Preface |
|
xv | |
Chapter 1 Basic Concepts |
|
1 | (68) |
|
1.1 Validity and Soundness |
|
|
4 | (12) |
|
|
10 | (1) |
|
|
11 | (5) |
|
|
16 | (20) |
|
|
16 | (3) |
|
Understanding Conditional Statements |
|
|
19 | (1) |
|
|
20 | (7) |
|
|
27 | (1) |
|
Summary of Famous Valid Forms |
|
|
27 | (1) |
|
|
28 | (2) |
|
|
30 | (1) |
|
|
31 | (5) |
|
1.3 Counterexamples and Invalidity |
|
|
36 | (20) |
|
|
37 | (3) |
|
The Counterexample Method |
|
|
40 | (3) |
|
Categorical Statements and Arguments |
|
|
43 | (7) |
|
The Counterexample Method |
|
|
50 | (1) |
|
|
51 | (1) |
|
|
52 | (4) |
|
|
56 | (12) |
|
|
63 | (1) |
|
|
64 | (4) |
|
|
68 | (1) |
Chapter 2 Identifying Arguments |
|
69 | (48) |
|
2.1 Arguments and Nonarguments |
|
|
69 | (9) |
|
|
74 | (1) |
|
|
74 | (4) |
|
2.2 Well-Crafted Arguments |
|
|
78 | (27) |
|
Summary of Principles for Constructing Well-Crafted Arguments |
|
|
94 | (1) |
|
|
94 | (1) |
|
|
94 | (11) |
|
|
105 | (11) |
|
|
109 | (7) |
|
|
116 | (1) |
Chapter 3 Logic and Language |
|
117 | (42) |
|
3.1 Logic, Meaning, and Emotive Force |
|
|
117 | (9) |
|
|
123 | (1) |
|
|
124 | (2) |
|
|
126 | (19) |
|
Extensional and Intensional Definitions |
|
|
127 | (6) |
|
|
133 | (1) |
|
Definition by Genus and Difference |
|
|
134 | (6) |
|
Summary of Criteria for Evaluating Definitions by Genus and Difference |
|
|
140 | (1) |
|
|
140 | (1) |
|
|
141 | (4) |
|
3.3 Using Definitions to Evaluate Arguments |
|
|
145 | (12) |
|
|
151 | (1) |
|
|
151 | (6) |
|
|
157 | (2) |
Chapter 4 Informal Fallacies |
|
159 | (52) |
|
4.1 Fallacies of Irrelevance |
|
|
161 | (19) |
|
Argument Against the Person (Ad Hominem Fallacy) |
|
|
161 | (3) |
|
|
164 | (1) |
|
Appeal to Force (Ad Baculum Fallacy) |
|
|
165 | (2) |
|
Appeal to the People (Ad Populum Fallacy) |
|
|
167 | (1) |
|
Appeal to Pity (Ad Misericordiam Fallacy) |
|
|
168 | (1) |
|
Appeal to Ignorance (Ad lgnorantiam Fallacy) |
|
|
169 | (2) |
|
Red Herring (Ignoratio Elenchi Fallacy) |
|
|
171 | (2) |
|
|
173 | (1) |
|
|
174 | (6) |
|
4.2 Fallacies Involving Ambiguity |
|
|
180 | (11) |
|
|
180 | (2) |
|
|
182 | (2) |
|
|
184 | (2) |
|
|
186 | (2) |
|
|
188 | (1) |
|
|
188 | (3) |
|
4.3 Fallacies Involving Unwarranted Assumptions |
|
|
191 | (19) |
|
Begging the Question (Petitio Principii) |
|
|
192 | (2) |
|
|
194 | (2) |
|
Appeal to Unreliable Authority (Ad Verecundiam Fallacy) |
|
|
196 | (1) |
|
|
197 | (3) |
|
|
200 | (2) |
|
|
202 | (1) |
|
|
203 | (7) |
|
|
210 | (1) |
Chapter 5 Categorical Logic: Statements |
|
211 | (34) |
|
5.1 Introducing Categorical Statements |
|
|
211 | (10) |
|
Summary of Standard Forms |
|
|
214 | (4) |
|
Summary of Stylistic Variants |
|
|
218 | (1) |
|
|
