Chapter II: Preface: v

CHAPTER I

INTRODUCTORY

Sec.1. Definition of Logic 1 Sec.2. General character of proof 2 Sec.3. Division of the subject 5 Sec.4. Uses of Logic 6 Sec.5. Relation of Logic to other sciences 8 to Mathematics (p. 8); to concrete Sciences (p. 10); to Metaphysics (p. 10); to regulative sciences (p. 11) Sec.6. Schools of Logicians 11 Relation to Psychology (p. 13)

CHAPTER II

GENERAL ANALYSIS OF PROPOSITIONS

Sec.1. Propositions and Sentences 16 Sec.2. Subject, Predicate and Copula 17 Sec.3. Compound Propositions 17 Sec.4. Import of Propositions 19 Sec.5. Form and Matter 22 Sec.6. Formal and Material Logic 23 Sec.7. Symbols used in Logic 24

CHAPTER III

OF TERMS AND THEIR DENOTATION

Sec.1. Some Account of Language necessary 27 Sec.2. Logic, Grammar and Rhetoric 28 Sec.3. Words are Categorematic or Syncategorematic 29 Sec.4. Terms Concrete or Abstract 30 Sec.5. Concrete Terms, Singular, General or Collective 33

CHAPTER IV

THE CONNOTATION OF TERMS

Sec.1. Connotation of General Names 37 Sec.2. Question of Proper Names 38 other Singular Names (p. 40) Sec.3. Question of Abstract Terms 40 Sec.4. Univocal and Equivocal Terms 41 Connotation determined by the _suppositio_ (p. 43) Sec.5. Absolute and Relative Terms 43 Sec.6. Relation of Denotation to Connotation 46 Sec.7. Contradictory Terms 47 Sec.8. Positive and Negative Terms 50 Infinites; Privitives; Contraries (pp. 50-51)

CHAPTER V

CLASSIFICATION OF PROPOSITIONS

Sec.1. As to Quantity 53 Quantity of the Predicate (p. 56) Sec.2. As to Quality 57 Infinite Propositions (p. 57) Sec.3. A. I. E. O. 58 Sec.4. As to Relation 59 Change of Relation (p. 60); Interpretation of 'either, or' (p. 63); Function of the hypothetical form (p. 64) Sec.5. As to Modality 66 Sec.6. Verbal and Real Propositions 67

CHAPTER VI

CONDITIONS OF IMMEDIATE INFERENCE

Sec.1. Meaning of Inference 69 Sec.2. Immediate and Mediate Inference 70 Sec.3. The Laws of Thought 72 Sec.4. Identity 73 Sec.5. Contradiction and Excluded Middle 74 Sec.6. The Scope of Formal Inference 76

CHAPTER VII

IMMEDIATE INFERENCES

Sec.1. Plan of the Chapter 79 Sec.2. Subalternation 79 Sec.3. Connotative Subalternation 80 Sec.4. Conversion 82 Reciprocality (p. 84) Sec.5. Obversion 85 Sec.6. Contrary Opposition 87 Sec.7. Contradictory Opposition 87 Sec.8. Sub-contrary Opposition 88 Sec.9. The Square of Opposition 89 Sec.10. Secondary modes of Immediate Inference 90 Sec.11. Immediate Inferences from Conditionals 93

CHAPTER VIII

ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT OF PROPOSITIONS

Sec.1. Order of Terms in a proposition 95 Sec.2. Euler's Diagrams 97 Sec.3. Propositions considered as Equations 101 Sec.4. Existential Import of Propositions 104

CHAPTER IX

FORMAL CONDITIONS OF MEDIATE INFERENCE

Sec.1. Nature of Mediate Inference and Syllogism 107
Sec.2. General Canons of the Syllogism 108
Definitions of Categorical Syllogism; Middle Term;
Minor Term; Major Term; Minor and Major Premise (p. 109)
Illicit Process (p. 110);
Distribution of the Middle (p. 110);
Negative Premises (p. 112);
Particular Premises (p. 113)
Sec.3. _Dictum de omni et nullo_ 115
Sec.4. Syllogism in relation to the Laws of Thought 116
Sec.5. Other Kinds of Mediate Inference 118

