Logic | Page 3

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
§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
§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
§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
§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
§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
§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
§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
§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
§ 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