218 | (1) |
|
|
219 | (2) |
|
5.2 The Traditional Square of Opposition |
|
|
221 | (10) |
|
|
227 | (1) |
|
|
227 | (4) |
|
5.3 Further Immediate Inferences |
|
|
231 | (14) |
|
|
231 | (2) |
|
|
233 | (1) |
|
|
233 | (4) |
|
Summary of Contraposition |
|
|
237 | (1) |
|
|
237 | (2) |
|
|
239 | (1) |
|
|
240 | (1) |
|
|
241 | (4) |
Chapter 6 Categorical Logic: Syllogisms |
|
245 | (66) |
|
6.1 Standard Form, Mood, and Figure |
|
|
245 | (10) |
|
|
251 | (1) |
|
|
252 | (3) |
|
6.2 Venn Diagrams and Categorical Statements |
|
|
255 | (10) |
|
Summary of Diagrams of Categorical Statements |
|
|
262 | (1) |
|
|
263 | (2) |
|
6.3 Venn Diagrams and Categorical Syllogisms |
|
|
265 | (8) |
|
|
270 | (3) |
|
6.4 The Modern Square of Opposition |
|
|
273 | (10) |
|
|
280 | (3) |
|
6.5 Rules for Evaluating Syllogisms |
|
|
283 | (9) |
|
Summary of Distributed Terms |
|
|
285 | (3) |
|
Summary of Rules for Determining the Validity of Categorical Syllogisms |
|
|
288 | (1) |
|
|
289 | (1) |
|
|
289 | (3) |
|
6.6 Reducing the Number of Terms |
|
|
292 | (5) |
|
Summary of Logical Equivalencies: Conversion, Contraposition, and Obversion |
|
|
295 | (1) |
|
|
296 | (1) |
|
|
297 | (8) |
|
Summary of Rules for Determining the Validity of Categorical Syllogisms |
|
|
298 | (5) |
|
|
303 | (2) |
|
|
305 | (5) |
|
|
308 | (2) |
|
|
310 | (1) |
Chapter 7 Statement Logic: Truth Tables |
|
311 | (74) |
|
7.1 Symbolizing English Arguments |
|
|
312 | (28) |
|
|
314 | (2) |
|
|
316 | (1) |
|
|
317 | (3) |
|
|
320 | (2) |
|
|
322 | (1) |
|
|
323 | (6) |
|
Symbol System for Statement Logic: A More Precise Formulation |
|
|
329 | (3) |
|
|
332 | (1) |
|
|
333 | (7) |
|
|
340 | (9) |
|
|
340 | (1) |
|
|
341 | (1) |
|
|
341 | (1) |
|
|
342 | (2) |
|
|
344 | (2) |
|
Summary of Truth Tables for the Five Compounds |
|
|
346 | (1) |
|
|
346 | (1) |
|
|
346 | (3) |
|
7.3 Using Truth Tables to Evaluate Arguments |
|
|
349 | (11) |
|
Remembering Truth Table Definitions for Compounds |
|
|
355 | (2) |
|
Summary of Truth-Table Method |
|
|
357 | (1) |
|
|
357 | (3) |
|
7.4 Abbreviated Truth Tables |
|
|
360 | (13) |
|
Summary of Abbreviated Truth Table-Method |
|
|
367 | (1) |
|
|
367 | (1) |
|
|
368 | (5) |
|
7.5 Logically Significant Categories and Relationships |
|
|
373 | (11) |
|
Tautology, Contradiction, and Contingency |
|
|
374 | (2) |
|
Equivalence, Contradictoriness, Consistency, and Inconsistency |
|
|
376 | (2) |
|
|
378 | (3) |
|
|
381 | (1) |
|
|
381 | (3) |
|
|
384 | (1) |
Chapter 8 Statement Logic: Proofs |
|
385 | (84) |
|
8.1 Implicational Rules of Inference |
|
|
385 | (25) |
|
Summary of lmplicational Rules |
|
|
399 | (1) |
|
|
400 | (1) |
|
|
400 | (10) |
|
8.2 Five Equivalence Rules |