CHAPTER X

CATEGORICAL SYLLOGISMS

Sec.1. Illustrations of the Syllogism 121 Sec.2. Of Figures 122 Sec.3. Of Moods 123 Sec.4. How valid Moods are determined 124 Sec.5. Special Canons of the Four Figures 126 Sec.6. Ostensive Reduction and the Mnemonic Verses 127 Sec.7. Another version of the Mnemonic Verses 132 Sec.8. Indirect Reduction 132 Sec.9. Uses of the several Figures 134 Sec.10. Scientific Value of Reduction 135 Sec.11. Euler's Diagrams for the Syllogism 136

CHAPTER XI

ABBREVIATED AND COMPOUND ARGUMENTS

Sec.1. Popular Arguments Informal 138 Sec.2. The Enthymeme 139 Sec.3. Monosyllogism, Polysyllogism, Prosyllogism, Episyllogism 141 Sec.4. The Epicheirema 142 Sec.5. The Sorites 142 Sec.6. The Antinomy 145

CHAPTER XII

CONDITIONAL SYLLOGISMS

Sec.1. The Hypothetical Syllogism 147 Sec.2. The Disjunctive Syllogism 152 Sec.3. The Dilemma 154

CHAPTER XIII

TRANSITION TO INDUCTION

Sec.1. Formal Consistency and Material Truth 159 Sec.2. Real General Propositions assert more than has been directly observed 160 Sec.3. Hence, formally, a Syllogism's Premises seem to beg the Conclusion 162 Sec.4. Materially, a Syllogism turns upon the resemblance of the Minor to the Middle Term; and thus extends the Major Premise to new cases 163 Sec.5. Restatement of the _Dictum_ for material reasoning 165 Sec.6. Uses of the Syllogism 167 Sec.7. Analysis of the Uniformity of Nature, considered as the formal ground of all reasoning 169 Sec.8. Grounds of our belief in Uniformity 173

CHAPTER XIV

CAUSATION

Sec.1. The most important aspect of Uniformity in relation to Induction is Causation 174 Sec.2. Definition of "Cause" explained: five marks of Causation 175 Sec.3. How strictly the conception of Cause can be applied depends upon the subject under investigation 183 Sec.4. Scientific conception of Effect. Plurality of Causes 185 Sec.5. Some condition, but not the whole cause, may long precede the Effect; and some co-effect, but not the whole effect, may long survive the Cause 187 Sec.6. Mechanical Causes and the homogeneous Intermixture of Effects; Chemical Causes and the heteropathic Intermixture of Effects 188 Sec.7. Tendency, Resultant, Counteraction, Elimination, Resolution, Analysis, Reciprocity 189

CHAPTER XV

INDUCTIVE METHOD

Sec.1. Outline of Inductive investigation 192 Sec.2. Induction defined 196 Sec.3. "Perfect Induction" 196 Sec.4. Imperfect Induction methodical or immethodical 197 Sec.5. Observation and Experiment, the material ground of Induction, compared 198 Sec.6. The principle of Causation is the formal ground of Induction 201 Sec.7. The Inductive Canons are derived from the principle of Causation, the more readily to detect it in facts observed 202

CHAPTER XVI

THE CANONS OF DIRECT INDUCTION

Sec.1. The Canon of Agreement 206
Negative Instances (p. 208);
Plurality of Causes (p. 208)
Agreement may show connection without direct Causation (p. 209)
Sec.2. The Canon of Agreement in Presence and in Absence 212
It tends to disprove a Plurality of Causes (p. 213)
Sec.3. The Canon of Difference 216
May be applied to observations (p. 221)
Sec.4. The Canon of Variations 222
How related to Agreement and Difference (p. 222);
The Graphic Method (p. 227);
Critical points (p. 230);
Progressive effects (p. 231);
Gradations (p. 231)
Sec.5. The Canon of Residues 232

CHAPTER XVII

COMBINATION OF INDUCTION WITH DEDUCTION

Sec.1. Deductive character of Formal Induction 236 Sec.2. Further complication of Deduction with Induction 238 Sec.3. The Direct Deductive (or Physical) Method 240 Sec.4. Opportunities of Error in the Physical Method 243 Sec.5. The Inverse Deductive (or Historical) Method 246 Sec.6. Precautions in using the Historical Method 251 Sec.7. The Comparative Method 255 Sec.8. Historical Evidence 261

