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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
[Transcriber's Note: The mathematical operator "therefore" is
represented below by .'.]
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 formulae 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
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
CHAPTER I
INTRODUCTORY
Sec. 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.
Sec. 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
shown that this yellow metal has that property.
Now, however, it may occur to us, that the liquid in which the metal was
dipped was not vinegar, or not pure vinegar, and that the greenness was
due to the impurity. Our friend must thereupon show by some means that
the vinegar was pure; and then his argument will be that, since nothing
but the vinegar came in contact with the metal, the greenness was due to
the vinegar; or, in other words, that contact with that vinegar was the
cause of the metal turning green.
Still, on second thoughts, we may suspect that we had formerly conceded
too much; we may reflect that, although it had often been shown that
copper turned green in vinegar, whilst gold did not, yet the same might
not always happen. May it not be, we might ask, that just at this
moment, and perhaps always for the future gold turns, and will turn
green in vinegar, whilst copper does not and never will again? He will
probably reply that this is to doubt the uniformity of causation: he may
hope that we are not serious: he may point out to us that in every
action of our life we take such uniformity for granted. But he will be
obliged to admit that, whatever he may say to induce us to assent to the
principle of Nature's uniformity, his arguments will not amount to
logical proof, because every argument in some way assumes that
principle. He has come, in fact, to the limits of Logic. Just as Euclid
does not try to prove that 'two magnitudes equal to the same third are
equal to one another,' so the Logician (as such) does not attempt to
prove the uniformity of causation and the other principles of his
science.
Even when our purpose is to ascertain some general truth, the results of
systematic inquiry may have various degrees of certainty. If Logic were
confined to strict demonstration, it would cover a narrow field. The
greater part of our conclusions can only be more or less probable. It
may, indeed, be maintained, not unreasonably, that no judgments
concerning matters of fact can be more than probable. Some say that all
scientific results should be considered as giving the average of cases,
from which deviations are to be expected. Many matters can only be
treated statistically and by the methods of Probability. Our ordinary
beliefs are adopted without any methodical examination. But it is the
aim, and it is characteristic, of a rational mind to distinguish degrees
of certainty, and to hold each judgment with the degree of confidence
that it deserves, considering the evidence for and against it. It takes
a long time, and much self-discipline, to make some progress toward
rationality; for there are many causes of belief that are not good
grounds for it--have no value as evidence. Evidence consists of (1)
observation; (2) reasoning checked by observation and by logical
principles; (3) memory--often inaccurate; (4) testimony--often
untrustworthy, but indispensable, since all we learn from books or from
other men is taken on testimony; (5) the agreement of all our results.
On the other hand, belief is caused by many influences that are not
evidence at all: such are (1) desire, which makes us believe in whatever
serves our purpose; fear and suspicion, which (paradoxically) make us
believe in whatever seems dangerous; (2) habit, which resists whatever
disturbs our prejudices; (3) vanity, which delights to think oneself
always right and consistent and disowns fallibility; (4) imitativeness,
suggestibility, fashion, which carry us along with the crowd. All these,
and nobler things, such as love and fidelity, fix our attention upon
whatever seems to support our prejudices, and prevent our attending to
any facts or arguments that threaten to overthrow them.
Sec. 3. Two departments of Logic are usually recognised, Deduction and
Induction; that is, to describe them briefly, proof from principles, and
proof from facts. Classification is sometimes made a third department;
sometimes its topics are distributed amongst those of the former two. In
the present work the order adopted is, Deduction in chaps. ii. to xiii.;
Induction in chaps. xiii. to xx.; and, lastly, Classification. But such
divisions do not represent fundamentally distinct and opposed aspects of
the science. For although, in discussing any question with an opponent
who makes admissions, it may be possible to combat his views with merely
deductive arguments based upon his admissions; yet in any question of
general truth, Induction and Deduction are mutually dependent and imply
one another.
