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Introduction to Non-Classical Logic: From If to Is 2nd Revised edition [Mīkstie vāki]

4.17/5 (249 ratings by Goodreads)
(University of Melbourne)
  • Formāts: Paperback / softback, 643 pages, height x width x depth: 246x174x36 mm, weight: 1290 g
  • Sērija : Cambridge Introductions to Philosophy
  • Izdošanas datums: 10-Apr-2008
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521670268
  • ISBN-13: 9780521670265
  • Mīkstie vāki
  • Cena: 50,81 €
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  • Formāts: Paperback / softback, 643 pages, height x width x depth: 246x174x36 mm, weight: 1290 g
  • Sērija : Cambridge Introductions to Philosophy
  • Izdošanas datums: 10-Apr-2008
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521670268
  • ISBN-13: 9780521670265
Clearly introduces the major topics in logic and their relation to current philosophical issues.

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Recenzijas

'Priest's Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.' Greg Restall, The University of Melbourne 'I've used your book (first edition, that is) for years now in my upper level philosophy of logic courses. It is easily the best introduction to non-classical logics. I especially like its coverage of conditionals, and the introduction to relevant logic. Over the years, your book has made my students come to appreciate the variety and scope that exists within in formal logic, I intend to use the new edition so as to carry similar investigations into first order theory.' Jeffry Pelletier, Simon Fraser University 'Graham Priest's Introduction to Non-Classical Logic made this fascinating material on alternative logics accessible to my students for the very first time. The very welcome new edition extends the range of what is addressed to include important questions about quantification for modal logic, and the other systems as well.' Tony Roy, California State University, San Bernardino 'The first edition of Graham Priest's Introduction to Non-Classical Logic turned out to be an extremely useful and well-written introductory guide to the vast and difficult to survey area of non-classical and philosophical logic. The substantially expanded second edition in two volumes is bound to become a standard reference.' Heinrich Wansing, Dresden University of Technology 'Clear, self-contained, generously complete: this is bound to be the classic on non-classical logics for many years to come.' Achille Varzi, Columbia University 'This is an excellent introductory book to modern non-classical logics, fully accessible to non-professionals, and useful to professionals too. I have used part of its content in teaching Non-Classical Logic in the past years, and the response from my students shows the great success of the author's intention. The proof system it employs and the meta-proofs it provides are extremely easy to follow, while those followed-up philosophical discussions it summarizes for each logic system are both concise and lucid. It is not only a work introducing modern non-classical logic systems, but also a work full of interesting philosophical discussions on the motivations, advantages and disadvantages of these systems. With one penetrating theme - what a logic of conditionals should be like - in mind, the author has effectively organized a variety of topics into one integrated work. I would recommend it both to logicians and to philosophers, to professionals and to non-professionals.' Wen-fang Wang, National Chung Chen University 'The second edition of Graham Priest's book is, like the first, clearly expressed, well thought out for the student and an essential work for all those studying philosophy who want an adequate grounding in non-classical logic. I have used the first edition successfully in my intermediate class for the last five years, and will certainly be adding the second edition to the reading list when it is available.' Steve Read, University of St Andrews 'Priest succeeds in offering a marvellously unified treatment of 11 varieties of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first-degree entailment, basic relevant, mainstream relevant, and fussy Excellent references support this concise but clear treatment.' Choice 'This book is just what the title says it is And it is a very good one ' Stewart Shapiro, University of Ohio ' for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement 'I've just picked up a copy of the second edition of Graham Preist's An Introduction to Non-Classical Logic from the CUP bookshop. It looks terrific. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too. I thought the fist edition was terrific: so this is a hugely welcome expansion and I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99, which is surely an amazing bargain for a well produced 613 page book. So a must-buy and a must-read!' Logic Matters

Papildus informācija

This book clearly introduces the major topics in logic and their relation to current philosophical issues.
