Sweet Reason : A Field Guide to Modern Logic

by Tymoczko, Thomas; Henle, James M.

• ISBN13: 9780387989303
• ISBN10: 0387989307
• Edition: 2nd
• Format: Paperback
• Copyright: 1999-08-01
• Publisher: Springer Verlag

Summary

Sweet Reasonis an introductory text for courses on modern logic unlike any other. The basic rudiments of formal and informal logical are here, all clearly described. Further, it focuses students on the real world, where the discipline of logic adds substance and meaning to all kinds of human discourse. Everything from puzzles, paradoxes, and mathematical proofs to campaign debate excerpts, government regulations, and cartoons are used to show how logic is put to work by philosophers, mathematicians, advertisers, computer scientists, politicians, and others. As the book alternately discusses, instructs, questions, teases, and challenges, readers will find themselves: 1) absorbing the fundamentals of the discipline, 2) becoming fluent in thte language of logic, 3) understanding how logic works in the real world, 4) enjoying logic's ability to entertain, surprise, subvert, and enlighten.

Table of Contents

Preface for the General Reader	xv
Preface for Logic Teachers: How to Use This Book in Logic Courses	xix
Introduction	1	(7)
Formal Logic with & about logic informal logic curiosities & puzzles
A Taste of Logic
Introducing the Language of Logic	8	(18)
paradox	17	(4)
negation	21	(3)
quiz	24	(2)
Everything all at Once and a Warning
Truth and Falsity	26	(5)
Logical form: The Key to Logic	31	(4)
Argument form: The Key to Reasoning	35	(41)
paradox and W. S. Gilbert	39	(2)
The Orb and Post	41	(1)
paradoxes and psychology	42	(2)
the title of the section on self-reference	44	(9)
how to argue	53	(6)
rebuttal	59	(5)
law boards: reading comprehension	64	(8)
The Digestor's Digest, page 1	72	(1)
exam warning I	73	(1)
talking heads	74	(2)
Statement Logic, Formal Languages, and Informal Arguments
Formal Languages: Sentential	76	(4)
Formal Languages: Variations on Sentential	80	(4)
Truth Tables	84	(6)
Logical Theory for Statement Logic	90	(3)
Some Basic Tautologies and Implications	93	(43)
buffalo buffalo buffalo	99	(1)
artificial and natural languages	100	(4)
rewrite rules and finite automata	104	(5)
loofah loofah loofah	109	(1)
conclusions	109	(6)
supporting statements	115	(4)
relevance	119	(5)
premises	124	(4)
Gathy has breakfast	128	(2)
The Digestor's Digest, page 2	130	(1)
exam warning II	131	(1)
a nonlogical puzzle	132	(1)
self-referential puzzles	132	(4)
Valid Arguments, Convincing Arguments, and Punk Logic
Valid Argument Forms	136	(2)
Formalizing for Validity	138	(4)
A Shortcut for Checking Arguments	142	(2)
Formalizing English	144	(40)
Miniac	153	(3)
flipism	156	(1)
sets	157	(5)
logic circuits	162	(2)
Betrand the First	164	(1)
criticizing arguments	165	(4)
writing arguments	169	(4)
a good paragraph	173	(3)
Gathy goes to war	176	(1)
The Digestor's Digest, page 3	177	(1)
exam warning III	178	(1)
the family reunion	179	(2)
punk logic	181	(3)
Predicates, Programs, and Antique Logic
Predicate Languages	184	(5)
Variations on the Theme of Predicate Languages	189	(4)
From Statement Logic to Predicate Logic	193	(3)
Interpreting Predicate Logic	196	(5)
Logical Theory for Predicate Logic	201	(3)
Logical Laws: Basic Valid Wffs and implications	204	(5)
Symbolization in Predicate Logic	209	(9)
Poles and Norwegians	218	(46)
games	220	(3)
Basic	223	(5)
binary	228	(3)
Trival	231	(2)
algorithm	233	(3)
the busy beaver	236	(2)
syllogisms	238	(3)
fallacies	241	(6)
rabbinic logic	247	(4)
Gathy meets god	251	(2)
The Digestor's Digest, page 4	253	(1)
exam warning IV	254	(1)
the game of logic	255	(3)
the sorites of Lewis Carroll	258	(6)
Deduction, Infinity, and A Haircut
Main Connectives	264	(2)
Deduction	266	(7)
Hypothetical Reasoning: Deduction from Assumptions	273	(6)
Proving Validity	279	(8)
Proving Invalidity	287	(5)
Formalizing for Validity in Predicate Logic	292	(42)
in Hell with Raymond Smullyan	294	(4)
no (certain) escape	298	(4)
infinite tasks	302	(4)
infinity potential and actual	306	(2)
proof by contradiction	308	(4)
Anita Hill and Arlen Specter	312	(4)
Bush, Clinton, and Perot	316	(5)
the adventure of the dancing men	321	(2)
commercial logic I	323	(1)
The Digestor's Digest, page 5	324	(1)
exam warning V	325	(1)
the barbershop problem	326	(3)
English 254	329	(5)
Symbolic Sophistication, Induction, and Business Logic
Quantifiers and Arithmetic	334	(3)
Functions	337	(6)
``The'': Russell's Theory of Definite Descriptions	343	(51)
measuring uncertainty	351	(3)
Bayes' law and Sherlock Holmes	354	(4)
inductive logic	358	(4)
logic programming	362	(9)
the W-4	371	(5)
Canadian customs	376	(1)
the logic tea	377	(6)
commercial logic II	383	(1)
The Digestor's Digest, page 6	384	(1)
exam warning VI	385	(2)
Lewis Carroll's ``what the tortoise said to Achilles''	387	(4)
the far side	391	(3)
Completeness, Disbelief, Debates, and Dinner
Geometry	394	(5)
The Completeness Theorem	399	(5)
Axiomatization and Boolean Algebra	404	(46)
Believing and knowing	411	(4)
the law of the excluded middle	415	(5)
from puzzle to paradox	420	(9)
more Bush, Clinton, and Perot	429	(6)
presidential debates	435	(4)
parliamentary debates	439	(2)
commercial logic III	441	(1)
The Digestor's Digest, page 7	442	(1)
exam warning VII	443	(1)
Peano's dots	444	(1)
Charles Dana Gibson	445	(1)
the family reunion II: the women	446	(4)
Paradox, Impossibility, and the Law
Where do Numbers Come From?	450	(8)
The Paradox of the Heap	458	(10)
Russell's Paradox and Frege's Mistake	468	(49)
life	474	(6)
hypergame	480	(1)
the busy beaver is not computable	481	(2)
impossibility	483	(3)
Quayle, Gore, and Stockdale	486	(5)
law boards: logical reasoning	491	(8)
law boards: analytical reasoning	499	(7)
law boards: rules and disputes	506	(7)
The Digestor's Digest, page 8	513	(1)
exam warning VIII	514	(1)
quiz on Polish notation	515	(1)
Tom and Jim's excellent adventure	516	(1)
The Last Word	517	(2)
NOTES, REFERENCES, HINTS, AND SOME ANSWERS
A Taste of Logic	519	(7)
Everything all at Once and a Warning	526	(5)
Statement Logic, Formal Languages, and Informal Arguments	531	(15)
Valid Arguments, Convincing Arguments, and Punk Logic	546	(16)
Predicates, Programs, and Antique Logic	562	(18)
Deduction, Infinity, and a Haircut	580	(21)
Symbolic Sophistication, Induction, and Business Logic	601	(12)
Completeness, Disbelief, Debates, and Dinner	613	(11)
Paradox, Impossibility, and the Law	624	(15)
Index	639