

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199651443
eISBN:
9780191741197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651443.003.0005
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

Poincaré had recommended a ‘Vicious Circle Principle’, and Russell accepted this in his final ‘ramified’ theory of types. He claims both that this principle resolves a range of paradoxes (including ... 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


TOPOLOGICAL STRINGS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Type-A and type-B topological sigma models are two topological field theories in two dimensions. Although they contain a lot of information in genus 0, they turn out to be trivial for g > 1. This is ... More


A Semantic Ontology for Dialogue

Jonathan Ginzburg

in The Interactive Stance

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199697922
eISBN:
9780191738425
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199697922.003.0003
Subject:
Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics, Semantics and Pragmatics

This chapter describes the semantic ontology which is the basis for subsequent representation of dialogue contexts. It suggests that a semantic ontology for dialogue needs to provide the following: ... More


Harrod‐Type Macrodynamics

John Hicks

in Methods of Dynamic Economics

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198772873
eISBN:
9780191596438
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198772874.003.0012
Subject:
Economics and Finance, Macro- and Monetary Economics

The Keynes-type theory, if formulated in the way that we have been formulating it, needs to be completed by a consideration of what happens when fixed capital investment is not given autonomously, ... More


Extraordinary Qm

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter highlights other surprising aspects of QM∞: unlike theories of ordinary QM, theories of QM∞ can traffic in algebras none of whose countably additive states are pure. The chapter sketches ... More


Constructibility and Open‐Sentences

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

Since the constructibility quantifiers, used in the mathematical system to be developed, will all assert the constructibility of open sentences, an explanation is given of the kinds of open sentences ... More


The Russellian Influence on Hilbert and His School

Paolo Mancosu

in The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199546534
eISBN:
9780191594939
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546534.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This chapter explores an aspect of Hilbert’s program that was considered to be an open problem in the literature, namely the influence of Russell’s type theory and logicism on Hilbert and his school ... More


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