Logic: Deductive and Inductive

CHAPTER IV. The Connotation of Terms

THE CONNOTATION OF TERMS

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

CHAPTER V. Classification of Propositions

CLASSIFICATION OF PROPOSITIONS

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

CHAPTER VI. Conditions of Immediate Inference

CONDITIONS OF IMMEDIATE INFERENCE

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

CHAPTER VII. Immediate Inferences

IMMEDIATE INFERENCES

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

CHAPTER VIII. Order of Terms, Euler's Diagrams, Logical Equations,

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

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

CHAPTER IX. Formal Conditions of Mediate Inference

FORMAL CONDITIONS OF MEDIATE INFERENCE

§1. Nature of Mediate Inference and Syllogism 107 §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) §3. Dictum de omni et nullo 115 §4. Syllogism in relation to the Laws of Thought 116 §5. Other Kinds of Mediate Inference 118

CHAPTER X. Categorical Syllogisms

CATEGORICAL SYLLOGISMS

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

CHAPTER XI. Abbreviated and Compound Arguments

ABBREVIATED AND COMPOUND ARGUMENTS

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

CHAPTER XII. Conditional Syllogisms

CONDITIONAL SYLLOGISMS

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

CHAPTER XIII

TRANSITION TO INDUCTION

§1. Formal Consistency and Material Truth 159 §2. Real General Propositions assert more than has been directly observed 160 §3. Hence, formally, a Syllogism's Premises seem to beg the Conclusion 162 §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 §5. Restatement of the Dictum for material reasoning 165 §6. Uses of the Syllogism 167 §7. Analysis of the Uniformity of Nature, considered as the formal ground of all reasoning 169 §8. Grounds of our belief in Uniformity 173

CHAPTER XIV. Causation

CAUSATION

§1. The most important aspect of Uniformity in relation to Induction is Causation 174 §2. Definition of "Cause" explained: five marks of Causation 175 §3. How strictly the conception of Cause can be applied depends upon the subject under investigation 183 §4. Scientific conception of Effect. Plurality of Causes 185 §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 §6. Mechanical Causes and the homogeneous Intermixture of Effects; Chemical Causes and the heteropathic Intermixture of Effects 188 §7. Tendency, Resultant, Counteraction, Elimination, Resolution, Analysis, Reciprocity 189

CHAPTER XV. Inductive Method

INDUCTIVE METHOD

§1. Outline of Inductive investigation 192 §2. Induction defined 196 §3. "Perfect Induction" 196 §4. Imperfect Induction methodical or immethodical 197 §5. Observation and Experiment, the material ground of Induction, compared 198 §6. The principle of Causation is the formal ground of Induction 201 §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

THE CANONS OF DIRECT INDUCTION

§1. The Canon of Agreement 206 Negative Instances (p. 208); Plurality of Causes (p. 208) Agreement may show connection without direct Causation (p. 209) §2. The Canon of Agreement in Presence and in Absence 212 It tends to disprove a Plurality of Causes (p. 213) §3. The Canon of Difference 216 May be applied to observations (p. 221) §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) §5. The Canon of Residues 232

CHAPTER XVII. Combination of Induction With Deduction

COMBINATION OF INDUCTION WITH DEDUCTION

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

CHAPTER XVIII. Hypotheses

HYPOTHESES

§1. Hypothesis defined and distinguished from Theory 266 §2. An Hypothesis must be verifiable 268 §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) §4. Hypotheses necessary in scientific investigation 280 §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

LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY

§1. Axioms; Primary Laws; Secondary Laws, Derivative or Empirical; Facts 288 §2. Secondary Laws either Invariable or Approximate Generalisations 292 §3. Secondary Laws trustworthy only in 'Adjacent Cases' 293 §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) §5. Explanation consists in tracing resemblance, especially of Causation 299 §6. Three modes of Explanation 302 Analysis (p. 302); Concatenation (p. 302); Subsumption (p. 303) §7. Limits of Explanation 305 §8. Analogy 307

CHAPTER XX. Probability

PROBABILITY

§1. Meaning of Chance and Probability 310 §2. Probability as a fraction or proportion 312 §3. Probability depends upon experience and statistics 313 §4. It is a kind of Induction, and pre-supposes Causation 315 §5. Of Averages and the Law of Error 318 §6. Interpretation of probabilities 324 Personal Equation (p. 325); meaning of 'Expectation' (p. 325) §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

DIVISION AND CLASSIFICATION

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

CHAPTER XXII. Nomenclature, Definition, Predicables

NOMENCLATURE, DEFINITION, PREDICABLES

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

CHAPTER XXIII. Definition of Common Terms

DEFINITION OF COMMON TERMS

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

CHAPTER XXIV. Fallacies

FALLACIES

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

QUESTIONS 405

LOGIC

CHAPTER I. Introductory

INTRODUCTORY

§ 1. Logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved, if it admits of proof. Not, indeed, every such proposition; for as to those that declare the equality or inequality of numbers or other magnitudes, to explain the conditions of their proof belongs to Mathematics: they are said to be quantitative. But as to all other propositions, called qualitative, like most of those that we meet with in conversation, in literature, in politics, and even in sciences so far as they are not treated mathematically (say, Botany and Psychology); propositions that merely tell us that something happens (as that salt dissolves in water), or that something has a certain property (as that ice is cold): as to these, it belongs to Logic to show how we may judge whether they are true, or false, or doubtful. When propositions are expressed with the universality and definiteness that belong to scientific statements, they are called laws; and laws, so far as they are not laws of quantity, are tested by the principles of Logic, if they at all admit of proof.

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