This may be seen in one of the above examples. It was argued that a
certain metal must be copper, because every metal is copper that turns
green when dipped in vinegar. So far the proof appealed to a general
proposition, and was deductive. But when we ask how the general
proposition is known to be true, experiments or facts must be alleged;
and this is inductive evidence. Deduction then depends on Induction. But
if we ask, again, how any number of past experiments can prove a general
proposition, which must be good for the future as well as for the past,
the uniformity of causation is invoked; that is, appeal is made to a
principle, and that again is deductive proof. Induction then depends
upon Deduction.
We may put it in this way: Deduction depends on Induction, if general
propositions are only known to us through the facts: Induction depends
on Deduction, because one fact can never prove another, except so far as
what is true of the one is true of the other and of any other of the
same kind; and because, to exhibit this resemblance of the facts, it
must be stated in a general proposition.
Sec. 4. The use of Logic is often disputed: those who have not studied it,
often feel confident of their ability to do without it; those who have
studied it, are sometimes disgusted with what they consider to be its
superficial analysis of the grounds of evidence, or needless
technicality in the discussion of details. As to those who, not having
studied Logic, yet despise it, there will be time enough to discuss its
utility with them, when they know something about it; and as for those
who, having studied it, turn away in disgust, whether they are justified
every man must judge for himself, when he has attained to equal
proficiency in the subject. Meanwhile, the following considerations may
be offered in its favour:
Logic states, and partly explains and applies, certain abstract
principles which all other sciences take for granted; namely, the axioms
above mentioned--the principles of Contradiction, of the Syllogism and
of Causation. By exercising the student in the apprehension of these
truths, and in the application of them to particular propositions, it
educates the power of abstract thought. Every science is a model of
method, a discipline in close and consecutive thinking; and this merit
Logic ought to possess in a high degree.
For ages Logic has served as an introduction to Philosophy that is, to
Metaphysics and speculative Ethics. It is of old and honourable
descent: a man studies Logic in very good company. It is the warp upon
which nearly the whole web of ancient, mediaeval and modern Philosophy is
woven. The history of thought is hardly intelligible without it.
As the science of proof, Logic gives an account of the _general_ nature
of evidence deductive and inductive, as applied in the physical and
social sciences and in the affairs of life. The _general_ nature of such
evidence: it would be absurd of the logician to pretend to instruct the
chemist, economist and merchant, as to the _special_ character of the
evidence requisite in their several spheres of judgment. Still, by
investigating the general conditions of proof, he sets every man upon
his guard against the insufficiency of evidence.
One application of the science of proof deserves special mention:
namely, to that department of Rhetoric which has been the most
developed, relating to persuasion by means of oratory, leader-writing,
or pamphleteering. It is usually said that Logic is useful to convince
the judgment, not to persuade the will: but one way of persuading the
will is to convince the judgment that a certain course is advantageous;
and although this is not always the readiest way, it is the most
honourable, and leads to the most enduring results. Logic is the
backbone of Rhetoric.
It has been disputed whether Logic is a science or an art; and, in fact,
it may be considered in both ways. As a statement of general truths, of
their relations to one another, and especially to the first principles,
it is a science; but it is an art when, regarding truth as an end
desired, it points out some of the means of attaining it--namely, to
proceed by a regular method, to test every judgment by the principles of
Logic, and to distrust whatever cannot be made consistent with them.
Logic does not, in the first place, teach us to reason. We learn to
reason as we learn to walk and talk, by the natural growth of our powers
with some assistance from friends and neighbours. The way to develop
one's power of reasoning is, first, to set oneself problems and try to
solve them. Secondly, since the solving of a problem depends upon one's
ability to call to mind parallel cases, one must learn as many facts as
possible, and keep on learning all one's life; for nobody ever knew
enough. Thirdly one must check all results by the principles of Logic.
It is because of this checking, verifying, corrective function of Logic
that it is sometimes called a Regulative or Normative Science. It cannot
give any one originality or fertility of invention; but it enables us to
check our inferences, revise our conclusions, and chasten the vagaries
of ambitious speculation. It quickens our sense of bad reasoning both in
others and in ourselves. A man who reasons deliberately, manages it
better after studying Logic than he could before, if he is sincere about
it and has common sense.
