An Introduction to Foundational Logic

Contents
P reface
....................................................................................................
...................xiii
Introduction—What Is
Logic?.................................................................................. 1
Correct Thinking Is Directed
Thinking.................................................................1
What Is Foundational
Logic?.................................................................................2
Logic Is a
Science.............................................................................................
..... 3
The Special Mind-Set Required for the Study of Logic..................................... 4
Logic Is a Practical
Science....................................................................................5
Logic Is an A
rt..................................................................................................
......5
Logic and Truth
....................................................................................................
.. 6
Being Logical and Being “Logical”
......................................................................7
Formal and Material
Logic.....................................................................................7
Chapter O ne—The Sources of Logic: The Three Acts of the Intellect......... 9
The Approach Taken by This
Book.......................................................................9
The First Act of the Intellect: Simple Apprehension........................................... 9
The Genesis of
Ideas.............................................................................................
11
The Internal
Senses..............................................................................................
. 11
The Sense Image As the Product of External and Internal Sensation................13
The Distinction Between Sense Images and Intellectual Images....................... 14
The Relation Between Sense Knowledge and Intellectual Knowledge............. 15
The Idea As
Means...............................................................................................
16
The Second Act of the Intellect: Judgment.........................................................
18
Composition and
Division................................................................................... 19
Propositions and Truth and
Falsity...................................................................... 20
The Third Act of the Intellect:
Reasoning...........................................................21
Inference...........................................................................................
.....................21
Reasoning and
Argument.....................................................................................22
Review Item
s...................................................................................................
...... 23
Exercises...........................................................................................
.....................23
Chapter Two—Ideas and Their
Expression..........................................................25
Distinctions........................................................................................
................... 2^
The T hing
....................................................................................................
..........27
The Idea
....................................................................................................
............ 2^
The
Word................................................................................................
..............
The Idea As
Universal.........................................................................................


VI C o n t e n t s
In What Sense Are Universals
Real?......................................................................30
Signs...............................................................................................
............................ 31
Natural Signs and Conventional Sign s
.................................................................. 31
Instrumental Signs and Formal
Signs.................................................................... 33
The Interpretation of
Signs..................................................................................... 34
Terms...............................................................................................
........................... 36
The Comprehension and Extension of Terms....................................................... 36
The
Predicables.........................................................................................
................38
Review Item
s...................................................................................................
.......... 41
Exercises...........................................................................................
......................... 42
Chapter Three—The Varieties of
Ideas...................................................................43
Complexity in
Ideas...............................................................................................
.. 43
Concrete and Abstract
Ideas....................................................................................44
Singular Terms and General
Terms....................................................................... 45
Uni vocal, Equivocal, and Analogous Terms........................................................47
The Analogy of
Attribution....................................................................................50
Metaphor............................................................................................
........................ 51
The Opposition of
Terms......................................................................................... 52
Sound and Unsound
Ideas....................................................................................... 55
Creative
Ideas...............................................................................................
............ 58
Review Item
s...................................................................................................
.......... 59
Exercises...........................................................................................
......................... 60
Chapter Four—The C
ategories................................................................................. 61
What Are the
Categories?........................................................................................6
1
Primary Substance and Secondary Substance.......................................................63
The General Nature of
Accident............................................................................. 65
The Accident of
Quantity....................................................................................... 65
The Accident of
Quality......................................................................................... 67
Action and
Passivity...........................................................................................
..... 73
Time and P lace
....................................................................................................
..... 74
Position and
Habit...............................................................................................
.... 76
Summary Comments on the Accidents.................................................................
76
Review Item
s...................................................................................................
.......... 77
Exercises...........................................................................................
.........................78
Chapter Five—Definition and Division
.................................................................. 79
The Need for Clarity in
Ideas................................................................................ 79
Definition and Division
.......................................................................................... 80
Essential
Definition..........................................................................................
.......80
The Rules for Essential
Definition........................................................................84
The Difficulties with Essential
Definition........................................................... 86
The Limitations of Essential
Definition............................................................... 87
Descriptive
Definition..........................................................................................
.. 89
Descriptive Definition by
Property.......................................................................90
Descriptive Definition by
Accident.......................................................................90
Descriptive Definition by
Cause........................................................................... 91
Descriptive Definition by Nam
e........................................................................... 92
Descriptive Definition by
Narration..................................................................... 93


