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First-Order Modal Logic : SYNTHESE LIBRARY - M. Fitting

First-Order Modal Logic

SYNTHESE LIBRARY

Hardcover Published: 31st October 1998
ISBN: 9780792353348
Number Of Pages: 292

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Fitting and Mendelsohn present a thorough treatment of first-order modal logic, together with some propositional background. They adopt throughout a threefold approach. Semantically, they use possible world models; the formal proof machinery is tableaus; and full philosophical discussions are provided of the way that technical developments bear on well-known philosophical problems.
The book covers quantification itself, including the difference between actualist and possibilist quantifiers; equality, leading to a treatment of Frege's morning star/evening star puzzle; the notion of existence and the logical problems surrounding it; non-rigid constants and function symbols; predicate abstraction, which abstracts a predicate from a formula, in effect providing a scoping function for constants and function symbols, leading to a clarification of ambiguous readings at the heart of several philosophical problems; the distinction between nonexistence and nondesignation; and definite descriptions, borrowing from both Fregean and Russellian paradigms.

"This Text is an excellent and most useful volume. It is pitched correctly: the exercises are just right... It sets a high standard for anything following. It is to be highly recommended." (Bulletin of Symbolic Logic, 8:3)

Prefacep. xi
Propositional Modal Logicp. 1
What is a Modal?p. 2
Can There Be a Modal Logic?p. 3
What Are The Formulas?p. 5
Aristotle's Modal Squarep. 7
Informal Interpretationsp. 8
What Are the Models?p. 11
Examplesp. 14
Some Important Logicsp. 18
Logical Consequencep. 21
Temporal Logicp. 24
Epistemic Logicp. 28
Historical Highlightsp. 32
Tableau Proof Systemsp. 46
What Is a Proofp. 46
Tableausp. 47
More Tableau Systemsp. 51
Logical Consequence and Tableausp. 55
Tableaus Workp. 57
Axiom Systemsp. 67
What Is an Axiomatic Proofp. 67
More Axiom Systemsp. 71
Logical Consequence, Axiomaticallyp. 73
Axiom Systems Work Toop. 74
Quantified Modal Logicp. 81
First-Order Formulasp. 81
An Informal Introductionp. 83
Necessity De Re and De Dictop. 85
Is Quantified Modal Logic Possible?p. 89
What the Quantifiers Quantify Overp. 92
Constant Domain Modelsp. 95
Varying Domain Modelsp. 101
Different Media, Same Messagep. 105
Barcan and Converse Barcan Formulasp. 108
First-Order Tableausp. 116
Constant Domain Tableausp. 116
Varying Domain Tableausp. 118
Tableaus Still Workp. 121
First-Order Axiom Systemsp. 132
A Classical First-Order Axiom Systemp. 132
Varying Domain Modal Axiom Systemsp. 135
Constant Domain Systemsp. 136
Miscellanyp. 138
Equalityp. 140
Classical Backgroundp. 140
Frege's Puzzlep. 142
The Indiscernibility of Identicalsp. 145
The Formal Detailsp. 149
Tableau Equality Rulesp. 150
Tableau Soundness and Completenessp. 152
An Examplep. 159
Existence and Actualist Quantificationp. 163
To Bep. 163
Tableau Proofsp. 165
The Paradox of NonBeingp. 167
Deflationistsp. 169
Parmenides' Principlep. 172
Inflationistsp. 175
Unactualized Possiblesp. 178
Barcan and Converse Barcan, Againp. 180
Using Validities in Tableausp. 182
On Symmetryp. 185
Terms and Predicate Abstractionp. 187
Why constants should not be constantp. 187
Scopep. 190
Predicate Abstractionp. 194
Abstraction in the Concretep. 195
Reading Predicate Abstractsp. 200
Abstraction Continuedp. 204
Equalityp. 204
Rigidityp. 210
A Dynamic Logic Examplep. 216
Rigid Designatorsp. 217
Existencep. 220
Tableau Rules, Varying Domainp. 221
Tableau Rules, Constant Domainp. 227
Designationp. 230
The Formal Machineryp. 231
Designation and Existencep. 233
Existence and Designationp. 235
Fictionp. 241
Tableau Rulesp. 245
Definite Descriptionsp. 248
Notationp. 248
Two Theories of Descriptionsp. 249
The Semantics of Definite Descriptionsp. 253
Some Examplesp. 255
Hintikka's Schema and Variationsp. 261
Varying Domain Tableausp. 265
Russell's Approachp. 273
Possibilist Quantifiersp. 275
Referencesp. 277
Indexp. 283
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792353348
ISBN-10: 079235334X
Series: SYNTHESE LIBRARY
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 292
Published: 31st October 1998
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.61
Edition Type: New edition

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