Logic, Inductive and Deductive
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Title: Logic, Inductive and Deductive
Author: William Minto
Release date: March 27, 2010 [eBook #31796]
Language: English
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*** START OF THE PROJECT GUTENBERG EBOOK LOGIC, INDUCTIVE AND DEDUCTIVE ***
Produced by Thierry Alberto, Lesley Halamek and the Online
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UNIVERSITY MANUALS
EDITED BY PROFESSOR KNIGHT
LOGIC
INDUCTIVE AND DEDUCTIVE
PUBLISHED MAY, 1893
_Reprinted December, 1893_
" _November, 1894_
" _January, 1899_
" _August, 1904_
" _June, 1909_
" _September, 1912_
" _July, 1913_
" _January, 1915_
LOGIC
INDUCTIVE AND DEDUCTIVE
BY WILLIAM MINTO, M.A.
HON. LL.D. ST. ANDREWS
LATE PROFESSOR OF LOGIC IN THE UNIVERSITY OF ABERDEEN
LONDON
JOHN MURRAY, ALBEMARLE STREET, W.
1915
PREFACE.
In this little treatise two things are attempted that at first might
appear incompatible. One of them is to put the study of logical
formulae on a historical basis. Strangely enough, the scientific
evolution of logical forms, is a bit of history that still awaits the
zeal and genius of some great scholar. I have neither ambition nor
qualification for such a _magnum opus_, and my life is already more
than half spent; but the gap in evolutionary research is so obvious
that doubtless some younger man is now at work in the field unknown to
me. All that I can hope to do is to act as a humble pioneer according
to my imperfect lights. Even the little I have done represents work
begun more than twenty years ago, and continuously pursued for the
last twelve years during a considerable portion of my time.
The other aim, which might at first appear inconsistent with this,
is to increase the power of Logic as a practical discipline. The main
purpose of this practical science, or scientific art, is conceived to
be the organisation of reason against error, and error in its various
kinds is made the basis of the division of the subject. To carry out
this practical aim along with the historical one is not hopeless,
because throughout its long history Logic has been a practical
science; and, as I have tried to show at some length in introductory
chapters, has concerned itself at different periods with the risks of
error peculiar to each.
To enumerate the various books, ancient and modern, to which I have
been indebted, would be a vain parade. Where I have consciously
adopted any distinctive recent contribution to the long line of
tradition, I have made particular acknowledgment. My greatest
obligation is to my old professor, Alexander Bain, to whom I owe my
first interest in the subject, and more details than I can possibly
separate from the general body of my knowledge.
W. M.
ABERDEEN, _January, 1893_.
Since these sentences were written, the author of this book has
died; and Professor Minto's _Logic_ is his last contribution to the
literature of his country. It embodies a large part of his teaching in
the philosophical class-room of his University, and doubtless reflects
the spirit of the whole of it.
Scottish Philosophy has lost in him one of its typical
representatives, and the University of the North one of its most
stimulating teachers. There have been few more distinguished men than
William Minto in the professoriate of Aberdeen; and the memory of what
he was, of his wide and varied learning, his brilliant conversation,
his urbanity, and his rare power of sympathy with men with whose
opinions he did not agree, will remain a possession to many who mourn
his loss.
It will be something if this little book keeps his memory alive, both
amongst the students who owed so much to him, and in the large circle
of friends who used to feel the charm of his personality.
WILLIAM KNIGHT.
_GENERAL PLAN OF THE SERIES._
_This Series is primarily designed to aid the University Extension
Movement throughout Great Britain and America, and to supply the need
so widely felt by students, of Text-books for study and reference, in
connexion with the authorised Courses of Lectures._
_The Manuals differ from those already in existence in that they are
not intended for School use, or for Examination purposes; and that
their aim is to educate, rather than to inform. The statement of
details is meant to illustrate the working of general laws, and the
development of principles; while the historical evolution of the
subject dealt with is kept in view, along with its philosophical
significance._
_The remarkable success which has attended University Extension in
Britain has been partly due to the combination of scientific treatment
with popularity, and to the union of simplicity with thoroughness.
This movement, however, can only reach those resident in the larger
centres of population, while all over the country there are thoughtful
persons who desire the same kind of teaching. It is for them also that
this Series is designed. Its aim is to supply the general reader with
the same kind of teaching as is given in the Lectures, and to reflect
the spirit which has characterised the movement, viz., the combination
of principles with facts, and of methods with results._
_The Manuals are also intended to be contributions to the Literature
of the Subjects with which they respectively deal, quite apart from
University Extension; and some of them will be found to meet a general
rather than a special want._
_They will be issued simultaneously in England and America. Volumes
dealing with separate sections of Literature, Science, Philosophy,
History, and Art have been assigned to representative literary men,
to University Professors, or to Extension Lecturers connected with
Oxford, Cambridge, London, and the Universities of Scotland and
Ireland._
_A list of the works in this Series will be found at the end of the
volume._
CONTENTS.
INTRODUCTION.
I.
PAGE
The Origin and Scope of Logic, 1
II.
Logic as a Preventive of Error or Fallacy--The Inner
Sophist, 17
III.
The Axioms of Dialectic and of Syllogism, 29
BOOK I.
THE LOGIC OF CONSISTENCY--SYLLOGISM AND
DEFINITION.
PART I.
THE ELEMENTS OF PROPOSITIONS.
CHAPTER I.
General Names and Allied Distinctions, 43
CHAPTER II.
The Syllogistic Analysis of Proposition, into Terms. (1)
The Bare Analytic Forms. (2) The Practice of Syllogistic
Analysis. (3) Some Technical Difficulties, 62
PART II.
DEFINITION.
CHAPTER I.
(1) Imperfect Understanding of Words. (2) Verification of
the Meaning--Dialectic. (3) Fixation of the Meaning--Division
or Classification, Definition, Naming, 82
CHAPTER II.
The Five Predicables--Verbal and Real Predication, 105
CHAPTER III.
Aristotle's Categories, 112
CHAPTER IV.
The Controversy about Universals--Difficulties concerning
the Relation of General Names to Thought and to Reality, 120
PART III.
THE INTERPRETATION OF PROPOSITIONS.
CHAPTER I.
Theories of Predication--Theories of Judgment, 131
CHAPTER II.
The "Opposition" of Propositions--The Interpretation of
"No," 139
CHAPTER III.
The Implication of Propositions--Immediate Formal Inference
--Eduction, 146
CHAPTER IV.
The Counter-Implication of Propositions, 156
PART IV.
THE INTERDEPENDENCE OF PROPOSITIONS.
CHAPTER I.
The Syllogism, 167
CHAPTER II.
The Figures and Moods of the Syllogism. (1) The First
Figure. (2) The Minor Figures and their Reduction to
the First. (3) Sorites, 173
CHAPTER III.
The Demonstration of the Syllogistic Moods--The Canons
of the Syllogism, 185
CHAPTER IV.
The Analysis of Arguments into Syllogistic Forms, 196
CHAPTER V.
Enthymemes, 205
CHAPTER VI.
The Utility of the Syllogism, 209
CHAPTER VII.
Conditional Arguments--Hypothetical Syllogism, Disjunctive
Syllogism and Dilemma, 215
CHAPTER VIII.
Fallacies in Deductive Argument--_Petitio Principii_ and
_Ignoratio Elenchi_, 226
CHAPTER IX.
Formal or Aristotelian Induction--Inductive Argument--The
Inductive Syllogism, 235
BOOK II.
INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.
Introduction, 243
CHAPTER I.
The Data of Experience as Grounds of Inference or Rational
Belief, 273
CHAPTER II.
Ascertainment of Simple Facts in their Order--Personal
Observation--Hearsay Evidence--Method of Testing
Traditional Evidence, 285
CHAPTER III.
Ascertainment of Facts of Causation. (1) _Post Hoc Ergo
Propter Hoc._ (2) Meaning of Cause--Methods of Observation
--Mill's Experimental Methods, 295
CHAPTER IV.
Method of Observation--Single Difference. (1) The Principle
of Single Difference. (2) Application of the Principle, 308
CHAPTER V.
Methods of Observation--Elimination--Single Agreement.
(1) The Principle of Elimination. (2) The Principle of
Single Agreement. (3) Mill's "Joint Method of Agreement
and Difference," 318
CHAPTER VI.
