Modern Logic A Text in Elementary Symbolic Logic

by Forbes, Graeme

• ISBN13: 9780195080292
• ISBN10: 0195080297
• Format: Paperback
• Copyright: 1994-01-20
• Publisher: Oxford University Press

Summary

Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a specialappendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, Modern Logic gives equal weight to semantics and proof theory and explains their relationship,and develops in detail techniques for symbolizing natural language in first-order logic. After a general introduction featuring the notion of logical form, the book offers sections on classical sentential logic, monadic predicate logic, and full first-order logic with identity. A concluding sectiondeals with extensions of and alternatives to classical logic, including modal logic, intuitionistic logic, and fuzzy logic. For students of philosophy, mathematics, computer science, or linguistics, Modern Logic provides a thorough understanding of basic concepts and a sound basis for more advancedwork.

Author Biography

Graeme Forbes is Professor of Philosophy at the University of Colorado at Boulder. He is the author of Attitude Problems (Oxford, 2006), Languages of Possibility (1989), and The Metaphysics of Modality (Oxford, 1985). He has held research fellowships at New College, Oxford, and Edinburgh University, and has taught at the University of California at Santa Barbara and at Riverside.

Table of Contents

Part I Classical Sentential Logic
What Is Logic?	3	(9)
Arguments	3	(2)
Logical form and validity	5	(3)
Complications	8	(2)
A note to the reader	10	(1)
Summary	11	(1)
First Steps in Symbolization	12	(33)
The sentential connectives	12	(2)
Negations, conjunctions and disjunctions	14	(6)
Conditionals and biconditionals	20	(7)
Symbolizing entire arguments	27	(8)
The syntax of the formal language	35	(5)
Quotation, selective and otherwise	40	(4)
Summary	44	(1)
Semantics for Sentential Logic	45	(41)
Truth-functions	45	(8)
Classifying formulae	53	(5)
Testing for validity by exhaustive search	58	(4)
Testing for validity by constructing interpretations	62	(6)
Testing for validity by with semantic tableaux	68	(4)
Properties of semantic consequence	72	(2)
Expressive completeness	74	(7)
Non-truth-functional connectives	81	(4)
Summary	85	(1)
Natural Deduction in Sentential Logic	86	(63)
The concept of proof	86	(2)
Rules for conjunction and the conditional	88	(12)
Sequents and theorems	100	(2)
Rules for negation	102	(7)
Rules for disjunction	109	(8)
The biconditional	117	(2)
Heuristics	119	(1)
Sequent and Theorem Introduction	120	(8)
Alternative formats for proofs	128	(5)
Systems equivalent to NK	133	(7)
Semantic and deductive consequence compared	140	(4)
Summary	144	(5)
Part II Monadic Predicate Logic
Prediction and Quantification in English	149	(21)
A different type of argument	149	(3)
Further steps in symbolization: the existential quantifier	152	(6)
More symbolizations: the universal quantifier	158	(7)
The syntax of LMPL	165	(4)
Summary	169	(1)
Validity and Provability in Monadic Predicate Logic	170	(49)
Semantics for the quantifiers	170	(10)
Constructing counterexamples	180	(5)
Deductive consequence: quantifiers in NK	185	(10)
The rule of Existential Elimination	195	(9)
Extensions of sequent introduction	204	(3)
Decision procedures	207	(4)
Tableaux for monadic predicate logic	211	(3)
Alternative formats	214	(2)
Summary	216	(3)
Part III First-Order Logic with Identity
Advanced Symbolizations	219	(31)
N-place predicates	219	(12)
Identity, number and descriptions	231	(10)
The syntax of LFOL	241	(2)
Ambiguity	243	(6)
Summary	249	(1)
Validity and Provability in First-Order Logic with Identity	250	(45)
Interpretations in LFOL	250	(7)
Demonstrating invalidity	257	(6)
Proofs in NK	263	(6)
Rules for identity in NK	269	(6)
Properties of binary relations	275	(7)
Alternative formats	282	(1)
Semantic consequence, deductive consequence and decidability	283	(3)
Some limitations of first-order logic	286	(5)
Summary	291	(4)
Part IV Extensions and Alternatives to Classical Logic
Modal Logic	295	(38)
Modal operators	295	(1)
A definition of semantic consequence for sentential modal logic	296	(5)
The canonical translation	301	(5)
Natural deduction in S5	306	(7)
First-order modal logic: S5 semantics	313	(8)
First-order modal logic: natural deduction	321	(11)
Summary	332	(1)
Intuitionistic Logic	333	(16)
The motivation for intuitionistic logic	333	(5)
Semantic consequence in intuitionistic sentential logic	338	(6)
Intuitionistic monadic predicate logic	344	(5)
Fuzzy Logic	349	(9)
Sorites paradoxes	349	(2)
Degrees of truth	351	(1)
Fuzzy semantics for LFOL	352	(4)
Resolution of the paradoxes	356	(2)
Appendix: Using MacLogic	358	(2)
Solutions to Selected Exercises	360	(31)
Bibliography	391	(2)
Index	393