Logic; Techniques of Formal Reasoning / Edition 2

Logic; Techniques of Formal Reasoning / Edition 2

by Donald Kalish, Robert J. Fogelin, Gary R. Mar, Richard Montague
     
 

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ISBN-10: 0155511815

ISBN-13: 9780155511811

Pub. Date: 04/28/1980

Publisher: Oxford University Press

Product Details

ISBN-13:
9780155511811
Publisher:
Oxford University Press
Publication date:
04/28/1980
Edition description:
2d ed
Pages:
520
Product dimensions:
6.48(w) x 9.58(h) x 1.20(d)

Table of Contents

Chapter I. 'NOT' and 'IF'
1(49)
1. Symbols and sentences
2(6)
EXERCISES
7(1)
2. From symbols to English and back
8(5)
EXERCISES
12(1)
3. Derivability and validity of symbolic arguments
13(19)
EXERCISES, GROUP I
27(5)
EXERCISES, GROUP II
32(1)
4. Validity of English arguments
32(3)
EXERCISES
34(1)
5. Fallacies
35(5)
6. Theorems
40(4)
EXERCISES, GROUP I
43(1)
EXERCISES, GROUP II
44(1)
7. Historical remarks
44(2)
8. Appendix: solutions to selected exercises
46(4)
Chapter II. 'AND', 'OR', 'IF AND ONLY IF'
50(67)
1. Symbols and sentences
50(3)
EXERCISES
52(1)
2. Translation and symbolization
53(6)
EXERCISES
57(2)
3. Inference rules and derivability
59(4)
EXERCISES
63(1)
4. Theorems with unabbreviated proofs
63(8)
EXERCISES
68(3)
5. Abbreviated derivations
71(4)
EXERCISES
75(1)
6. Theorems with abbreviated proofs
75(11)
EXERCISES
82(4)
7. Arguments
86(1)
EXERCISES, GROUP I
87(1)
EXERCISES, GROUP II
87(1)
8. Truth-value analysis of sentences
87(12)
EXERCISES, GROUP I
92(3)
EXERCISES, GROUP II
95(4)
9. Truth-value analysis of arguments
99(6)
EXERCISES, GROUP I
100(1)
EXERCISES, GROUP II
101(2)
EXERCISES, GROUP III
103(2)
10. Historical remarks
105(2)
11. Appendix: list of theorems of chapters I and II
107(5)
12. Appendix: solutions to selected exercises
112(5)
Chapter III. 'ALL' and 'SOME'
117(84)
1. Variables, quantifiers, formulas
117(6)
EXERCISES
121(2)
2. Bondage and freedom
123(3)
EXERCISES
125(1)
3. Informal notational conventions
126(1)
4. Translation and symbolization
126(13)
EXERCISES, GROUP I
132(1)
EXERCISES, GROUP II
133(4)
EXERCISES, GROUP III
137(2)
5. Inference rules
139(4)
EXERCISES
141(2)
6. Derivations
143(3)
EXERCISES
145(1)
7. Theorems with unabbreviated proofs
146(3)
EXERCISES
149(1)
8. Abbreviated derivations
149(4)
EXERCISES
153(1)
9. Fallacies
153(8)
EXERCISES
159(2)
10. Theorems with abbreviated proofs
161(9)
EXERCISES
169(1)
11. Arguments
170(4)
EXERCISES, GROUP I
171(1)
EXERCISES, GROUP II
172(1)
EXERCISES, GROUP III
173(1)
12. Invalidity: truth-functional expansions and models
174(10)
EXERCISES, GROUP I
180(2)
EXERCISES, GROUP II
182(1)
EXERCISES, GROUP III
182(1)
EXERCISES, GROUP IV
183(1)
13. Historical remarks
184(1)
14. Appendix: list of theorems of chapter III
185(2)
15. Appendix: solutions to selected exercises
187(10)
16. Appendix: summary of the system of logic developed in chapters I-III
197(4)
Chapter IV. 'ALL' and 'SOME', continued
201(62)
1. Terms and formulas
201(5)
EXERCISES
206(1)
2. Bondage and freedom
206(2)
EXERCISES
207(1)
3. Informal notational conventions
208(1)
EXERCISES
208(1)
4. Translation and symbolization
209(10)
EXERCISES, GROUP I
213(2)
EXERCISES, GROUP II
215(1)
EXERCISES, GROUP III
216(2)
EXERCISES, GROUP IV
218(1)
5. Revised inference rules
219(3)
EXERCISES, GROUP I
221(1)
EXERCISES, GROUP II
222(1)
EXERCISES, GROUP III
222(1)
6. Theorems
222(6)
EXERCISES
228(1)
7. Invalidity: truth-functional expansions and models
228(9)
EXERCISES
236(1)
8. Invalidity: false arithmetical translations
237(9)
EXERCISES, GROUP I
245(1)
EXERCISES, GROUP II
246(1)
9. Arguments of English
246(4)
EXERCISES, GROUP I
247(1)
EXERCISES, GROUP II
248(1)
EXERCISES, GROUP III
248(1)
EXERCISES, GROUP IV
249(1)
10. Historical remarks
250(1)
11. Appendix: list of theorems of chapter IV
250(1)