Sec. 5. The relation of Logic to other sciences:
(a) Logic is regarded by Spencer as co-ordinate with Mathematics, both
being Abstract Sciences--that is, sciences of the _relations_ in which
things stand to one another, whatever the particular things may be that
are so related; and this view seems to be, on the whole, just--subject,
however, to qualifications that will appear presently.
Mathematics treats of the relations of all sorts of things considered as
quantities, namely, as equal to, or greater or less than, one another.
Things may be quantitatively equal or unequal in _degree_, as in
comparing the temperature of bodies; or in _duration_; or in _spatial
magnitude_, as with lines, superficies, solids; or in _number_. And it
is assumed that the equality or inequality of things that cannot be
directly compared, may be proved indirectly on the assumption that
'things equal to the same thing are equal,' etc.
Logic also treats of the relations of all sorts of things, but not as to
their quantity. It considers (i) that one thing may be like or unlike
another in certain attributes, as that iron is in many ways like tin or
lead, and in many ways unlike carbon or sulphur: (ii) that attributes
co-exist or coinhere (or do not) in the same subject, as metallic
lustre, hardness, a certain atomic weight and a certain specific gravity
coinhere in iron: and (iii) that one event follows another (or is the
effect of it), as that the placing of iron in water causes it to rust.
The relations of likeness and of coinherence are the ground of
Classification; for it is by resemblance of coinhering attributes that
things form classes: coinherence is the ground of judgments concerning
Substance and Attribute, as that iron is metallic; and the relation of
succession, in the mode of Causation, is the chief subject of the
department of Induction. It is usual to group together these relations
of attributes and of order in time, and call them qualitative, in order
to contrast them with the quantitative relations which belong to
Mathematics. And it is assumed that qualitative relations of things,
when they cannot be directly perceived, may be proved indirectly by
assuming the axiom of the Syllogism (chap. ix.) and the law of Causation
(chap. xiv.).
So far, then, Logic and Mathematics appear to be co-ordinate and
distinct sciences. But we shall see hereafter that the satisfactory
treatment of that special order of events in time which constitutes
Causation, requires a combination of Logic with Mathematics; and so does
the treatment of Probability. And, again, Logic may be said to be, in a
certain sense, 'prior to' or 'above' Mathematics as usually treated. For
the Mathematics assume that one magnitude must be either equal or
unequal to another, and that it cannot be both equal and unequal to it,
and thus take for granted the principles of Contradiction and Excluded
Middle; but the statement and elucidation of these Principles are left
to Logic (chap. vi.). The Mathematics also classify and define
magnitudes, as (in Geometry) triangles, squares, cubes, spheres; but the
principles of classification and definition remain for Logic to
discuss.
(b) As to the concrete Sciences, such as Astronomy, Chemistry, Zoology,
Sociology--Logic (as well as Mathematics) is implied in them all; for
all the propositions of which they consist involve causation,
co-existence, and class-likeness. Logic is therefore said to be prior to
them or above them: meaning by 'prior' not that it should be studied
earlier, for that is not a good plan; meaning by 'above' not in dignity,
for distinctions of dignity amongst liberal studies are absurd. But it
is a philosophical idiom to call the abstract 'prior to,' or 'higher
than,' the concrete (see Porphyry's Tree, chap. xxii. Sec. 8); and Logic is
more abstract than Astronomy or Sociology. Philosophy may thank that
idiom for many a foolish notion.
(c) But, as we have seen, Logic does not investigate the truth,
trustworthiness, or validity of its own principles; nor does
Mathematics: this task belongs to Metaphysics, or Epistemology, the
criticism of knowledge and beliefs.