Methods of Observation--Minor Methods. (1) Concomitant
Variations. (2) Single Residue, 329
CHAPTER VII.
The Method of Explanation. (1) The Four Stages of Orderly
Procedure. (2) Obstacles to Explanation--Plurality of Causes
and Intermixture of Effects. (3) The Proof of a Hypothesis, 334
CHAPTER VIII.
Supplementary Methods of Investigation. (1) The Maintenance
of Averages--Supplement to the Method of Difference.
(2) The Presumption from Extra-Casual Coincidence, 351
CHAPTER IX.
Probable Inference to Particulars--The Measurement of
Probability, 362
CHAPTER X.
Inference from Analogy, 367
INTRODUCTION.
I.--THE ORIGIN AND SCOPE OF LOGIC.
The question has sometimes been asked, Where should we begin in Logic?
Particularly within the present century has this difficulty been felt,
when the study of Logic has been revived and made intricate by the
different purposes of its cultivators.
Where did the founder of Logic begin? Where did Aristotle begin? This
seems to be the simplest way of settling where we should begin, for
the system shaped by Aristotle is still the trunk of the tree, though
there have been so many offshoots from the old stump and so many
parasitic plants have wound themselves round it that Logic is now
almost as tangled a growth as the Yews of Borrowdale--
An intertwisted mass of fibres serpentine
Upcoiling and inveterately convolved.
It used to be said that Logic had remained for two thousand years
precisely as Aristotle left it. It was an example of a science or
art perfected at one stroke by the genius of its first inventor.
The bewildered student must often wish that this were so: it is only
superficially true. Much of Aristotle's nomenclature and his central
formulae have been retained, but they have been very variously
supplemented and interpreted to very different purposes--often to no
purpose at all.
The Cambridge mathematician's boast about his new theorem--"The best
of it all is that it can never by any possibility be made of the
slightest use to anybody for anything"--might be made with truth about
many of the later developments of Logic. We may say the same, indeed,
about the later developments of any subject that has been a playground
for generation after generation of acute intellects, happy in
their own disinterested exercise. Educational subjects--subjects
appropriated for the general schooling of young minds--are
particularly apt to be developed out of the lines of their original
intention. So many influences conspire to pervert the original aim.
The convenience of the teacher, the convenience of the learner,
the love of novelty, the love of symmetry, the love of subtlety;
easy-going indolence on the one hand and intellectual restlessness
on the other--all these motives act from within on traditional
matter without regard to any external purpose whatever. Thus in
Logic difficulties have been glossed over and simplified for the dull
understanding, while acute minds have revelled in variations and new
and ingenious manipulations of the old formulae, and in multiplication
and more exact and symmetrical definition of the old distinctions.
To trace the evolution of the forms and theories of Logic under these
various influences during its periods of active development is a task
more easily conceived than executed, and one far above the ambition of
an introductory treatise. But it is well that even he who writes for
beginners should recognise that the forms now commonly used have been
evolved out of a simpler tradition. Without entering into the details
of the process, it is possible to indicate its main stages, and thus
furnish a clue out of the modern labyrinthine confusion of purposes.
How did the Aristotelian Logic originate? Its central feature is the
syllogistic forms. In what circumstances did Aristotle invent these?
For what purpose? What use did he contemplate for them? In rightly
understanding this, we shall understand the original scope or province
of Logic, and thus be in a position to understand more clearly how it
has been modified, contracted, expanded, and supplemented.
Logic has always made high claims as the _scientia scientiarum_,
the science of sciences. The builders of this Tower of Babel are
threatened in these latter days with confusion of tongues. We may
escape this danger if we can recover the designs of the founder, and
of the master-builders who succeeded him.
Aristotle's Logic has been so long before the world in abstract
isolation that we can hardly believe that its form was in any way
determined by local accident. A horror as of sacrilege is excited by
the bare suggestion that the author of this grand and venerable work,
one of the most august monuments of transcendent intellect, was in his
day and generation only a pre-eminent tutor or schoolmaster, and
that his logical writings were designed for the accomplishment of his
pupils in a special art in which every intellectually ambitious young
Athenian of the period aspired to excel. Yet such is the plain fact,
baldly stated. Aristotle's Logic in its primary aim was as practical
as a treatise on Navigation, or "Cavendish on Whist". The latter is
the more exact of the two comparisons. It was in effect in its various
parts a series of handbooks for a temporarily fashionable intellectual
game, a peculiar mode of disputation or dialectic,[1] the game of
Question and Answer, the game so fully illustrated in the Dialogues of
Plato, the game identified with the name of Socrates.
We may lay stress, if we like, on the intellectuality of the game, and
the high topics on which it was exercised. It was a game that could
flourish only among a peculiarly intellectual people; a people less
acute would find little sport in it. The Athenians still take a
singular delight in disputation. You cannot visit Athens without being
struck by it. You may still see groups formed round two protagonists
in the cafes or the squares, or among the ruins of the Acropolis, in
a way to remind you of Socrates and his friends. They do not argue as
Gil Blas and his Hibernians did with heat and temper, ending in blows.
They argue for the pure love of arguing, the audience sitting
or standing by to see fair play with the keenest enjoyment of
intellectual thrust and parry. No other people could argue like the
Greeks without coming to blows. It is one of their characteristics
now, and so it was in old times two thousand years ago. And about
a century before Aristotle reached manhood, they had invented this
peculiarly difficult and trying species of disputative pastime, in
which we find the genesis of Aristotle's logical treatises.
To get a proper idea of this debate by Question and Answer, which we
may call Socratic disputation after its most renowned master, one
must read some of the dialogues of Plato. I will indicate merely
the skeleton of the game, to show how happily it lent itself to
Aristotle's analysis of arguments and propositions.
A thesis or proposition is put up for debate, _e.g._, that knowledge
is nothing else than sensible perception,[2] that it is a greater
evil to do wrong than to suffer wrong,[3] that the love of gain is not
reprehensible.[4] There are two disputants, but they do not speak on
the question by turns, so many minutes being allowed to each as in
a modern encounter of wits. One of the two, who may be called the
Questioner, is limited to asking questions, the other, the Respondent,
is limited to answering. Further, the Respondent can answer only "Yes"
or "No," with perhaps a little explanation: on his side the Questioner
must ask only questions that admit of the simple answer "Yes" or "No".
The Questioner's business is to extract from the Respondent admissions
involving the opposite of what he has undertaken to maintain. The
Questioner tries in short to make him contradict himself. Only a very
stupid Respondent would do this at once: the Questioner plies him
with general principles, analogies, plain cases; leads him on from
admission to admission, and then putting the admissions together
convicts him out of his own mouth of inconsistency.[5]
Now mark precisely where Aristotle struck in with his invention of the
Syllogism, the invention on which he prided himself as specially his
own, and the forms of which have clung to Logic ever since, even
in the usage of those who deride Aristotle's Moods and Figures as
antiquated superstitions. Suppose yourself the Questioner, where did
he profess to help you with his mechanism? In effect, as the word
Syllogism indicates, it was when you had obtained a number of
admissions, and wished to reason them together, to demonstrate how
they bore upon the thesis in dispute, how they hung together, how they
necessarily involved what you were contending for. And the essence of
his mechanism was the reduction of the admitted propositions to common
terms, and to certain types or forms which are manifestly equivalent
or inter-dependent. Aristotle advised his pupils also in the
tactics of the game, but his grand invention was the form or type
of admissions that you should strive to obtain, and the effective
manipulation of them when you had got them.
An example will show the nature of this help, and what it was worth.
To bring the thing nearer home, let us, instead of an example from
Plato, whose topics often seem artificial to us now, take a thesis
from last century, a paradox still arguable, Mandeville's famous--some
would say infamous--paradox that Private Vices are Public Benefits.
Undertake to maintain this, and you will have no difficulty in getting
a respondent prepared to maintain the negative. The plain men, such as
Socrates cross-questioned, would have declared at once that a vice is
a vice, and can never do any good to anybody. Your Respondent denies
your proposition simply: he upholds that private vices never are
public benefits, and defies you to extract from him any admission
inconsistent with this. Your task then is to lure him somehow into
admitting that in some cases what is vicious in the individual may
be of service to the State. This is enough: you are not concerned to
establish that this holds of all private vices. A single instance
to the contrary is enough to break down his universal negative. You
cannot, of course, expect him to make the necessary admission in
direct terms: you must go round about. You know, perhaps, that he
has confidence in Bishop Butler as a moralist. You try him with the
saying: "To aim at public and private good are so far from being
inconsistent that they mutually promote each other". Does he admit
this?