12. Appendix: solutions to selected exercises
251(12)
Chapter V. 'IS' (in one sense)
263(43)
1. Terms and formulas
263(1)
2. Translation and symbolization
264(5)
EXERCISES, GROUP I
267(1)
EXERCISES, GROUP II
268(1)
3. Inference rules
269(6)
EXERCISES
274(1)
4. Theorems
275(10)
EXERCISES, GROUP I
281(1)
EXERCISES, GROUP II
282(1)
EXERCISES, GROUP III
283(1)
EXERCISES, GROUP IV
284(1)
5. Invalidity
285(10)
EXERCISES, GROUP I
290(1)
EXERCISES, GROUP II
290(1)
EXERCISES, GROUP III
291(1)
EXERCISES, GROUP IV
291(1)
EXERCISES, GROUP V
292(1)
EXERCISES, GROUP VI
293(1)
EXERCISES, GROUP VII
294(1)
6. Historical remarks
295(1)
7. Appendix: list of theorems of chapter V
296(1)
8. Appendix: solutions to selected exercises
297(9)
Chapter VI. 'THE'
306(40)
1. Descriptive phrases, terms, formulas
306(5)
EXERCISES
311(1)
2. Bondage and freedom
311(3)
EXERCISES
313(1)
3. Informal notational conventions
314(1)
EXERCISES
314(1)
4. Translation and symbolization
315(3)
EXERCISES
317(1)
5. Inference rules
318(3)
EXERCISES
320(1)
6. Theorems
321(6)
EXERCISES
327(1)
7. Invalidity
327(12)
EXERCISES
337(2)
8. Arguments of English
339(2)
EXERCISES, GROUP I
340(1)
EXERCISES, GROUP II
340(1)
9. Historical remarks
341(1)
10. Appendix: list of theorems of chapter VI
342(1)
11. Appendix: solutions to selected exercises
343(3)
Chapter VII. ADDITIONAL DERIVATIONAL PROCEDURES
346(46)
1. Alphabetic variance
346(3)
EXERCISES
348(1)
2. Substitution
349(11)
EXERCISES
355(5)
3. Abbreviated derivations reconsidered; biconditional derivations
360(11)
EXERCISES
368(3)
4. Formulas without overlay and prenex normal form, again
371(4)
EXERCISES
373(2)
5. Abbreviated derivations justified; generalized principles of interchange
375(6)
EXERCISES
379(2)
6. Historical remarks
381(1)
7. Appendix: list of theorems of chapter VII
381(1)
8. Appendix: solutions to selected exercises
381(5)
9. Appendix: summary of the system of logic developed in chapters I-VII
386(6)
Chapter VIII. 'THE' again: A RUSSELLIAN THEORY OF DESCRIPTIONS
392(19)
1. The Fregean theory of chapter VI reconsidered
392(2)
EXERCISES
394(1)
2. A Russellian theory of descriptions
394(13)
EXERCISES
407(1)
3. Historical remarks
407(1)
4. Appendix: list of theorems of chapter VIII
408(1)
5. Appendix: solutions to selected exercises
409(1)
6. Appendix: summary of the Russellian system of logic developed in Chapter VIII
410(1)
Chapter IX. AUTOMATIC PROCEDURES
411(27)
1. Introduction
411(1)
2. Tautologies reconsidered
411(7)
EXERCISES
418(1)
3. Tautological implication; generalized indirect derivation
418(1)
4. A proof procedure for prenex formulas
419(6)
EXERCISES
424(1)
5. A derivation procedure for prenex arguments
425(2)
EXERCISES
426(1)
6. Conversion to prenex form
427(3)
EXERCISES
430(1)
7. A derivation procedure for arbitrary symbolic arguments
430(3)
EXERCISES
432(1)
8. A decision procedure for certain prenex formulas
433(2)
EXERCISES
435(1)
9. A decision procedure for certain prenex arguments
435(2)
EXERCISES
436(1)
10. Historical remarks
437(1)
Chapter X. DEFINITIONS: FORMAL THEORIES
438(37)
1. The vocabulary of formal languages
438(3)
2. Bondage and freedom; proper substitution; alphabetic variance
441(3)
3. Informal notational conventions
444(1)
4. Derivability
445(1)
5. Formal theories; the theory of commutative ordered fields
446(6)
6. Extensions of theories; the theory of real numbers
452(9)
7. Definitions
461(14)
Chapter XI. VARIABLE-BINDING OPERATORS
475(34)
1. Definitions reconsidered
475(2)
2. The theory of convergence
477(14)
3. A sketch of further developments
491(6)
4. Historical remarks
497(1)
5. Appendix: list of constants used in chapters X and XI
498(1)
6. Appendix: list of axioms, definitions, and theorems of chapters X and XI
499(10)
BIBLIOGRAPHY 509(6)
INDEX OF PROPER NAMES 515(2)
INDEX OF SUBJECTS 517

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