C o n t e n t s vii




Division
....................................................................................................
.............. 93
Physical Division or
Partition.............................................................................. 94
Logical
Division............................................................................................
.........95
The Rules for Logical
Division............................................................................96
Classification......................................................................................
................... 100
Review Item
s...................................................................................................
....... 101
Exercises...........................................................................................
...................... 101
Chapter
Six—Judgment........................................................................................
.... 103
The Second Act of the
Intellect............................................................................ 103
Predication.........................................................................................
......................104
The First Principles of All Human Reasoning................................................... 105
The Principle of
Identity........................................................................................107
The Principle of
Contradiction............................................................................. 107
The Principle of Excluded
Middle....................................................................... 108
The Principle of Sufficient
Reason...................................................................... 109
The Categorical
Proposition.................................................................................109
The Anatomy of a
Proposition............................................................................. 110
The Logical Form of
Propositions....................................................................... 112
The Quantity of
Propositions............................................................................... 113
The Quality of
Propositions..................................................................................116
Modal
Propositions........................................................................................
....... 116
The Distribution of Terms in Propositions........................................................
119
Diagraming
Propositions......................................................................................12
1
Propositions Are Either True or
False................................................................ 122
The Correspondence Criterion of
Truth.............................................................123
The Coherence Criterion of
Truth...................................................................... 124
Propositional Truth Is Absolute
Truth............................................................... 124
Review Item
s...................................................................................................
.......126
Exercises...........................................................................................
......................127
Chapter Seven—The Varieties of Propositions.................................................
128
Complex
Propositions........................................................................................
.. 128
Compound
Propositions.......................................................................................1
29
Inference,
Again...............................................................................................
..... 130
Conjunctive
Propositions.....................................................................................130

Disjunctive
Propositions......................................................................................13
2
Inferences To Be Drawn from Conjunctive and Disjunctive Propositions.....134
Truth
Tables..............................................................................................
.............136
The Obversion of
Propositions............................................................................138
The Conversion of
Propositions..........................................................................140
Review Item
s...................................................................................................
...... 144
Exercises...........................................................................................
..................... 144
Chapter Eight—Further Explorations in Immediate Inference.....................146
The Interrelations Among General Propositions............................................. 146
Shorthand Ways of Expressing General Propositions..................................... 147
The Opposition of
Propositions......................................................................... 148
Contradictory
Opposition....................................................................................149
Contrary Opposition...............................................................................
..............152


viii

C o n t e n t s



Subcontrary
Opposition.........................................................................................
155
Subalternation......................................................................................
....................156
Summary of Possible Inferences Among General Propositions....................... 158
The Square of
Opposition..................................................................................... 159
Other Forms of Immediate
Inference...................................................................164
Review Item
s...................................................................................................
........ 166
Exercises...........................................................................................
....................... 166
Chapter
Nine—Reasoning......................................................................................
...168
The Third Act of the
Intellect................................................................................ 168
Reasoning and
Argument.......................................................................................169
Complexity in
Argument........................................................................................171
Deductive
Reasoning...........................................................................................
.. 174
Mediate
Reasoning...........................................................................................
..... 177
Syllogistic
Reasoning...........................................................................................
178
Validity and
Truth...............................................................................................
.. 179
The Anatomy of a Syllogism
................................................................................180
The Essence of Syllogistic
Reasoning................................................................ 182
The Principle of the Identifying
Third................................................................ 184
The Principle of the Separating
Third................................................................. 185
The Dictum de Omni
Principle.............................................................................. 187
The Dictum de Nullo
Principle.............................................................................. 187
Diagraming Syllogism
s........................................................................................ 188
Review Item
s...................................................................................................
........190
Exercises...........................................................................................
...................... 191
Chapter Ten—The Figures and Moods of the Syllogism................................ 192
The Categorical Syllogism
................................................................................... 192
The Figure of a Syllogism
.................................................................................... 193
The Mood of a Syllogism
.....................................................................................194
The Darii and Ferio Moods of the First Figure ..................................................197
The Potency and Versatility of First Figure Syllogism s..................................199
Are There Only Four Valid Moods in the First Figure?...................................200
The Valid Moods of the Second Figure: Cesare and Camestres...................... 201
The Valid Moods of the Second Figure: Baroco and Festino........................... 205
The Valid Moods of the Third Figure: Darapti, Datisi, Disamis..................... 207
The Valid Moods of the Third Figure: Bocardo, Felapton, Ferison.................209
The Controversial Fourth Figure
........................................................................ 211
Reducing Imperfect Syllogisms to the First Figure.......................................... 213
Categorical Syllogisms Containing Non-Factual Propositions....................... 215
Review
....................................................................................................
................ 216
Exercises...........................................................................................
..................... 217
Chapter Eleven—The Rules of the Syllogism................................................... 219
Determining Validity by Figure and M ood...................................................... 219
The Rules of the Syllogism
.................................................................................220
The Rule Governing the Number of Terms....................................................... 221
The Problem of Equivocation in Argument...................................................... 222
The Rule Governing the Extreme Terms...........................................................225
The Problem of the Illicit
Minor........................................................................ 226


