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Past, Present and Future

Arthur Prior

Published in print:
1967
Published Online:
October 2011
ISBN:
9780198243113
eISBN:
9780191680632
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198243113.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This book is a sequel to Time and Modality. Many problems raised in that book have been resolved, and new ones have been raised in their turn. The author has recorded some of these developments, and ... More


Modal Logic: An Introduction to its Syntax and Semantics

Nino B. Cocchiarella and Max A. Freund

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.001.0001
Subject:
Philosophy, Philosophy of Language

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision, and philosophical insight. All of the S1-S5 modal logics of ... More


A Method of Modal Proof In Aristotle

Jacob Rosen and Marko Malink

in Oxford Studies in Ancient Philosophy: Volume 42

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199644384
eISBN:
9780191743344
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199644384.003.0006
Subject:
Philosophy, Ancient Philosophy

In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can ... More


INTERPOLATION AND DEFINABILITY IN QUANTIFIED LOGICS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a proof of Lyndon's interpolation property (LIP) for quantified extensions of basic modal logics K, T, D, K4, and S4, and for some others, including the propositional S5 has ... More


INTRODUCTION AND DISCUSSION

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This introductory chapter explains various options and aspects of interpolation. It gives some case study examples and presents an overview of the book's contents.


Modal Logic from Kant to Possible Worlds Semantics

Tapio Korte, Ari Maunu, and Tuomo Aho

in The Development of Modern Logic

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195137316
eISBN:
9780199867912
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195137316.003.0035
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner ... More


Modality: Metaphysics, Logic, and Epistemology

Bob Hale and Aviv Hoffmann (eds)

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199565818
eISBN:
9780191722004
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199565818.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

The philosophy of modality investigates necessity and possibility, and related notions — are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be ... More


The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Charles S. Chihara

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This book gives a critical exposition of modal realism, the philosophical doctrine that there exist many possible worlds of which the actual world — the universe in which we live — is just one. The ... More


The Development of Modern Logic

Leila Haaparanta (ed.)

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195137316
eISBN:
9780199867912
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195137316.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the ... More


Quantified Modal Logic

Nino B. Cocchiarella and Max A. Freund

in Modal Logic: An Introduction to its Syntax and Semantics

Published in print:
2008
Published Online:
October 2011
ISBN:
9780195366587
eISBN:
9780199851898
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195366587.003.0007
Subject:
Philosophy, Philosophy of Language

This chapter describes the syntax of first-order modal predicate logic and develops the first-order extensions of the different sentential modal logics constructed in Chapter 2. The authors ... More


AN ANALOGUE OF BETH'S THEOREM IN NORMAL EXTENSIONS OF THE MODAL LOGIC K4

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0011
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Beth's theorems state that in the classical predicate logic, any implicitly definable predicate is explicitly definable. This chapter proves an analogue of this theorem for all extensions of K4. It ... More


Modality without Worlds III: Explorations, Developments, and Defences

Charles S. Chihara

in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter explores, develops, and defends some of the major features of the anti-realist position. One feature of Graeme Forbes's anti-realistic analysis of modal logic is the absence of any ... More


Necessity

Keith Hossack

in The Metaphysics of Knowledge

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199206728
eISBN:
9780191709777
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206728.003.0004
Subject:
Philosophy, Metaphysics/Epistemology

This chapter offers an epistemic account of necessity: a fact is necessary if it has an a priori mode of presentation, contingent otherwise. The discussion proceeds as follows. Section 1 gives the ... More


Mathematics without Numbers: Towards a Modal-Structural Interpretation

Geoffrey Hellman

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198240341
eISBN:
9780191597664
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198240341.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to ... More


Possible Worlds Semantics

Charles S. Chihara

in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses the philosophical theories and presuppositions of applying possible worlds semantics in order to draw conclusions about matters involving what are called conceptual or broadly ... More


Modal Realism

Charles S. Chihara

in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

Published in print:
2001
Published Online:
October 2011
ISBN:
9780199246557
eISBN:
9780191697609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199246557.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

The models studied in modal logic are set theoretical structures. So one can regard the model theory of modal logic as a branch of set theory. The philosophical question arises: what is the ... More


INTERPOLATION IN MODAL INFINITE SLICE LOGICS CONTAINING THE LOGIC K4

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter examines the family NE(K) of normal extensions of K4. With any such logic L its reflexive fragment r(L) is associated, which contains the logic S4. A logic L is of infinite slice if ... More


 From First-Order to Higher-Order Modal Logic

Timothy Williamson

in Modal Logic as Metaphysics

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199552078
eISBN:
9780191752506
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552078.003.0005
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

First-order logic permits quantification into name position. Second-order logic permits quantification into predicate or sentence position too. Higher-order logic takes the generalization even ... More


A Backward Look at Quine's Animadversions on Modalities

Ruth Barcan Marcus

in Modalities: Philosophical Essays

Published in print:
1995
Published Online:
November 2003
ISBN:
9780195096576
eISBN:
9780199833412
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195096576.003.0014
Subject:
Philosophy, General

This paper reflects, in a loosely historical and personally reminiscent fashion, on Quine's animadversions on modalities, the debates they provoked, and some of its outcomes.


Non‐reductive Naturalism

Ralph Wedgwood

in The Nature of Normativity

Published in print:
2007
Published Online:
May 2008
ISBN:
9780199251315
eISBN:
9780191719127
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251315.003.0010
Subject:
Philosophy, Moral Philosophy

This chapter attempts to answer the central objection that many philosophers will raise against the idea (which was defended in the previous chapter) that there are irreducible normative facts. ... More


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