Perhaps he wants some little explanation or exemplification to enable
him to grasp your meaning. This was within the rules of the game. You
put cases to him, asking for his "Yes" or "No" to each. Suppose a man
goes into Parliament, not out of any zeal for the public good, but in
pure vainglory, or to serve his private ends, is it possible for him
to render the State good service? Or suppose a milk-seller takes
great pains to keep his milk pure, not because he cares for the public
health, but because it pays, is this a benefit to the public?
Let these questions be answered in the affirmative, putting you in
possession of the admission that some actions undertaken for private
ends are of public advantage, what must you extract besides to make
good your position as against the Respondent? To see clearly at this
stage what now is required, though you have to reach it circuitously,
masking your approach under difference of language, would clearly be
an advantage. This was the advantage that Aristotle's method offered
to supply. A disputant familiar with his analysis would foresee at
once that if he could get the Respondent to admit that all actions
undertaken for private ends are vicious, the victory was his, while
nothing short of this would serve.
Here my reader may interject that he could have seen this without any
help from Aristotle, and that anybody may see it without knowing
that what he has to do is, in Aristotelian language, to construct a
syllogism in Bokardo. I pass this over. I am not concerned at this
point to defend the utility of Aristotle's method. All that I want
is to illustrate the kind of use that it was intended for. Perhaps if
Aristotle had not habituated men's minds to his analysis, we should
none of us have been able to discern coherence and detect incoherence
as quickly and clearly as we do now.
But to return to our example. As Aristotle's pupil, you would have
seen at the stage we are speaking of that the establishment of your
thesis must turn upon the definition of virtue and vice. You must
proceed, therefore, to cross-examine your Respondent about this. You
are not allowed to ask him what he means by virtue, or what he means
by vice. In accordance with the rules of the dialectic, it is your
business to propound definitions, and demand his Yes or No to them.
You ask him, say, whether he agrees with Shaftesbury's definition of a
virtuous action as an action undertaken purely for the good of others.
If he assents, it follows that an action undertaken with any suspicion
of a self-interested motive cannot be numbered among the virtues.
If he agrees, further, that every action must be either vicious
or virtuous, you have admissions sufficient to prove your original
thesis. All that you have now to do to make your triumph manifest, is
to display the admissions you have obtained in common terms.
Some actions done with a self-interested motive are public
benefits. All actions done with a self-interested motive are
private vices.
From these premisses it follows irresistibly that
Some private vices are public benefits.
This illustration may serve to show the kind of disputation for which
Aristotle's logic was designed, and thus to make clear its primary
uses and its limitations.
To realise its uses, and judge whether there is anything analogous
to them in modern needs, conceive the chief things that it behoved
Questioner and Respondent in this game to know. All that a proposition
necessarily implies; all that two propositions put together imply; on
what conditions and to what extent one admission is inconsistent with
another; when one admission necessarily involves another; when two
necessarily involve a third. And to these ends it was obviously
necessary to have an exact understanding of the terms used, so as to
avoid the snares of ambiguous language.
That a Syllogistic or Logic of Consistency should emerge out of
Yes-and-No Dialectic was natural. Things in this world come when they
are wanted: inventions are made on the spur of necessity. It was above
all necessary in this kind of debate to avoid contradicting yourself:
to maintain your consistency. A clever interrogator spread out
proposition after proposition before you and invited your assent,
choosing forms of words likely to catch your prejudices and lure
you into self-contradiction. An organon, instrument, or discipline
calculated to protect you as Respondent and guide you as Questioner
by making clear what an admission led to, was urgently called for,
and when the game had been in high fashion for more than a century
Aristotle's genius devised what was wanted, meeting at the same time,
no doubt, collateral needs that had arisen from the application of
Dialectic to various kinds of subject-matter.
The thoroughness of Aristotle's system was doubtless due partly to
the searching character of the dialectic in which it had its birth.
No other mode of disputation makes such demands upon the disputant's
intellectual agility and precision, or is so well adapted to lay bare
the skeleton of an argument.
The uses of Aristotle's logical treatises remained when the fashion
that had called them forth had passed.[6] Clear and consistent
thinking, a mastery of the perplexities and ambiguities of language,
power to detect identity of meaning under difference of expression, a
ready apprehension of all that a proposition implies, all that may
be educed or deduced from it--whatever helps to these ends must be of
perpetual use. "To purge the understanding of those errors which lie
in the confusion and perplexities of an inconsequent thinking," is
a modern description of the main scope of Logic.[7] It is a good
description of the branch of Logic that keeps closest to the
Aristotelian tradition.
The limitations as well as the uses of Aristotle's logic may be traced
to the circumstances of its origin. Both parties to the disputation,
Questioner and Respondent alike, were mainly concerned with the
inter-dependence of the propositions put forward. Once the Respondent
had given his assent to a question, he was bound in consistency to all
that it implied. He must take all the consequences of his admission.
It might be true or it might be false as a matter of fact: all the
same he was bound by it: its truth or falsehood was immaterial to his
position as a disputant. On the other hand, the Questioner could not
go beyond the admissions of the Respondent. It has often been alleged
as a defect in the Syllogism that the conclusion does not go beyond
the premisses, and ingenious attempts have been made to show that
it is really an advance upon the premisses. But having regard to the
primary use of the syllogism, this was no defect, but a necessary
character of the relation. The Questioner could not in fairness assume
more than had been granted by implication. His advance could only be
an argumentative advance: if his conclusion contained a grain more
than was contained in the premisses, it was a sophistical trick, and
the Respondent could draw back and withhold his assent. He was bound
in consistency to stand by his admissions; he was not bound to go a
fraction of an inch beyond them.
We thus see how vain it is to look to the Aristotelian tradition
for an organon of truth or a criterion of falsehood. Directly and
primarily, at least, it was not so; the circumstances of its origin
gave it a different bent. Indirectly and secondarily, no doubt, it
served this purpose, inasmuch as truth was the aim of all serious
thinkers who sought to clear their minds and the minds of others by
Dialectic. But in actual debate truth was represented merely by the
common-sense of the audience. A dialectician who gained a triumph
by outraging this, however cleverly he might outwit his antagonist,
succeeded only in amusing his audience, and dialecticians of the
graver sort aimed at more serious uses and a more respectful homage,
and did their best to discountenance merely eristic disputation.
Further, it would be a mistake to conclude because Aristotle's Logic,
as an instrument of Dialectic, concerned itself with the syllogism
of propositions rather than their truth, that it was merely an art of
quibbling. On the contrary, it was essentially the art of preventing
and exposing quibbling. It had its origin in quibbling, no doubt,
inasmuch as what we should call verbal quibbling was of the essence
of Yes-and-No Dialectic, and the main secret of its charm for an
intellectual and disputatious people; but it came into being as a
safeguard against quibbling, not a serviceable adjunct.
The mediaeval developments of Logic retained and even exaggerated
the syllogistic character of the original treatises. Interrogative
dialectic had disappeared in the Middle Ages whether as a diversion or
as a discipline: but errors of inconsistency still remained the errors
against which principally educated men needed a safeguard. Men had
to keep their utterances in harmony with the dogmas of the Church. A
clear hold of the exact implications of a proposition, whether singly
or in combination with other propositions, was still an important
practical need. The Inductive Syllogism was not required, and its
treatment dwindled to insignificance in mediaeval text-books, but the
Deductive Syllogism and the formal apparatus for the definition of
terms held the field.
It was when observation of Nature and its laws became a paramount
pursuit that the defects of Syllogistic Logic began to be felt. Errors
against which this Logic offered no protection then called for a
safeguard--especially the errors to which men are liable in the
investigation of cause and effect. "Bring your thoughts into harmony
one with another," was the demand of Aristotle's age. "Bring your
thoughts into harmony with authority," was the demand of the Middle
Ages. "Bring them into harmony with fact," was the requirement most
keenly felt in more recent times. It is in response to this demand
that what is commonly but not very happily known as Inductive Logic
has been formulated.
In obedience to custom, I shall follow the now ordinary division of
Logic into Deductive and Inductive. The titles are misleading in many
ways, but they are fixed by a weight of usage which it would be vain
to try to unsettle. Both come charging down the stream of time
each with its cohort of doctrines behind it, borne forward with
irresistible momentum.