C o n t e n t s IX
The Problem of the Illicit
Major.........................................................................227
The Rule Governing the Middle Term...............................................................
228
Guilt by
Association.........................................................................................
.....229
The Rule Governing Negative Premisses...........................................................
231
The Rule Governing Particular Premisses..........................................................
232
The Rule Governing Weaknesses in Premisses.................................................235
Summary of the Rules of the Syllogism ............................................................
236
False Premisses and a True Conclusion?...........................................................
237
Review
....................................................................................................
............... 240
Exercises...........................................................................................
.................... 240
Chapter Twelve—Variations oh Syllogistic Reasoning;
Making
Arguments........................................................................................
244
Polysyllogisms......................................................................................
...............244
The Advantages and Disadvantages of Polysyllogistic Argument................. 245
The Rules of the Polysyllogism
...........................................................................246
The Logical Limitations of Polysyllogistic Reasoning................................... 247
Sorites.............................................................................................
...................... 249
The Rules of the Sorites
Argument................................................................... 250
Enthymemes..........................................................................................
............... 252
The Ways in Which Syllogisms Are Commonly Abbreviated....................... 253
Responding to
Enthymemes.............................................................................. 254
Making an Argument: the Conclusion................................................................
257
Making an Argument: The Premisses.................................................................
260
A Psychological N
ote............................................................................................ 264
Review Item
s...................................................................................................
........265
Exercises...........................................................................................
...................... 266
Chapter Thirteen—Conditional
Reasoning..........................................................269
The Conditional Way of
Thinking...................................................................... 269
Hypothetical
Argument........................................................................................
270
The Anatomy of the Hypothetical Syllogism .....................................................271
The Pure Hypothetical Syllogism
........................................................................273
The Mixed Hypothetical Syllogism:Modus Ponens........................................ 275
The Mixed Hypothetical SyllogismrAforfws Tollens............................... 276
Affirming the
Consequent.................................................................................... 277
A Reciprocal Relation Between Antecedent and Consequent.......................... 279
Denying the
Antecedent.......................................................................................
280
The Relation Between Categorical Syllogisms and
Hypothetical Syllogism
s...................................................................................282
The Dilemma Argument: Modus Ponens............................................................283
The Dilemma Argument: Modus Tollens............................................................285
Probable Hypothetical
Arguments....................................................................... 287
Review
....................................................................................................
.................290
Exercises...........................................................................................
...................... 291
Chapter Fourteen—Inductive Reasoning.............................................................
294
Deduction and
Induction...................................................................................... 294
Where Inductive Reasoning
Begins....................................................................295
The Uniformity of Nature .......................................................
296


X C o n t e n t s
Inductive Reasoning as Ordered to the Discovery of Causes........................... 299
Scientific
Method..............................................................................................
...... 302
Observation and
Experiment.................................................................................303
Forming
Hypotheses..........................................................................................
.... 305
Testing
Hypotheses..........................................................................................
....... 307
From Hypotheses to
Laws..................................................................................... 309
The Canons of
Induction.......................................................................................
310
Inductive Reasoning as Ordered to the Confirmation of Properties................313
Opinion P olls .............................................................
317
Inductive Reasoning and the Social Sciences.....................................................
318
Argument by
Analogy............................................................................................
320
Review Item
s...................................................................................................
.........322
Exercises...........................................................................................
....................... 322
Chapter Fifteen—Fallacious
Reasoning.................................................................325
What Is Fallacious
Reasoning?............................................................................ 325
Why Study Fallacious
Reasoning?.......................................................................327
Formal and Informal
Fallacies.............................................................................. 327
General Review of the Formal
Fallacies.............................................................. 328
Fallacies Related to
Language.............................................................................. 329
Begging the
Question............................................................................................
. 332
Missing the
Point...............................................................................................
..... 333
Straw M an
....................................................................................................
............334
Hasty
Conclusion..........................................................................................
..........335
Sweeping
Generalization......................................................................................
. 337
False
Dilemma.............................................................................................
........... 337
Fallacy of
Composition.........................................................................................
339
The Appeal to
Ignorance.......................................................................................340
Improper Appeal to
Authority.............................................................................. 340
Two Wrongs Make a
Right................................................................................... 342
The End Justifies the M
eans................................................................................. 343
Tu
Quoque..............................................................................................
................. 344
Ad
Hominem.............................................................................................
............... 345
The Genetic
Fallacy.............................................................................................
...346
Simplistic
Reductionism........................................................................................
347
Special
Pleading............................................................................................
......... 348
Dismissive
Ridicule............................................................................................
....349
Red
Herring.............................................................................................
................ 350
Ad Populum
....................................................................................................
......... 351
Ad Misericordiam
..................................................................................................
352
Ad Baculum
....................................................................................................
.........352
The Last Word:
Truth............................................................................................
353
Review Item
s...................................................................................................
........354
Exercises...........................................................................................
.......................354
A
ppendices...........................................................................................
.........................359
Chapter O n e
....................................................................................................
........ 359
Chapter T w o
....................................................................................................
........ 362
Chapter
Three...............................................................................................
.......... 367

C o n t e n t s
XI
Chapter
Four................................................................................................
...........370
Chapter
Five................................................................................................
............374
Chapter S ix
....................................................................................................
..........375
Chapter Seven
....................................................................................................
.....377
Chapter
Eight...............................................................................................
...........381
Chapter N ine
....................................................................................................
.......382
ChapterTen..........................................................................................
...................385
Chapter Eleven
....................................................................................................
... 390
ChapterTwelve.......................................................................................
............... 391
Chapter
Thirteen............................................................................................
........ 395
Chapter
Fourteen............................................................................................
........ 396
Chapter
Fifteen.............................................................................................
.......... 399
N o te s
....................................................................................................
.......................... 403
Bibliography........................................................................................
..........................405
In d e x
....................................................................................................
.......................... 411