## 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