Logic assumes, for example, that things are what to a careful scrutiny
they seem to be; that animals, trees, mountains, planets, are bodies
with various attributes, existing in space and changing in time; and
that certain principles, such as Contradiction and Causation, are true
of things and events. But Metaphysicians have raised many plausible
objections to these assumptions. It has been urged that natural objects
do not really exist on their own account, but only in dependence on some
mind that contemplates them, and that even space and time are only our
way of perceiving things; or, again, that although things do really
exist on their own account, it is in an entirely different way from that
in which we know them. As to the principle of Contradiction--that if an
object has an attribute, it cannot at the same time and in the same way
be without it (e.g., if an animal is conscious, it is false that it is
not conscious)--it has been contended that the speciousness of this
principle is only due to the obtuseness of our minds, or even to the
poverty of language, which cannot make the fine distinctions that exist
in Nature. And as to Causation, it is sometimes doubted whether events
always have physical causes; and it is often suggested that, granting
they have physical causes, yet these are such as we can neither perceive
nor conceive; belonging not to the order of Nature as we know it, but to
the secret inwardness and reality of Nature, to the wells and reservoirs
of power, not to the spray of the fountain that glitters in our
eyes--'occult causes,' in short. Now these doubts and surmises are
metaphysical spectres which it remains for Metaphysics to lay. Logic has
no direct concern with them (although, of course, metaphysical
discussion is expected to be logical), but keeps the plain path of plain
beliefs, level with the comprehension of plain men. Metaphysics, as
examining the grounds of Logic itself, is sometimes regarded as 'the
higher Logic'; and, certainly, the study of Metaphysics is necessary to
every one who would comprehend the nature and functions of Logic, or the
place of his own mind and of Reason in the world.
(d) The relation of Logic to Psychology will be discussed in the next
section.
(e) As a Regulative Science, pointing out the conditions of true
inference (within its own sphere), Logic is co-ordinate with (i) Ethics,
considered as assigning the conditions of right conduct, and with (ii)
AEsthetics, considered as determining the principles of criticism and
good taste.
Sec. 6. Three principal schools of Logicians are commonly recognised:
Nominalist, Conceptualist, and Materialist, who differ as to what it is
that Logic really treats of: the Nominalists say, 'of language'; the
Conceptualists, 'of thought'; the Materialists, 'of relations of fact.'
To illustrate these positions let us take authors who, if some of them
are now neglected, have the merit of stating their contrasted views with
a distinctness that later refinements tend to obscure.
(a) Whately, a well-known Nominalist, regarded Logic as the Science and
Art of Reasoning, but at the same time as "entirely conversant about
language"; that is to say, it is the business of Logic to discover those
modes of statement which shall ensure the cogency of an argument, no
matter what may be the subject under discussion. Thus, _All fish are
cold-blooded_, .'. _some cold-blooded things are fish:_ this is a sound
inference by the mere manner of expression; and equally sound is the
inference, _All fish are warm-blooded_, .'. _some warm-blooded things are
fish_. The latter proposition may be false, but it follows; and
(according to this doctrine) Logic is only concerned with the consistent
use of words: the truth or falsity of the proposition itself is a
question for Zoology. The short-coming of extreme Nominalism lies in
speaking of language as if its meaning were unimportant. But Whately did
not intend this: he was a man of great penetration and common-sense.
(b) Hamilton, our best-known Conceptualist, defined Logic as the science
of the "formal laws of thought," and "of thought as thought," that is,
without regard to the matter thought about. Just as Whately regarded
Logic as concerned merely with cogent forms of statement, so Hamilton
treated it as concerned merely with the necessary relations of thought.
This doctrine is called Conceptualism, because the simplest element of
thought is the Concept; that is, an abstract idea, such as is signified
by the word _man, planet, colour, virtue_; not a representative or
generic image, but the thought of all attributes common to any class of
things. Men, planets, colours, virtuous actions or characters, have,
severally, something in common on account of which they bear these
general names; and the thought of what they have in common, as the
ground of these names, is a Concept. To affirm or deny one concept of
another, as _Some men are virtuous_, or _No man is perfectly virtuous_,
is to form a Judgment, corresponding to the Proposition of which the
other schools of Logic discourse. Conceptualism, then, investigates the
conditions of consistent judgment.
