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Introduction

Thomas J. McKay

in Plural Predication

Published in print:
2006
Published Online:
January 2007
ISBN:
9780199278145
eISBN:
9780191707971
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278145.003.0001
Subject:
Philosophy, Philosophy of Language

This introductory chapter begins with a brief discussion of the codification, interpretation, and development of first-order logic. It then argues that first-order logic should be extended to allow ... More


Among

Thomas J. McKay

in Plural Predication

Published in print:
2006
Published Online:
January 2007
ISBN:
9780199278145
eISBN:
9780191707971
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278145.003.0007
Subject:
Philosophy, Philosophy of Language

This chapter develops some axioms that express the fundamental features of the among relationship. It shows that although among is interdefinable with one of on one understanding of the one of ... 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


Predication

George Bealer

in Quality and Concept

Published in print:
1982
Published Online:
October 2011
ISBN:
9780198244288
eISBN:
9780191680762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198244288.003.0005
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Mind

First-order quantifier logic is complete; higher-order quantifier logic is not. A few formally minded philosophers of logic — such as Quine and some of his followers — appear to believe that this is ... More


Against Singularism

Thomas J. McKay

in Plural Predication

Published in print:
2006
Published Online:
January 2007
ISBN:
9780199278145
eISBN:
9780191707971
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199278145.003.0003
Subject:
Philosophy, Philosophy of Language

Because of the power and significance of first-order logic in its traditional form, restricted to distributive predication, it has been natural to try to express non-distributive plurals within that ... More


The Emergence of Generalized Quantifiers in Modern Logic

Stanley Peters

in Quantifiers in Language and Logic

Published in print:
2008
Published Online:
October 2011
ISBN:
9780199291267
eISBN:
9780191700590
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199291267.003.0003
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter presents a semantic tool, the concept of a (generalised) quantifier introduced by logicians in the mid-20th century. Logicians call these objects ‘generalised’ quantifiers, since they ... 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


The Semantics of Classical Predicate Logic

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/9780199246557.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

One striking feature of both Graeme Forbes and Gideon Rosen's anti-realism is the absence of any analysis of the role that possible worlds interpretations or structures play in modal logic. To avoid ... More


Regimentation

Gary Ebbs

in Truth and Words

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199557936
eISBN:
9780191721403
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199557936.003.0002
Subject:
Philosophy, General

This chapter sketches a pragmatic account of regimentation that is presupposed in the rest of the book. The basic idea, due to Quine, is that to regiment a given natural language sentence S, as one ... More


Logic and Mathematics

Jr. Henry E. Kyburg

in Science & Reason

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195062533
eISBN:
9780199853038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195062533.003.0002
Subject:
Philosophy, Philosophy of Science

This chapter discusses the philosophy and logic behind the mathematical ideas of first-order logic, metalanguages, arithmetic, and geometry. It familiarizes the reader to these mathematical ideas, ... More


The Semantics of 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/9780195366587.003.0008
Subject:
Philosophy, Philosophy of Language

The authors develop semantics for first-order modal predicate logic in terms of standard model theory, the models of which we take to be set-theoretic counterparts of possible worlds. A primary ... More


Applications to Monadic Definability

Stanley Peters

in Quantifiers in Language and Logic

Published in print:
2008
Published Online:
October 2011
ISBN:
9780199291267
eISBN:
9780191700590
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199291267.003.0015
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter applies the Ehrenfeucht-Fraïssé (EF) technique to present a variety of results about the expressive power of certain monadic quantifiers. After repeating the general method, ... More


Quantification and Ontology

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:
10.1093/0195096576.003.0005
Subject:
Philosophy, General

Interpretations of standard first‐order logic fail as vehicles for paraphrase of important segments of discourse involving tenses, modalities, and the like. This paper considers substitutional ... More


Predicate Languages

Jon Williamson

in In Defence of Objective Bayesianism

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199228003
eISBN:
9780191711060
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228003.003.0005
Subject:
Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy

Thus far we have considered objective Bayesian probability to be defined over finite propositional languages. This chapter extends the formalism to predicate languages. As well as reaping the rewards ... More


A Common Framework for Strategies

John P. Burgess and Gideon Rosen

in A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

Sets up a schematic framework for the formal representation of current scientific theories and nominalistic alternatives thereto, presupposing only some previous acquaintance with first‐order logic. ... More


Two Proposals for Causal Grammars

Thomas L. Griffiths and Joshua B. Tenenbaum

in Causal Learning: Psychology, Philosophy, and Computation

Published in print:
2007
Published Online:
April 2010
ISBN:
9780195176803
eISBN:
9780199958511
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195176803.003.0021
Subject:
Psychology, Developmental Psychology

A causal theory can be thought of as a grammar that generates events, and that can be used to parse events to identify underlying causal structure. This chapter considers what the components of such ... More


A first-order inquisitive semantics

Ivano Ciardelli, Jeroen Groenendijk, and Floris Roelofsen

in Inquisitive Semantics

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198814788
eISBN:
9780191852473
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198814788.003.0004
Subject:
Linguistics, Semantics and Pragmatics

Chapter 4 defines an inquisitive semantics for the language of firstorder logic, which includes the logical connectives (conjunction, disjunction, negation, and implication) as well as universal and ... More


From Sentence to Concept

Preller Anne

in Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199646296
eISBN:
9780191747847
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646296.003.0009
Subject:
Mathematics, Applied Mathematics

The compositional functional logical models of natural language are recast as compact closed categories. Composition is based on the geometrical representation of information flow characteristic for ... More


The Ontology and Logic of Higher-Order Multitudes

Peter Simons

in Unity and Plurality: Logic, Philosophy, and Linguistics

Published in print:
2016
Published Online:
June 2016
ISBN:
9780198716327
eISBN:
9780191785030
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198716327.003.0004
Subject:
Philosophy, Philosophy of Language

This chapter argues on the basis of examples, and the crucial role of difference as a generating notion, for the ontological acceptance of higher-order multitudes, that is, multitudes whose members ... More


Model Theory (with Stephen Isard)

Mark Steedman

in Taking Scope: The Natural Semantics of Quantifiers

Published in print:
2011
Published Online:
August 2013
ISBN:
9780262017077
eISBN:
9780262301404
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262017077.003.0005
Subject:
Linguistics, Semantics and Pragmatics

This chapter describes a model theory based on a standard statically scoped model theory for first-order logic and generalizes it to the case of relations whose arguments name propositions. It first ... More


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