Preface to the First Edition xvii
Preface to the Second Edition xxi
Mathematical Prolegomenon xxvii
Set-theoretic Notation xxvii
Proof by Induction xxix
Equivalence Relations and Equivalence Classes xxx
Part I Propositional Logic
1(240)
Classical Logic and the Material Conditional
3(17)
Introduction
3(1)
The Syntax of the Object Language
4(1)
Semantic Validity
5(1)
Tableaux
6(4)
Counter-models
10(1)
Conditionals
11(1)
The Material Conditional
12(1)
Subjunctive and Counterfactual Conditionals
13(1)
More Counter-examples
14(1)
Arguments for
15(1)
*Proofs of Theorems
16(2)
History
18(1)
Further Reading
18(1)
Problems
18(2)
Basic Modal Logic
20(16)
Introduction
20(1)
Necessity and Possibility
20(1)
Modal Semantics
21(3)
Modal Tableaux
24(4)
Possible Worlds: Representation
28(1)
Modal Realism
28(1)
Modal Actualism
29(1)
Meinongianism
30(1)
*Proofs of Theorems
31(2)
History
33(1)
Further Reading
34(1)
Problems
34(2)
Normal Modal Logics
36(28)
Introduction
36(1)
Semantics for Normal Modal Logics
36(2)
Tableaux for Normal Modal Logics
38(4)
Infinite Tableaux
42(3)
S5
45(1)
Which System Represents Necessity?
46(3)
The Tense Logic Kt
49(2)
Extensions of Kt
51(5)
*Proofs of Theorems
56(4)
History
60(1)
Further Reading
60(1)
Problems
60(4)
Non-normal Modal Logics; Strict Conditionals
64(18)
Introduction
64(1)
Non-normal Worlds
64(1)
Tableaux for Non-normal Modal Logics
65(2)
The Properties of Non-normal Logics
67(2)
S0.5
69(3)
Strict Conditionals
72(1)
The Paradoxes of Strict Implication
72(1)
...and their Problems
73(1)
The Explosion of Contradictions
74(2)
Lewis' Argument for Explosion
76(1)
*Proofs of Theorems
77(2)
History
79(1)
Further Reading
80(1)
Problems
80(2)
Conditional Logics
82(21)
Introduction
82(1)
Some More Problematic Inferences
82(2)
Conditional Semantics
84(2)
Tableaux for C
86(1)
Extensions of C
87(3)
Similarity Spheres
90(4)
C1 and C2
94(3)
Further Philosophical Reflections
97(1)
*Proofs of Theorems
98(2)
History
100(1)
Further Reading
101(1)
Problems
101(2)
Intuitionist Logic
103(17)
Introduction
103(1)
Intuitionism: The Rationale
103(2)
Possible-world Semantics for Intuitionism
105(2)
Tableaux for Intuitionist Logic
107(5)
The Foundations of Intuitionism
112(1)
The Intuitionist Conditional
113(1)
*Proofs of Theorems
114(2)
History
116(1)
Further Reading
117(1)
Problems
117(3)
Many-valued Logics
120(22)
Introduction
120(1)
Many-valued Logic: The General Structure
120(2)
The 3-valued Logics of Kleene and Lukasiewicz
122(2)
LP and RM3
124(1)
Many-valued Logics and Conditionals
125(2)
Truth-value Gluts: Inconsistent Laws
127(2)
Truth-value Gluts: Paradoxes of Self-reference
129(1)
Truth-value Gaps: Denotation Failure
130(2)
Truth-value Gaps: Future Contingents
132(1)
Supervaluations, Modality and Many-valued Logic
133(4)
*Proofs of Theorems
137(2)
History
139(1)
Further Reading
140(1)
Problems
140(2)
First Degree Entailment
142(21)
Introduction
142(1)
The Semantics of FDE
142(2)
Tableaux for FDE
144(2)
FDE and Many-valued Logics
146(3)
Relational Semantics and Tableaux for L3 and RM3
149(2)
The Routley Star
151(3)