The best way of preventing confusion now is to retain the established
titles, recognise that the doctrines behind each have a radically
different aim or end, and supply the interpretation of this end from
history. What they have in common may be described as the prevention
of error, the organisation of reason against error. I have shown
that owing to the bent impressed upon it by the circumstances of its
origin, the errors chiefly safeguarded by the Aristotelian logic
were the errors of inconsistency. The other branch of Logic, commonly
called Induction, was really a separate evolution, having its origin
in a different practical need. The history of this I will trace
separately after we have seen our way through the Aristotelian
tradition and its accretions. The Experimental Methods are no less
manifestly the germ, the evolutionary centre or starting-point, of
the new Logic than the Syllogism is of the old, and the main errors
safeguarded are errors of fact and inference from fact.
At this stage it will be enough to indicate briefly the broad
relations between Deductive Logic and Inductive Logic.
Inductive Logic, as we now understand it--the Logic of Observation and
Explanation--was first formulated and articulated to a System of Logic
by J. S. Mill. It was he that added this wing to the old building.
But the need of it was clearly expressed as early as the thirteenth
century. Roger Bacon, the Franciscan friar (1214-1292), and not his
more illustrious namesake Francis, Lord Verulam, was the real founder
of Inductive Logic. It is remarkable that the same century saw
Syllogistic Logic advanced to its most complete development in the
system of Petrus Hispanus, a Portuguese scholar who under the title of
John XXI. filled the Papal Chair for eight months in 1276-7.
A casual remark of Roger Bacon's in the course of his advocacy of
Experimental Science in the _Opus Majus_ draws a clear line between
the two branches of Logic. "There are," he says, "two ways of knowing,
by Argument and by Experience. Argument concludes a question, but
it does not make us feel certain, unless the truth be also found in
experience."
On this basis the old Logic may be clearly distinguished from the new,
taking as the general aim of Logic the protection of the mind against
the errors to which it is liable in the acquisition of knowledge.
All knowledge, broadly speaking, comes either from Authority, _i.e._,
by argument from accepted premisses, or from Experience. If it comes
from Authority it comes through the medium of words: if it comes from
Experience it comes through the senses. In taking in knowledge through
words we are liable to certain errors; and in taking in knowledge
through the senses we are liable to certain errors. To protect against
the one is the main end of "Deductive" Logic: to protect against the
other is the main end of "Inductive" Logic. As a matter of fact the
pith of treatises on Deduction and Induction is directed to those ends
respectively, the old meanings of Deduction and Induction as formal
processes (to be explained afterwards) being virtually ignored.
There is thus no antagonism whatever between the two branches of
Logic. They are directed to different ends. The one is supplementary
to the other. The one cannot supersede the other.
Aristotelian Logic can never become superfluous as long as men are apt
to be led astray by words. Its ultimate business is to safeguard in
the interpretation of the tradition of language. The mere syllogistic,
the bare forms of equivalent or consistent expression, have a very
limited utility, as we shall see. But by cogent sequence syllogism
leads to proposition, and proposition to term, and term to a close
study of the relations between words and thoughts and things.
[Footnote 1: We know for certain--and it is one of the
evidences of the importance attached to this trivial-looking
pastime--that two of the great teacher's logical treatises,
the Topics and the Sophistical Refutations, were written
especially for the guidance of Questioners and Respondents.
The one instructs the disputant how to qualify himself
methodically for discussion before an ordinary audience, when
the admissions extracted from the respondent are matters of
common belief, the questioner's skill being directed to make
it appear that the respondent's position is inconsistent
with these. The other is a systematic exposure of sophistical
tricks, mostly verbal quibbles, whereby a delusive appearance
of victory in debate may be obtained. But in the concluding
chapter of the _Elenchi_, where Aristotle claims not only
that his method is superior to the empirical methods of
rival teachers, but that it is entirely original, it is the
Syllogism upon which he lays stress as his peculiar and
chief invention. The Syllogism, the pure forms of which are
expounded in his Prior Analytics, is really the centre of
Aristotle's logical system, whether the propositions to
which it is applied are matters of scientific truth as in the
Posterior Analytics, or matters of common opinion as in
the Topics. The treatise on Interpretation, _i.e._, the
interpretation of the Respondent's "Yes" and "No," is
preliminary to the Syllogism, the reasoning of the admissions
together. Even in the half-grammatical half-logical treatise
on the Categories, the author always keeps an eye on the
Syllogistic analysis.]
[Footnote 2: Theaetetus, 151 E.]
[Footnote 3: Gorgias, 473 D.]
[Footnote 4: Hipparchus, 225 A.]
[Footnote 5: In its leading and primary use, this was a mode
of debate, a duel of wits, in which two men engaged before
an audience. But the same form could be used, and was used,
notably by Socrates, not in an eristic spirit but as a means
of awakening people to the consequences of certain admissions
or first principles, and thus making vague knowledge explicit
and clear. The mind being detained on proposition after
proposition as assent was given to it, dialectic was a
valuable instrument of instruction and exposition. But
whatever the purpose of the exercise, controversial triumph,
or solid grounding in the first principles--"the evolution
of in-dwelling conceptions"--the central interest lay in the
syllogising or reasoning together of the separately assumed or
admitted propositions.]
[Footnote 6: Like every other fashion, Yes-and-No Dialectic
had its period, its rise and fall. The invention of it is
ascribed to Zeno the Eleatic, the answering and questioning
Zeno, who flourished about the middle of the fifth century
B.C. Socrates (469-399) was in his prime at the beginning of
the great Peloponnesian War when Pericles died in 429. In that
year Plato was born, and lived to 347, "the olive groves of
Academe" being established centre of his teaching from
about 386 onwards. Aristotle (384-322), who was the tutor of
Alexander the Great, established his school at the Lyceum
when Alexander became king in 336 and set out on his career
of conquest. That Yes-and-No Dialectic was then a prominent
exercise, his logical treatises everywhere bear witness. The
subsequent history of the game is obscure. It is probable that
Aristotle's thorough exposition of its legitimate arts and
illegitimate tricks helped to destroy its interest as an
amusement.]
[Footnote 7: Hamilton's _Lectures_, iii. p. 37.]
II.--LOGIC AS A PREVENTIVE OF ERROR OR FALLACY.--THE INNER SOPHIST.
Why describe Logic as a system of defence against error? Why say that
its main end and aim is the organisation of reason against confusion
and falsehood? Why not rather say, as is now usual, that its end is
the attainment of truth? Does this not come to the same thing?
Substantially, the meaning is the same, but the latter expression
is more misleading. To speak of Logic as a body of rules for the
investigation of truth has misled people into supposing that Logic
claims to be an art of Discovery, that it claims to lay down rules
by simply observing which investigators may infallibly arrive at new
truths. Now, this does not hold even of the Logic of Induction, still
less of the older Logic, the precise relation of which to truth will
become apparent as we proceed. It is only by keeping men from going
astray and by disabusing them when they think they have reached their
destination that Logic helps men on the road to truth. Truth often
lies hid in the centre of a maze, and logical rules only help the
searcher onwards by giving him warning when he is on the wrong track
and must try another. It is the searcher's own impulse that carries
him forward: Logic does not so much beckon him on to the right path
as beckon him back from the wrong. In laying down the conditions of
correct interpretation, of valid argument, of trustworthy evidence,
of satisfactory explanation, Logic shows the inquirer how to test and
purge his conclusions, not how to reach them.
To discuss, as is sometimes done, whether Fallacies lie within the
proper sphere of Logic, is to obscure the real connexion between
Fallacies and Logic. It is the existence of Fallacies that calls Logic
into existence; as a practical science Logic is needed as a protection
against Fallacies. Such historically is its origin. We may, if we
like, lay down an arbitrary rule that a treatise on Logic should be
content to expound the correct forms of interpretation and reasoning
and should not concern itself with the wrong. If we take this view we
are bound to pronounce Fallacies extra-logical. But to do so is
simply to cripple the usefulness of Logic as a practical science.
The manipulation of the bare logical forms, without reference to
fallacious departures from them, is no better than a nursery exercise.
Every correct form in Logic is laid down as a safeguard against some
erroneous form to which men are prone, whether in the interpretation
of argument or the interpretation of experience, and the statement and
illustration of the typical forms of wrong procedure should accompany
_pari passu_ the exposition of the right procedure.