To distinguish Logic from Psychology is most important in connection
with Conceptualism. Concepts and Judgments being mental acts, or
products of mental activity, it is often thought that Logic must be a
department of Psychology. It is recognised of course, that Psychology
deals with much more than Logic does, with sensation, pleasure and pain,
emotion, volition; but in the region of the intellect, especially in its
most deliberate and elaborate processes, namely, conception, judgment,
and reasoning, Logic and Psychology seem to occupy common ground. In
fact, however, the two sciences have little in common except a few
general terms, and even these they employ in different senses. It is
usual to point out that Psychology tries to explain the subjective
_processes_ of conception, judgment and reasoning, and to give their
natural history; but that Logic is wholly concerned with the _results_
of such processes, with concepts, judgments and reasonings, and merely
with the validity of the results, that is, with their truth or
consistency; whilst Psychology has nothing to do with their validity,
but only with their causes. Besides, the logical judgment (in Formal
Logic at least) is quite a different thing from the psychological: the
latter involves feeling and belief, whereas the former is merely a given
relation of concepts. _S is P_: that is a model logical judgment; there
can be no question of believing it; but it is logically valid if _M is
P_ and _S is M_. When, again, in Logic, one deals with belief, it
depends upon evidence; whereas, in Psychology belief is shown to depend
upon causes which may have evidentiary value or may not; for Psychology
explains quite impartially the growth of scientific insight and the
growth of prejudice.
(c) Mill, Bain, and Venn are the chief Materialist logicians; and to
guard against the error of confounding Materialism in Logic with the
ontological doctrine that nothing exists but Matter, it may suffice to
remember that in Metaphysics all these philosophers are Idealists.
Materialism in Logic consists in regarding propositions as affirming or
denying relations (_cf._ Sec. 5) between matters-of-fact in the widest
sense; not only physical facts, but ideas, social and moral relations;
it consists, in short, in attending to the meaning of propositions. It
treats the first principles of Contradiction and Causation as true of
things so far as they are known to us, and not merely as conditions or
tendencies of thought; and it takes these principles as conditions of
right thinking, because they seem to hold good of Nature and human life.
To these differences of opinion it will be necessary to recur in the
next chapter (Sec. 4); but here I may observe that it is easy to exaggerate
their importance in Logic. There is really little at issue between
schools of logicians as such, and as far as their doctrines run
parallel; it is on the metaphysical grounds of their study, or as to its
scope and comprehension, that they find a battle-field. The present work
generally proceeds upon the third, or Materialist doctrine. If Deduction
and Induction are regarded as mutually dependent parts of one science,
uniting the discipline of consistent discourse with the method of
investigating laws of physical phenomena, the Materialist doctrine, that
the principles of Logic are founded on fact, seems to be the most
natural way of thinking. But if the unity of Deduction and Induction is
not disputed by the other schools, the Materialist may regard them as
allies exhibiting in their own way the same body of truths. The
Nominalist may certainly claim that his doctrine is indispensable:
consistently cogent forms of statement are necessary both to the
Conceptualist and to the Materialist; neither the relations of thought
nor those of fact can be arrested or presented without the aid of
language or some equivalent system of signs. The Conceptualist may urge
that the Nominalist's forms of statement and argument exist for the sake
of their meaning, namely, judgments and reasonings; and that the
Materialist's laws of Nature are only judgments founded upon our
conceptions of Nature; that the truth of observations and experiments
depends upon our powers of perception; that perception is inseparable
from understanding, and that a system of Induction may be constructed
upon the axiom of Causation, regarded as a principle of Reason, just as
well as by considering it as a law of Nature, and upon much the same
lines. The Materialist, admitting all this, may say that a judgment is
only the proximate meaning of a proposition, and that the ultimate
meaning, the meaning of the judgment itself, is always some
matter-of-fact; that the other schools have not hitherto been eager to
recognise the unity of Deduction and Induction or to investigate the
conditions of trustworthy experiments and observations within the limits
of human understanding; that thought is itself a sort of fact, as
complex in its structure, as profound in its relations, as subtle in its
changes as any other fact, and therefore at least as hard to know; that
to turn away from the full reality of thought in perception, and to
confine Logic to artificially limited concepts, is to abandon the effort
to push method to the utmost and to get as near truth as possible; and
that as to Causation being a principle of Reason rather than of Nature,
the distinction escapes his apprehension, since Nature seems to be that
to which our private minds turn upon questions of Causation for
correction and instruction; so that if he does not call Nature the
Universal Reason, it is because he loves severity of style.