CHAPTER XVIII

HYPOTHESES

Sec.1. Hypothesis defined and distinguished from Theory 266
Sec.2. An Hypothesis must be verifiable 268
Sec.3. Proof of Hypotheses 270
(1) Must an hypothetical agent be directly observable? (p. 270);
_Vera causa_ (p. 271)
(2) An Hypothesis must be adequate to its pretensions (p. 272);
_Exceptio probat regulam_ (p. 274)
(3) Every competing Hypothesis must be excluded (p. 275);
Crucial instance (p. 277)
(4) Hypotheses must agree with the laws of Nature (p. 279)
Sec.4. Hypotheses necessary in scientific investigation 280
Sec.5. The Method of Abstractions 283
Method of Limits (p. 284);
In what sense all knowledge is hypothetical (p. 286)

CHAPTER XIX

LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY

Sec.1. Axioms; Primary Laws; Secondary Laws, Derivative or Empirical;
Facts 288
Sec.2. Secondary Laws either Invariable or Approximate Generalisations 292
Sec.3. Secondary Laws trustworthy only in 'Adjacent Cases' 293
Sec.4. Secondary Laws of Succession or of Co-existence 295
Natural Kinds (p. 296);
Co-existence of concrete things to be deduced from
Causation (p. 297)
Sec.5. Explanation consists in tracing resemblance, especially
of Causation 299
Sec.6. Three modes of Explanation 302
Analysis (p. 302);
Concatenation (p. 302);
Subsumption (p. 303)
Sec.7. Limits of Explanation 305
Sec.8. Analogy 307

CHAPTER XX

PROBABILITY

Sec.1. Meaning of Chance and Probability 310 Sec.2. Probability as a fraction or proportion 312 Sec.3. Probability depends upon experience and statistics 313 Sec.4. It is a kind of Induction, and pre-supposes Causation 315 Sec.5. Of Averages and the Law of Error 318 Sec.6. Interpretation of probabilities 324 Personal Equation (p. 325); meaning of 'Expectation' (p. 325) Sec.7. Rules of the combination of Probabilities 325 Detection of a hidden Cause (p. 326); oral tradition (p. 327); circumstantial and analogical evidence (p. 328)

CHAPTER XXI

DIVISION AND CLASSIFICATION

Sec.1. Classification, scientific, special and popular 330 Sec.2. Uses of classification 332 Sec.3. Classification, Deductive and Inductive 334 Sec.4. Division, or Deductive Classification: its Rules 335 Sec.5. Rules for testing a Division 337 Sec.6. Inductive Classification 339 Sec.7. Difficulty of Natural Classification 341 Sec.8. Darwin's influence on the theory of Classification 342 Sec.9. Classification of Inorganic Bodies also dependent on Causation 346

CHAPTER XXII

NOMENCLATURE, DEFINITION, PREDICABLES

Sec.1. Precise thinking needs precise language 348 Sec.2. Nomenclature and Terminology 349 Sec.3. Definition 352 Sec.4. Rules for testing a Definition 352 Sec.5. Every Definition is relative to a Classification 353 Sec.6. Difficulties of Definition 356 Proposals to substitute the Type (p. 356) Sec.7. The Limits of Definition 357 Sec.8. The five Predicables 358 Porphyry's Tree (p. 361) Sec.9. Realism and Nominalism 364 Sec.10. The Predicaments 366

CHAPTER XXIII

DEFINITION OF COMMON TERMS

Sec.1. The rigour of scientific method must be qualified 369 Sec.2. Still, Language comprises the Nomenclature of an imperfect Classification, to which every Definition is relative; 370 Sec.3. and an imperfect Terminology 374 Sec.4. Maxims and precautions of Definition 375 Sec.5. Words of common language in scientific use 378 Sec.6. How Definitions affect the cogency of arguments 380

CHAPTER XXIV

FALLACIES

Sec.1. Fallacy defined and divided 385 Sec.2. Formal Fallacies of Deduction 385 Sec.3. Formal Fallacies of Induction 388 Sec.4. Material Fallacies classified 394 Sec.5. Fallacies of Observation 394 Sec.6. Begging the Question 396 Sec.7. Surreptitious Conclusion 398 Sec.8. Ambiguity 400 Sec.9. Fallacies, a natural rank growth of the Human mind, not easy to classify, or exterminate 403

QUESTIONS 405

LOGIC