In accordance with this principle, I shall deal with special
fallacies, special snares or pitfalls--misapprehension of words,
misinterpretation of propositions, misunderstanding of arguments,
misconstruction of facts, evidences, or signs--each in connexion
with its appropriate safeguard. This seems to me the most profitable
method. But at this stage, it may be worth while, by way of
emphasising the need for Logic as a science of rational belief, to
take a survey of the most general tendencies to irrational belief,
the chief kinds of illusion or bias that are rooted in the human
constitution. We shall then better appreciate the magnitude of the
task that Logic attempts in seeking to protect reason against its own
fallibility and the pressure of the various forces that would usurp
its place.
It is a common notion that we need Logic to protect us against the
arts of the Sophist, the dishonest juggler with words and specious
facts. But in truth the Inner Sophist, whose instruments are our own
inborn propensities to error, is a much more dangerous enemy. For once
that we are the victims of designing Sophists, we are nine times the
victims of our own irrational impulses and prejudices. Men generally
deceive themselves before they deceive others.
Francis Bacon drew attention to these inner perverting influences,
these universal sources of erroneous belief, in his _De Augmentis_
and again in his _Novum Organum_, under the designation of _Idola_
([Greek: eidola]), deceptive appearances of truth, illusions. His
classification of _Idola--Idola Tribus_, illusions common to all men,
illusions of the race; _Idola Specus_, personal illusions, illusions
peculiar to the "den" in which each man lives; _Idola Fori_, illusions
of conversation, vulgar prejudices embodied in words; _Idola Theatri_,
illusions of illustrious doctrine, illusions imposed by the dazzling
authority of great names--is defective as a classification inasmuch as
the first class includes all the others, but like all his writings it
is full of sagacious remarks and happy examples. Not for the sake of
novelty, but because it is well that matters so important should be
presented from more than one point of view, I shall follow a division
adapted from the more scientific, if less picturesque, arrangement
of Professor Bain, in his chapter on the Fallacious Tendencies of the
Human Mind.[1]
The illusions to which we are all subject may best be classified
according to their origin in the depths of our nature. Let us try to
realise how illusory beliefs arise.
What is a belief? One of the uses of Logic is to set us thinking about
such simple terms. An exhaustive analysis and definition of belief is
one of the most difficult of psychological problems. We cannot enter
upon that: let us be content with a few simple characters of belief.
First, then, belief is a state of mind. Second, this state of mind is
outward-pointing: it has a reference beyond itself, a reference to the
order of things outside us. In believing, we hold that the world as it
is, has been, or will be, corresponds to our conceptions of it.
Third, belief is the guide of action: it is in accordance with what we
believe that we direct our activities. If we want to know what a man
really believes, we look at his action. This at least is the clue to
what he believes at the moment. "I cannot," a great orator once said,
"read the minds of men." This was received with ironical cheers. "No,"
he retorted, "but I can construe their acts." Promoters of companies
are expected to invest their own money as a guarantee of good faith.
If a man says he believes the world is coming to an end in a year,
and takes a lease of a house for fifteen years, we conclude that his
belief is not of the highest degree of strength.
The close connexion of belief with our activities, enables us to
understand how illusions, false conceptions of reality, arise. The
illusions of Feeling and the illusions of Custom are well understood,
but other sources of illusion, which may be designated Impatient
Impulse and Happy Exercise, are less generally recognised. An example
or two will show what is meant. We cannot understand the strength of
these perverting influences till we realise them in our own case. We
detect them quickly enough in others. Seeing that in common speech the
word illusion implies a degree of error amounting almost to insanity,
and the illusions we speak of are such as no man is ever quite free
from, it is perhaps less startling to use the word _bias_.
_The Bias of Impatient Impulse._
As a being formed for action, not only does healthy man take
a pleasure in action, physical and mental, for its own sake,
irrespective of consequences, but he is so charged with energy that
he cannot be comfortable unless it finds a free vent. In proportion
to the amount and excitability of his energy, restraint, obstruction,
delay is irksome, and soon becomes a positive and intolerable pain.
Any bar or impediment that gives us pause is hateful even to think of:
the mere prospect annoys and worries.
Hence it arises that belief, a feeling of being prepared for action,
a conviction that the way is clear before us for the free exercise of
our activities, is a very powerful and exhilarating feeling, as much
a necessity of happy existence as action itself. We see this when we
consider how depressing and uncomfortable a condition is the opposite
state to belief, namely, doubt, perplexity, hesitation, uncertainty as
to our course. And realising this, we see how strong a bias we have in
this fact of our nature, this imperious inward necessity for action;
how it urges us to act without regard to consequences, and to jump at
beliefs without inquiry. For, unless inquiry itself is our business, a
self-sufficient occupation, it means delay and obstruction.
This ultimate fact of our nature, this natural inbred constitutional
impatience, explains more than half of the wrong beliefs that we form
and persist in. We must have a belief of some kind: we cannot be happy
till we get it, and we take up with the first that seems to show the
way clear. It may be right or it may be wrong: it is not, of course,
necessarily always wrong: but that, so far as we are concerned, is a
matter of accident. The pressing need for a belief of some sort, upon
which our energies may proceed in anticipation at least, will not
allow us to stop and inquire. Any course that offers a relief from
doubt and hesitation, any conviction that lets the will go free, is
eagerly embraced.
It may be thought that this can apply only to beliefs concerning
the consequences of our own personal actions, affairs in which we
individually play a part. It is from them, no doubt, that our nature
takes this set: but the habit once formed is extended to all sorts
of matters in which we have no personal interest. Tell an ordinary
Englishman, it has been wittily said, that it is a question whether
the planets are inhabited, and he feels bound at once to have a
confident opinion on the point. The strength of the conviction bears
no proportion to the amount of reason spent in reaching it, unless it
may be said that as a general rule the less a belief is reasoned the
more confidently it is held.
"A grocer," writes Mr. Bagehot in an acute essay on "The Emotion of
Conviction,"[2] "has a full creed as to foreign policy, a young lady a
complete theory of the Sacraments, as to which neither has any doubt.
A girl in a country parsonage will be sure that Paris never can be
taken, or that Bismarck is a wretch." An attitude of philosophic
doubt, of suspended judgment, is repugnant to the natural man. Belief
is an independent joy to him.
This bias works in all men. While there is life, there is pressure
from within on belief, tending to push reason aside. The force of
the pressure, of course, varies with individual temperament, age, and
other circumstances. The young are more credulous than the old, as
having greater energy: they are apt, as Bacon puts it, to be "carried
away by the sanguine element in their temperament". Shakespeare's
Laertes is a study of the impulsive temperament, boldly contrasted
with Hamlet, who has more discourse of reason. When Laertes hears that
his father has been killed, he hurries home, collects a body of armed
sympathisers, bursts into the presence of the king, and threatens with
his vengeance--the wrong man. He never pauses to make inquiry: like
Hotspur he is "a wasp-stung and impatient fool"; he must wreak his
revenge on somebody, and at once. Hamlet's father also has been
murdered, but his reason must be satisfied before he proceeds to his
revenge, and when doubtful proof is offered, he waits for proof more
relative.
Bacon's _Idola Tribus_ and Dr. Bain's illustrations of incontinent
energy, are mostly examples of unreasoning intellectual activity,
hurried generalisations, unsound and superficial analogies, rash
hypotheses. Bacon quotes the case of the sceptic in the temple of
Poseidon, who, when shown the offerings of those who had made vows
in danger and been delivered, and asked whether he did not now
acknowledge the power of the god, replied: "But where are they who
made vows and yet perished?" This man answered rightly, says Bacon.
In dreams, omens, retributions, and such like, we are apt to remember
when they come true and to forget the cases when they fail. If we
have seen but one man of a nation, we are apt to conclude that all his
countrymen are like him; we cannot suspend our judgment till we have
seen more. Confident belief, as Dr. Bain remarks, is the primitive
attitude of the human mind: it is only by slow degrees that this is
corrected by experience. The old adage, "Experience teaches fools,"
has a meaning of its own, but in one sense it is the reverse of the
truth. The mark of a fool is that he is not taught by experience, and
we are all more or less intractable pupils, till our energies begin to
fail.