Paraconsistency and the Disjunctive Syllogism
154(1)
*Proofs of Theorems
155(6)
History
161(1)
Further Reading
161(1)
Problems
161(2)
Logics with Gaps, Gluts and Worlds
163(25)
Introduction
163(1)
Adding→
163(1)
Tableaux for K4
164(2)
Non-normal Worlds Again
166(2)
Tableaux for N4
168(1)
Star Again
169(2)
Impossible Worlds and Relevant Logic
171(4)
Logics of Constructible Negation
175(4)
*Proofs of Theorems
179(5)
History
184(1)
Further Reading
185(1)
Problems
185(3)
Relevant Logics
188(33)
Introduction
188(1)
The Logic B
188(2)
Tableaux for B
190(4)
Extensions of B
194(3)
Content Inclusion
197(6)
The System R
203(3)
The Ternary Relation
206(2)
Ceteris Paribus Enthymemes
208(3)
*Proofs of Theorems
211(5)
History
216(1)
Further Reading
217(1)
Problems
218(3)
Fuzzy Logics
221(20)
Introduction
221(1)
Sorites Paradoxes
221(1)
...and Responses to Them
222(2)
The Continuum-valued Logic L
224(3)
Axioms for L
227(3)
Conditionals in L
230(1)
Fuzzy Relevant Logic
231(3)
*Appendix: t-norm Logics
234(3)
History
237(1)
Further Reading
238(1)
Problems
239(2)
Appendix: Many-valued Modal Logics
241(18)
Introduction
241(1)
General Structure
241(2)
Illustration: Modal Lukasiewicz Logic
243(1)
Modal FDE
244(3)
Tableaux
247(3)
Variations
250(1)
Future Contingents Revisited
251(3)
A Glimpse Beyond
254(1)
*Proofs of Theorems
255(4)
Postscript: An Historical Perspective on Conditionals
259(2)
Part II Quantification and Identity
261(323)
Classical First-order Logic
263(27)
Introduction
263(1)
Syntax
263(1)
Semantics
264(2)
Tableaux
266(6)
Identity
272(3)
Some Philosophical Issues
275(2)
Some Final Technical Comments
277(1)
*Proofs of Theorems 1
278(5)
*Proofs of Theorems 2
283(2)
*Proofs of Theorems 3
285(2)
History
287(1)
Further Reading
287(1)
Problems
288(2)
Free Logics
290(18)
Introduction
290(1)
Syntax and Semantics
290(1)
Tableaux
291(2)
Free Logics: Positive, Negative and Neutral
293(2)
Quantification and Existence
295(2)
Identity in Free Logic
297(3)
*Proofs of Theorems
300(4)
History
304(1)
Further Reading
305(1)
Problems
305(3)
Constant Domain Modal Logics
308(21)
Introduction
308(1)
Constant Domain K
308(1)
Tableaux for CK
309(5)
Other Normal Modal Logics
314(1)
Modality De Re and De Dicto
315(3)
Tense Logic
318(2)
*Proofs of Theorems
320(5)
History
325(1)
Further Reading
326(1)
Problems
327(2)
Variable Domain Modal Logics
329(20)
Introduction
329(1)
Prolegomenon
329(1)
Variable Domain K and its Normal Extensions
330(1)
Tableaux for VK and its Normal Extensions
331(4)
Variable Domain Tense Logic
335(1)
Extensions
336(3)
Existence Across Worlds
339(2)
Existence and Wide-Scope Quantifiers
341(1)
*Proofs of Theorems
342(4)
History
346(1)
Further Reading
346(1)
Problems
347(2)
Necessary Identity in Modal Logic
349(18)
Introduction
349(1)
Necessary Identity
350(2)
The Negativity Constraint
352(2)
Rigid and Non-rigid Designators
354(3)
Names and Descriptions
357(1)
*Proofs of Theorems 1
358(4)
*Proofs of Theorems 2
362(2)
History
364(1)
Further Reading
364(1)
Problems
365(2)
Contingent Identity in Modal Logic
367(17)
Introduction
367(1)
Contingent Identity
367(6)
