Logic | Page 3

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 far as they are not laws of quantity, are tested by the principles of Logic, if they at all admit of proof.
But it is plain that the process of proving cannot go on for ever; something must be taken for granted; and this is usually considered to be the case (1) with particular facts that can only be perceived and observed, and (2) with those highest laws that are called 'axioms' or 'first principles,' of which we can only say that we know of no exceptions to them, that we cannot help believing them, and that they are indispensable to science and to consistent thought. Logic, then, may