_The Bias of Happy Exercise._
If an occupation is pleasant in itself, if it fully satisfies our
inner craving for action, we are liable to be blinded thereby to its
consequences. Happy exercise is the fool's Paradise. The fallacy lies
not in being content with what provides a field for the full activity
of our powers: to be content in such a case may be the height of
wisdom: but the fallacy lies in claiming for our occupation results,
benefits, utilities that do not really attend upon it. Thus we see
subjects of study, originally taken up for some purpose, practical,
artistic, or religious, pursued into elaborate detail far beyond their
original purpose, and the highest value, intellectual, spiritual,
moral, claimed for them by their votaries, when in truth they merely
serve to consume so much vacant energy, and may be a sheer waste of
time that ought to be otherwise employed.
But as I am in danger of myself furnishing an illustration of this
bias--it is nowhere more prevalent than in philosophy--I will pass to
our next head.
_The Bias of the Feelings._
This source of illusion is much more generally understood. The
blinding and perverting influence of passion on reason has been a
favourite theme with moralists ever since man began to moralise, and
is acknowledged in many a popular proverb. "Love is blind;" "The wish
is father to the thought;" "Some people's geese are all swans;" and so
forth.
We need not dwell upon the illustration of it. Fear and Sloth magnify
dangers and difficulties; Affection can see no imperfection in its
object: in the eyes of Jealousy a rival is a wretch. From the nature
of the case we are much more apt to see examples in others than in
ourselves. If the strength of this bias were properly understood by
everybody, the mistake would not so often be committed of suspecting
bad faith, conscious hypocrisy, when people are found practising
the grossest inconsistencies, and shutting their eyes apparently in
deliberate wilfulness to facts held under their very noses. Men are
inclined to ascribe this human weakness to women. Reasoning from
feeling is said to be feminine logic. But it is a human weakness.
To take one very powerful feeling, the feeling of self-love or
self-interest--this operates in much more subtle ways than most people
imagine, in ways so subtle that the self-deceiver, however honest,
would fail to be conscious of the influence if it were pointed out to
him. When the slothful man saith, There is a lion in the path, we can
all detect the bias to his belief, and so we can when the slothful
student says that he will work hard to-morrow, or next week, or next
month; or when the disappointed man shows an exaggerated sense of
the advantages of a successful rival or of his own disadvantages. But
self-interest works to bias belief in much less palpable ways than
those. It is this bias that accounts for the difficulty that men of
antagonistic interests have in seeing the arguments or believing
in the honesty of their opponents. You shall find conferences
held between capitalists and workmen in which the two sides, both
represented by men incapable of consciously dishonest action, fail
altogether to see the force of each other's arguments, and are
mutually astonished each at the other's blindness.
_The Bias of Custom._
That custom, habits of thought and practice, affect belief, is also
generally acknowledged, though the strength and wide reach of the bias
is seldom realised. Very simple cases of unreasoning prejudice were
adduced by Locke, who was the first to suggest a general explanation
of them in the "Association of Ideas" (_Human Understanding_, bk. ii.
ch. xxxiii.). There is, for instance, the fear that overcomes many
people when alone in the dark. In vain reason tells them that there is
no real danger; they have a certain tremor of apprehension that they
cannot get rid of, because darkness is inseparably connected in
their minds with images of horror. Similarly we contract unreasonable
dislikes to places where painful things have happened to us. Equally
unreasoning, if not unreasonable, is our attachment to customary
doctrines or practices, and our invincible antipathy to those who do
not observe them.
Words are very common vehicles for the currency of this kind of
prejudice, good or bad meanings being attached to them by custom. The
power of words in this way is recognised in the proverb: "Give a dog
a bad name, and then hang him". These verbal prejudices are Bacon's
_Idola Fori_, illusions of conversation. Each of us is brought up in a
certain sect or party, and accustomed to respect or dishonour
certain sectarian or party names, Whig, Tory, Radical, Socialist,
Evolutionist, Broad, Low, or High Church. We may meet a man without
knowing under what label he walks and be charmed with his company:
meet him again when his name is known, and all is changed.
Such errors are called Fallacies of Association to point to the
psychological explanation. This is that by force of association
certain ideas are brought into the mind, and that once they are there,
we cannot help giving them objective reality. For example, a doctor
comes to examine a patient, and finds certain symptoms. He has lately
seen or heard of many cases of influenza, we shall say; influenza is
running in his head. The idea once suggested has all the advantage of
possession.
But why is it that a man cannot get rid of an idea? Why does it force
itself upon him as a belief? Association, custom, explains how it got
there, but not why it persists in staying.
To explain this we must call in our first fallacious principle, the
Impatience of Doubt or Delay, the imperative inward need for a belief
of some sort.
And this leads to another remark, that though for convenience of
exposition, we separate these various influences, they are not
separated in practice. They may and often do act all together, the
Inner Sophist concentrating his forces.
Finally, it may be asked whether, seeing that illusions are the
offspring of such highly respectable qualities as excess of energy,
excess of feeling, excess of docility, it is a good thing for man to
be disillusioned. The rose-colour that lies over the world for youth
is projected from the abundant energy and feeling within: disillusion
comes with failing energies, when hope is "unwilling to be fed". Is
it good then to be disillusioned? The foregoing exposition would
be egregiously wrong if the majority of mankind did not resent the
intrusion of Reason and its organising lieutenant Logic. But really
there is no danger that this intrusion succeeds to the extent of
paralysing action and destroying feeling, and uprooting custom.
The utmost that Logic can do is to modify the excess of these good
qualities by setting forth the conditions of rational belief. The
student who masters those conditions will soon see the practical
wisdom of applying his knowledge only in cases where the grounds of
rational belief are within his reach. To apply it to the consequences
of every action would be to yield to that bias of incontinent activity
which is, perhaps, our most fruitful source of error.
[Footnote 1: Bain's _Logic_, bk. vi. chap. iii. Bacon intended
his _Idola_ to bear the same relation to his _Novum Organum_
that Aristotle's Fallacies or Sophistical Tricks bore to the
old Organum. But in truth, as I have already indicated, what
Bacon classifies is our inbred tendencies to form _idola_ or
false images, and it is these same tendencies that make
us liable to the fallacies named by Aristotle. Some of
Aristotle's, as we shall see, are fallacies of Induction.]
[Footnote 2: Bagehot's _Literary Studies_, ii. 427.]
III.--THE AXIOMS OF DIALECTIC AND OF SYLLOGISM.
There are certain principles known as the Laws of Thought or the
Maxims of Consistency. They are variously expressed, variously
demonstrated, and variously interpreted, but in one form or another
they are often said to be the foundation of all Logic. It is even said
that all the doctrines of Deductive or Syllogistic Logic may be educed
from them. Let us take the most abstract expression of them, and see
how they originated. Three laws are commonly given, named respectively
the Law of Identity, the Law of Contradiction and the Law of Excluded
Middle.
1. _The Law of Identity._ A is A. Socrates is Socrates. Guilt is
guilt.
2. _The Law of Contradiction._ A is not not-A. Socrates is not other
than Socrates. Guilt is not other than guilt. Or A is not at once _b_
and not-_b_. Socrates is not at once good and not-good. Guilt is not
at once punishable and not-punishable.
3. _The Law of Excluded Middle._ Everything is either A or not-A;
or, A is either _b_ or not-_b_. A given thing is either Socrates
or not-Socrates, either guilty or not-guilty. It must be one or the
other: no middle is possible.
Why lay down principles so obvious, in some interpretations, and so
manifestly sophistical in others? The bare forms of modern Logic have
been reached by a process of attenuation from a passage in Aristotle's
_Metaphysics_[1] (iii. 3, 4, 1005_b_ - 1008). He is there laying down
the first principle of demonstration, which he takes to be that "it is
impossible that the same predicate can both belong, and not belong,
to the same subject, at the same time, and in the same sense".[2]
That Socrates knows grammar, and does not know grammar--these two
propositions cannot both be true at the same time, and in the same
sense. Two contraries cannot exist together in the same subject. The
double answer Yes and No cannot be given to one and the same question
understood in the same sense.
But why did Aristotle consider it necessary to lay down a principle
so obvious? Simply because among the subtle dialecticians who
preceded him the principle had been challenged. The Platonic dialogue
Euthydemus shows the farcical lengths to which such quibbling was
carried. The two brothers vanquish all opponents, but it is by
claiming that the answer No does not preclude the answer Yes. "Is not
the honourable honourable, and the base base?" asks Socrates. "That is
as I please," replies Dionysodorus. Socrates concludes that there
is no arguing with such men: they repudiate the first principles of
dialectic.