SI Again, and the Nature of Avatars
373(3)
*Proofs of Theorems
376(6)
History
382(1)
Further Reading
382(1)
Problems
382(2)
Non-normal Modal Logics
384(15)
Introduction
384(1)
Non-normal Modal Logics and Matrices
384(1)
Constant Domain Quantified L
385(1)
Tableaux for Constant Domain L
386(1)
Ringing the Changes
387(4)
Identity
391(2)
*Proofs of Theorems
393(4)
History
397(1)
Further Reading
397(1)
Problems
397(2)
Conditional Logics
399(22)
Introduction
399(1)
Constant and Variable Domain C
399(4)
Extensions
403(5)
Identity
408(5)
Some Philosophical Issues
413(2)
*Proofs of Theorems
415(4)
History
419(1)
Further Reading
419(1)
Problems
419(2)
Intuitionist Logic
421(35)
Introduction
421(1)
Existence and Construction
421(1)
Quantified Intuitionist Logic
422(2)
Tableaux for Intuitionist Logic 1
424(3)
Tableaux for Intuitionist Logic 2
427(4)
Mental Constructions
431(1)
Necessary Identity
432(2)
Intuitionist Identity
434(3)
*Proofs of Theorems 1
437(11)
*Proofs of Theorems 2
448(5)
History
453(1)
Further Reading
453(1)
Problems
453(3)
Many-valued Logics
456(20)
Introduction
456(1)
Quantified Many-valued Logics
456(1)
A and E
457(2)
Some 3-valued Logics
459(2)
Their Free Versions
461(1)
Existence and Quantification
462(3)
Neutral Free Logics
465(2)
Identity
467(1)
Non-classical Identity
468(1)
Supervaluations and Subvaluations
469(2)
*Proofs of Theorems
471(2)
History
473(1)
Further Reading
474(1)
Problems
474(2)
First Degree Entailment
476(28)
Introduction
476(1)
Relational and Many-valued Semantics
476(3)
Tableaux
479(2)
Free Logics with Relational Semantics
481(2)
Semantics with the Routley*
483(3)
Identity
486(3)
*Proofs of Theorems 1
489(4)
*Proofs of Theorems 2
493(6)
*Proofs of Theorems 3
499(3)
History
502(1)
Further Reading
502(1)
Problems
502(2)
Logics with Gaps, Gluts and Worlds
504(31)
Introduction
504(1)
Matrix Semantics Again
505(1)
N4
505(3)
N*
508(2)
K4 and K*
510(2)
Relevant Identity
512(3)
Relevant Predication
515(2)
Logics with Constructible Negation
517(4)
Identity for Logics with Constructible Negation
521(2)
*Proofs of Theorems 1
523(4)
*Proofs of Theorems 2
527(3)
*Proofs of Theorems 3
530(2)
History
532(1)
Further Reading
532(1)
Problems
533(2)
Relevant Logics
535(29)
Introduction
535(1)
Quantified B
535(2)
Extensions of B
537(4)
Restricted Quantification
541(2)
Semantics vs Proof Theory
543(5)
Identity
548(5)
Properties of Identity
553(2)
*Proofs of Theorems 1
555(4)
*Proofs of Theorems 2
559(2)
History
561(1)
Further Reading
561(1)
Problems
562(2)
Fuzzy Logics
564(20)
Introduction
564(1)
Quantified Lukasiewicz Logic
564(1)
Validity in L
565(5)
Deductions
570(2)
The Sorites Again
572(1)
Fuzzy Identity
573(3)
Vague Objects
576(2)
*Appendix: Quantification and Identity in t-norm Logics
578(3)
History
581(1)
Further Reading
582(1)
Problems
582(2)
Postscript: A Methodological Coda
584(3)
References 587(16)
Index of Names 603(4)
Index of Subjects 607
Graham Priest is Boyce Gibson Professor of Philosophy, University of Melbourne. His most recent publications include Towards Non-Being (2005) and Doubt Truth to be a Liar (2006).