## 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

## 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

## 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

## 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

## 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

## 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

## The Barcan Formula and its Converse: Early Developments

*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/9780199552078.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

Necessitists accept both the Barcan formula (or schema) and its converse in quantified modal logic; contingentists typically reject both formulas. Their controversial implications are explained. Both ... More