There were, however, more respectable practitioners who canvassed on
more plausible grounds any form into which ultimate doctrines about
contraries and contradictions, truth and falsehood, could be put, and
therefore Aristotle considered it necessary to put forth and defend
at elaborate length a statement of a first principle of demonstration.
"Contradictions cannot both be true of the same subject at the same
time and in the same sense." This is the original form of the Law of
Contradiction.
The words "of the same subject," "at the same time," and "in the
same sense," are carefully chosen to guard against possible quibbles.
"_Socrates knows grammar._" By Socrates we must mean the same
individual man. And even of the same man the assertion may be true at
one time and not at another. There was a time when Socrates did not
know grammar, though he knows it now. And the assertion may be true
in one sense and not in another. It may be true that Socrates knows
grammar, yet not that he knows everything that is to be known about
grammar, or that he knows as much as Aristarchus.
Aristotle acknowledges that this first principle cannot itself be
demonstrated, that is, deduced from any other. If it is denied, you
can only reduce the denier to an absurdity. And in showing how to
proceed in so doing, he says you must begin by coming to an agreement
about the words used, that they signify the same for one and the other
disputant.[3] No dialectic is possible without this understanding.
This first principle of Dialectic is the original of the Law of
Identity. While any question as to the truth or falsehood of a
question is pending, from the beginning to the end of any logical
process, the words must continue to be accepted in the same sense.
Words must have an identical reference to things.
Incidentally in discussing the Axiom of Contradiction ([Greek:
axioma tes antiphaseos]),[4] Aristotle lays down what is now known
as the Law of Excluded Middle. Of two contradictories one or other
must be true: we must either affirm or deny any one thing of any
other: no mean or middle is possible.
In their origin, then, these so-called Laws of Thought were simply the
first principles of Dialectic and Demonstration. Consecutive argument,
coherent ratiocination, is impossible unless they are taken for
granted.
If we divorce or abstract them from their original application, and
consider them merely as laws of thinking or of being, any abstract
expression, or illustration, or designation of them may easily be
pushed into antagonism with other plain truths or first principles
equally rudimentary. Without entering into the perplexing and
voluminous discussion to which these laws have been subjected by
logicians within the last hundred years, a little casuistry is
necessary to enable the student to understand within what limits they
hold good.
_Socrates is Socrates._ The name Socrates is a name for something to
which you and I refer when we use the name. Unless we have the same
reference, we cannot hold any argument about the thing, or make any
communication one to another about it.
But if we take _Socrates is Socrates_ to mean that, "An object of
thought or thing is identical with itself," "An object of thought or
thing cannot be other than itself," and call this a law of thought, we
are met at once by a difficulty. Thought, properly speaking, does
not begin till we pass beyond the identity of an object with itself.
Thought begins only when we recognise the likeness between one object
and others. To keep within the self-identity of the object is to
suspend thought. "Socrates was a native of Attica," "Socrates was
a wise man," "Socrates was put to death as a troubler of the
commonweal"--whenever we begin to think or say anything about
Socrates, to ascribe any attributes to him, we pass out of his
self-identity into his relations of likeness with other men, into what
he has in common with other men.
Hegelians express this plain truth with paradoxical point when they
say: "Of any definite existence or thought, therefore, it may be said
with quite as much truth that it _is not_, as that it _is_, its own
bare self".[5] Or, "A thing must other itself in order to be itself".
Controversialists treat this as a subversion of the laws of Identity
and Contradiction. But it is only Hegel's fun--his paradoxical way of
putting the plain truth that any object has more in common with other
objects than it has peculiar to itself. Till we enter into those
aspects of agreement with other objects, we cannot truly be said to
think at all. If we say merely that a thing is itself, we may as well
say nothing about it. To lay down this is not to subvert the Law of
Identity, but to keep it from being pushed to the extreme of appearing
to deny the Law of Likeness, which is the foundation of all the
characters, attributes, or qualities of things in our thoughts.
That self-same objects are like other self-same objects, is an
assumption distinct from the Law of Identity, and any interpretation
of it that excludes this assumption is to be repudiated. But does not
the law of Identity as well as the law of the likeness of mutually
exclusive identities presuppose that there are objects self-same,
like others, and different from others? Certainly: this is one of the
presuppositions of Logic.[6] We assume that the world of which we talk
and reason is separated into such objects in our thoughts. We assume
that such words as _Socrates_ represent individual objects with a
self-same being or substance; that such words as _wisdom_, _humour_,
_ugliness_, _running_, _sitting_, _here_, _there_, represent
attributes, qualities, characters or predicates of individuals; that
such words as _man_ represent groups or classes of individuals.
Some logicians in expressing the Law of Identity have their eye
specially upon the objects signified by general names or abstract
names, _man_, _education_.[7] "A concept is identical with the sum
of its characters," or, "Classes are identical with the sum of
the individuals composing them". The assumptions thus expressed in
technical language which will hereafter be explained are undoubtedly
assumptions that Logic makes: but since they are statements of the
internal constitution of some of the identities that words represent,
to call them the Law of Identity is to depart confusingly from
traditional usage.[8]
That throughout any logical process a word must signify the same
object, is one proposition: that the object signified by a general
name is identical with the sum of the individuals to each of whom it
is applicable, or with the sum of the characters that they bear in
common, is another proposition. Logic assumes both: Aristotle assumed
both: but it is the first that is historically the original of all
expressions of the Law of Identity in modern text-books.
Yet another expression of a Law of Identity which is really distinct
from and an addition to Aristotle's original. _Socrates was an
Athenian, a philosopher, an ugly man, an acute dialectician, etc._
Let it be granted that the word Socrates bears the same signification
throughout all these and any number more of predicates, we may still
ask: "But what is it that Socrates signifies?" The title Law of
Identity is sometimes given[9] to a theory on this point. _Socrates is
Socrates._ "An individual is the identity running through the totality
of its attributes." Is this not, it may be asked, to confuse thought
and being, to resolve Socrates into a string of words? No: real
existence is one of the admissible predicates of Socrates: one of
the attributes under which we conceive him. But whether we accept
or reject this "Law of Identity," it is an addition to Aristotle's
dialectical "law of identity"; it is a theory of the metaphysical
nature of the identity signified by a Singular name. And the same may
be said of yet another theory of Identity, that, "An individual is
identical with the totality of its predicates," or (another way
of putting the same theory), "An individual is a conflux of
generalities".
To turn next to the Laws of Contradiction and Excluded Middle. These
also may be subjected to Casuistry, making clearer what they assert by
showing what they do not deny.
They do not deny that things change, and that successive states of the
same thing may pass into one another by imperceptible degrees. A thing
may be neither here nor there: it may be on the passage from here to
there: and, while it is in motion, we may say, with equal truth, that
it is neither here nor there, or that it is both here and there. Youth
passes gradually into age, day into night: a given man or a given
moment may be on the borderland between the two.
Logic does not deny the existence of indeterminate margins: it merely
lays down that for purposes of clear communication and coherent
reasoning the line must be drawn somewhere between _b_, and not-_b_.
A difference, however, must be recognised between logical negation
and the negations of common thought and common speech. The latter are
definite to a degree with which the mere Logic of Consistency does
not concern itself. To realise this is to understand more clearly the
limitations of Formal Logic.
In common speech, to deny a quality of anything is by implication to
attribute to it some other quality of the same kind. Let any man tell
me that "the streets of such and such a town are not paved with wood,"
I at once conclude that they are paved with some other material. It
is the legitimate effect of his negative proposition to convey this
impression to my mind. If, proceeding on this, I go on to ask: "Then
they are paved with granite or asphalt, or this or that?" and he turns
round and says: "I did not say they were paved at all," I should be
justified in accusing him of a quibble. In ordinary speech, to deny
one kind of pavement is to assert pavement of some kind. Similarly, to
deny that So-and-so is not in the Twenty-first Regiment, is to
imply that he is in another regiment, that he is in the army in some
regiment. To retort upon this inference: "He is not in the army at
all," is a quibble: as much so as it would be to retort: "There is no
such person in existence".
