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LOGIC

DEDUCTIVE AND INDUCTIVE


First Edition, June 1898. (Grant Richards.)
Second Edition, November 1901. (Grant Richards.)
Third Edition, January 1906. (A. Moring Ltd.)
Reprinted, January 1908. (A. Moring Ltd.)
Reprinted, May 1909. (A. Moring Ltd.)
Reprinted, July 1910. (A. Moring Ltd.)
Reprinted, September 1911. (A. Moring Ltd.)
Reprinted, November 1912. (A. Moring Ltd.)
Reprinted, April 1913. (A. Moring Ltd.)
Reprinted, May 1920. (Simpkin.)


LOGIC

DEDUCTIVE AND INDUCTIVE


BY

CARVETH READ, M.A.


AUTHOR OF

"THE METAPHYSICS OF NATURE"

"NATURAL AND SOCIAL MORALS"

ETC.


FOURTH EDITION

ENLARGED, AND PARTLY REWRITTEN


SIMPKIN, MARSHALL, HAMILTON, KENT & CO. LTD.,
4 STATIONERS' HALL COURT.
LONDON, E.C.4


PREFACE


In this edition of my _Logic_, the text has been revised throughout,
several passages have been rewritten, and some sections added. The chief
alterations and additions occur in cc. i., v., ix., xiii., xvi., xvii.,
xx.

The work may be considered, on the whole, as attached to the school of
Mill; to whose _System of Logic_, and to Bain's _Logic_, it is deeply
indebted. Amongst the works of living writers, the _Empirical Logic_ of
Dr. Venn and the _Formal Logic_ of Dr. Keynes have given me most
assistance. To some others acknowledgments have been made as occasion
arose.

For the further study of contemporary opinion, accessible in English,
one may turn to such works as Mr. Bradley's _Principles of Logic_, Dr.
Bosanquet's _Logic; or the Morphology of Knowledge_, Prof. Hobhouse's
_Theory of Knowledge_, Jevon's _Principles of Science_, and Sigwart's
_Logic_. Ueberweg's _Logic, and History of Logical Doctrine_ is
invaluable for the history of our subject. The attitude toward Logic of
the Pragmatists or Humanists may best be studied in Dr. Schiller's
_Formal Logic_, and in Mr. Alfred Sidgwick's _Process of Argument_ and
recent _Elementary Logic_. The second part of this last work, on the
"Risks of Reasoning," gives an admirably succinct account of their
position. I agree with the Humanists that, in all argument, the
important thing to attend to is the meaning, and that the most serious
difficulties of reasoning occur in dealing with the matter reasoned
about; but I find that a pure science of relation has a necessary place
in the system of knowledge, and that the formulæ known as laws of
contradiction, syllogism and causation are useful guides in the framing
and testing of arguments and experiments concerning matters of fact.
Incisive criticism of traditionary doctrines, with some remarkable
reconstructions, may be read in Dr. Mercier's _New Logic_.

In preparing successive editions of this book, I have profited by the
comments of my friends: Mr. Thomas Whittaker, Prof. Claude Thompson, Dr.
Armitage Smith, Mr. Alfred Sidgwick, Dr. Schiller, Prof. Spearman, and
Prof. Sully, have made important suggestions; and I might have profited
more by them, if the frame of my book, or my principles, had been more
elastic.

As to the present edition, useful criticisms have been received from Mr.
S.C. Dutt, of Cotton College, Assam, and from Prof. M.A. Roy, of
Midnapore; and, especially, I must heartily thank my colleague, Dr.
Wolf, for communications that have left their impress upon nearly every
chapter.


CARVETH READ.

LONDON,
_August_, 1914


CONTENTS

PAGE

PREFACE v


CHAPTER I


INTRODUCTORY

§1. Definition of Logic 1
§2. General character of proof 2
§3. Division of the subject 5
§4. Uses of Logic 6
§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)
§6. Schools of Logicians 11
Relation to Psychology (p. 13)


CHAPTER II

GENERAL ANALYSIS OF PROPOSITIONS

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


CHAPTER III

OF TERMS AND THEIR DENOTATION

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


CHAPTER IV

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

§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

§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

§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,
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

§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

§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

§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

§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

§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

§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

§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

§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 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
be briefly defined as the science of proof with respect to _qualitative_
laws and propositions, except those that are axiomatic.

§ 2. Proof may be of different degrees or stages of completeness.
Absolute proof would require that a proposition should be shown to agree
with all experience and with the systematic explanation of experience,
to be a necessary part of an all-embracing and self-consistent
philosophy or theory of the universe; but as no one hitherto has been
able to frame such a philosophy, we must at present put up with
something less than absolute proof. Logic, assuming certain principles
to be true of experience, or at least to be conditions of consistent
discourse, distinguishes the kinds of propositions that can be shown to
agree with these principles, and explains by what means the agreement
can best be exhibited. Such principles are those of Contradiction (chap.
vi.), the Syllogism (chap. ix.), Causation (chap. xiv.), and
Probabilities (chap. xx.). To bring a proposition or an argument under
them, or to show that it agrees with them, is logical proof.

The extent to which proof is requisite, again, depends upon the present
purpose: if our aim be general truth for its own sake, a systematic
investigation is necessary; but if our object be merely to remove some
occasional doubt that has occurred to ourselves or to others, it may be
enough to appeal to any evidence that is admitted or not questioned.
Thus, if a man doubts that _some acids are compounds of oxygen_, but
grants that _some compounds of oxygen are acids_, he may agree to the
former proposition when you point out that it has the same meaning as
the latter, differing from it only in the order of the words. This is
called proof by immediate inference.

Again, suppose that a man holds in his hand a piece of yellow metal,
which he asserts to be copper, and that we doubt this, perhaps
suggesting that it is really gold. Then he may propose to dip it in
vinegar; whilst we agree that, if it then turns green, it is copper and
not gold. On trying this experiment the metal does turn green; so that
we may put his argument in this way: -

_Whatever yellow metal turns green in vinegar is copper;
This yellow metal turns green in vinegar;
Therefore, this yellow metal is copper._

Such an argument is called proof by mediate inference; because one
cannot see directly that the yellow metal is copper; but it is admitted
that any yellow metal is copper that turns green in vinegar, and we are



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