|
|
410 | (16) |
|
Summary of the First Set of Equivalence Rules |
|
|
416 | (1) |
|
|
417 | (2) |
|
|
419 | (7) |
|
8.3 Five More Equivalence Rules |
|
|
426 | (13) |
|
Summary of the Second Set of Equivalence Rules |
|
|
430 | (1) |
|
|
431 | (8) |
|
|
439 | (11) |
|
|
445 | (1) |
|
|
445 | (5) |
|
|
450 | (12) |
|
Summary of Tips for Constructing Proofs |
|
|
453 | (2) |
|
|
455 | (7) |
|
|
462 | (5) |
|
|
466 | (1) |
|
|
466 | (1) |
|
|
467 | (2) |
Chapter 9 Predicate Logic |
|
469 | (94) |
|
9.1 The Language of Predicate Logic |
|
|
470 | (17) |
|
Predicates, Constants, and Variables |
|
|
470 | (1) |
|
|
471 | (3) |
|
The Existential Quantifier |
|
|
474 | (3) |
|
The Language of Predicate Logic: A More Precise Formulation |
|
|
477 | (3) |
|
Summary of Symbolizations |
|
|
480 | (2) |
|
|
482 | (1) |
|
|
482 | (5) |
|
9.2 Demonstrating Invalidity |
|
|
487 | (11) |
|
Summary of the Finite Universe Method |
|
|
495 | (1) |
|
|
495 | (1) |
|
|
496 | (2) |
|
|
498 | (22) |
|
|
500 | (2) |
|
Summary of Universal Instantiation (UI) |
|
|
502 | (1) |
|
Existential Generalization |
|
|
503 | (2) |
|
Summary of Existential Generalization (EG) |
|
|
505 | (1) |
|
Existential Instantiation |
|
|
505 | (3) |
|
Summary of Existential Instantiation (El) |
|
|
508 | (1) |
|
|
509 | (2) |
|
Summary of Universal Generalization (UG) |
|
|
511 | (1) |
|
|
512 | (8) |
|
9.4 Quantifier Negation, RAA, and CP |
|
|
520 | (10) |
|
Summary of Tips for Predicate Logic |
|
|
526 | (1) |
|
|
526 | (4) |
|
9.5 The Logic of Relations: Symbolizations |
|
|
530 | (10) |
|
Summary of Symbolizations |
|
|
533 | (2) |
|
|
535 | (1) |
|
|
535 | (5) |
|
9.6 The Logic of Relations: Proofs |
|
|
540 | (10) |
|
|
545 | (5) |
|
9.7 Identity: Symbolizations |
|
|
550 | (7) |
|
|
555 | (2) |
|
|
557 | (5) |
|
|
560 | (2) |
|
|
562 | (1) |
Chapter 10 Inductive Logic |
|
563 | (64) |
|
10.1 Inductive and Deductive Logic |
|
|
563 | (8) |
|
|
568 | (1) |
|
|
569 | (2) |
|
10.2 Ordinary Reasoning: Authority, Analogy, and Enumeration |
|
|
571 | (17) |
|
|
571 | (2) |
|
Summary of Arguments from Authority |
|
|
573 | (1) |
|
|
573 | (4) |
|
Summary of Arguments from Analogy |
|
|
577 | (1) |
|
|
577 | (4) |
|
Summary of Induction by Enumeration |
|
|
581 | (1) |
|
|
582 | (1) |
|
|
582 | (6) |
|
10.3 Scientific Reasoning: Mill's Methods |
|
|
588 | (15) |
|
|
588 | (4) |
|
|
592 | (5) |
|
|
597 | (1) |
|
|
598 | (5) |
|
10.4 Probabilistic Reasoning: The Rules of Probability |
|
|
603 | (21) |
|
|
603 | (8) |
|
|
611 | (5) |
|
Summary of the Rules of Probability |
|
|
616 | (1) |
|
|
617 | (1) |
|
|
617 | (7) |
|
|
624 | (3) |
Answer Key |
|
627 | (74) |
Glossary/Index |
|
701 | |