Now Logic does not take account of this implication, and nothing has
contributed more to bring upon it the reproach of quibbling. In Logic,
to deny a quality is simply to declare a repugnance between it and the
subject; negation is mere sublation, taking away, and implies nothing
more. Not-_b_ is entirely indefinite: it may cover anything except
_b_.
Is Logic then really useless, or even misleading, inasmuch as it
ignores the definite implication of negatives in ordinary thought
and speech? In ignoring this implication, does Logic oppose this
implication as erroneous? Does Logic shelter the quibbler who
trades upon it? By no means: to jump to this conclusion were a
misunderstanding. The fact only is that nothing beyond the logical
Law of Contradiction needs to be assumed for any of the processes
of Formal Logic. Aristotle required to assume nothing more for his
syllogistic formulae, and Logic has not yet included in its scope any
process that requires any further assumption. "If not-_b_ represent
everything except _b_, everything outside _b_, then that A is _b_, and
that A is not-_b_, cannot both be true, and one or other of them must
be true."
Whether the scope of Logic ought to be extended is another question.
It seems to me that the scope of Logic may legitimately be extended so
as to take account both of the positive implication of negatives and
the negative implication of positives. I therefore deal with this
subject in a separate chapter following on the ordinary doctrines of
Immediate Inference, where I try to explain the simple Law of Thought
involved. When I say that the extension is legitimate, I mean that it
may be made without departing from the traditional view of Logic as
a practical science, conversant with the nature of thought and its
expression only in so far as it can provide practical guidance against
erroneous interpretations and inferences. The extension that I propose
is in effect an attempt to bring within the fold of Practical Logic
some of the results of the dialectic of Hegel and his followers,
such as Mr. Bradley and Mr. Bosanquet, Professor Caird and Professor
Wallace.[10]
The logical processes formulated by Aristotle are merely stages in the
movement of thought towards attaining definite conceptions of reality.
To treat their conclusions as positions in which thought may dwell and
rest, is an error, against which Logic itself as a practical science
may fairly be called upon to guard. It may even be conceded that the
Aristotelian processes are artificial stages, courses that thought
does not take naturally, but into which it has to be forced for a
purpose. To concede this is not to concede that the Aristotelian logic
is useless, as long as we have reason on our side in holding that
thought is benefited and strengthened against certain errors by
passing through those artificial stages.
[Footnote 1: The first statement of the Law of Identity in the
form _Ens est ens_ is ascribed by Hamilton (_Lectures_, iii.
91) to Antonius Andreas, a fourteenth century commentator
on the _Metaphysics_. But Andreas is merely expounding what
Aristotle sets forth in iii. 4, 1006 _a, b_. _Ens est ens_
does not mean in Andreas what A is A means in Hamilton.]
[Footnote 2: Greek: to gar auto hama huparchein te kai me
huparchein adynaton to auto kai kata to auto, . . . ahute de
pason esti bebaiotate ton archon. iii. 3, 1005_b_, 19-23.]
[Footnote 3: Hamilton credits Andreas with maintaining,
"against Aristotle," that "the principle of Identity, and not
the principle of Contradiction, is the one absolutely first".
Which comes first, is a scholastic question on which ingenuity
may be exercised. But in fact Aristotle put the principle
of Identity first in the above plain sense, and Andreas only
expounded more formally what Aristotle had said.]
[Footnote 4: [Greek: Metaxu antiphaseos endechetai einai outhen,
all' ananke e phanai e apophanai en kath henos hotioun.]
_Metaph._ iii. 7, 1011_b_, 23-4.]
[Footnote 5: Prof. Caird's _Hegel_, p. 138.]
[Footnote 6: See Venn, _Empirical Logic_, 1-8.]
[Footnote 7: _E.g._, Hamilton, lect. v.; Veitch's _Institutes
of Logic_, chaps, xii., xiii.]
[Footnote 8: The confusion probably arises in this way. First,
these "laws" are formulated as laws of thought that Logic
assumes. Second, a notion arises that these laws are the
only postulates of Logic: that all logical doctrines can be
"evolved" from them. Third, when it is felt that more than the
identical reference of words or the identity of a thing
with itself must be assumed in Logic, the Law of Identity is
extended to cover this further assumption.]
[Footnote 9: _E.g._, Bosanquet's _Logic_, ii. 207.]
[Footnote 10: Bradley, _Principles of Logic_; Bosanquet,
_Logic or The Morphology of Knowledge_; Caird, _Hegel_ (in
Blackwood's Philosophical Classics); Wallace, _The Logic of
Hegel_.]
BOOK I.
THE LOGIC OF CONSISTENCY. SYLLOGISM AND DEFINITION.
PART I.
THE ELEMENTS OF PROPOSITIONS.
CHAPTER I.
GENERAL NAMES AND ALLIED DISTINCTIONS.
To discipline us against the errors we are liable to in receiving
knowledge through the medium of words--such is one of the objects of
Logic, the main object of what may be called the Logic of Consistency.
Strictly speaking, we may receive knowledge about things through signs
or single words, as a nod, a wink, a cry, a call, a command. But an
assertory sentence, proposition, or predication, is the unit with
which Logic concerns itself--a sentence in which a subject is
named and something is said or predicated about it. Let a man once
understand the errors incident to this regular mode of communication,
and he may safely be left to protect himself against the errors
incident to more rudimentary modes.
A proposition, whether long or short, is a unit, but it is an
analysable unit. And the key to syllogistic analysis is the General
Name. Every proposition, every sentence in which we convey knowledge
to another, contains a general name or its equivalent. That is to say,
every proposition may be resolved into a form in which the predicate
is a general name. A knowledge of the function of this element of
speech is the basis of all logical discipline. Therefore, though we
must always remember that the proposition is the real unit of speech,
and the general name only an analytic element, we take the general
name and its allied distinctions in thought and reality first.
How propositions are analysed for syllogistic purposes will be shown
by-and-by, but we must first explain various technical terms that
logicians have devised to define the features of this cardinal
element. The technical terms CLASS, CONCEPT, NOTION, ATTRIBUTE,
EXTENSION or DENOTATION, INTENSION or CONNOTATION, GENUS, SPECIES,
DIFFERENTIA, SINGULAR NAME, COLLECTIVE NAME, ABSTRACT NAME, all centre
round it.
A general name is a name applicable to a number of different things on
the ground of some likeness among them, as _man_, _ratepayer_, _man of
courage_, _man who fought at Waterloo_.
From the examples it will be seen that a general name logically is
not necessarily a single word. Any word or combination of words that
serves a certain function is technically a general name. The different
ways of making in common speech the equivalent of a general name
logically are for the grammarian to consider.
In the definition of a general name attention is called to two
distinct considerations, the individual objects to each of which
the name is applicable, and the points of resemblance among them, in
virtue of which they have a common name. For those distinctions there
are technical terms.
CLASS is the technical term for the objects, different yet agreeing,
to each of which a general name may be applied.
The points of resemblance are called the common ATTRIBUTES of the
class.
A class may be constituted on one attribute or on several.
_Ratepayer_, _woman ratepayer_, _unmarried woman ratepayer_;
_soldier_, _British soldier_, _British soldier on foreign service_.
But every individual to which the general name can be applied must
possess the common attribute or attributes.
These common attributes are also called the NOTION of the class,
inasmuch as it is these that the mind notes or should note when the
general name is applied. CONCEPT is a synonym perhaps in more common
use than notion; the rationale of this term (derived from _con_ and
_capere_, to take or grasp together) being that it is by means of
the points of resemblance that the individuals are grasped or held
together by the mind. These common points are the one in the many, the
same amidst the different, the identity signified by the common name.
The name of an attribute as thought of by itself without reference to
any individual or class possessing it, is called an ABSTRACT name. By
contradistinction, the name of an individual or a class is CONCRETE.
Technical terms are wanted also to express the relation of the
individuals and the attributes to the general name. The individuals
jointly are spoken of as the DENOTATION, or EXTENSION or SCOPE of
the name; the common attributes as its CONNOTATION, INTENSION,
COMPREHENSION, or GROUND. The whole denotation, etc., is the class;
the whole connotation, etc., is the concept.[1] The limits of a
"class" in Logic are fixed by the common attributes. Any individual
object that possesses these is a member. The statement of them is the
DEFINITION.
To predicate a general name of any object, as, "This is a cat," "This
is a very sad affair," is to refer that object to a class, which is
equivalent to saying that it has certain features of resemblance with
other objects, that it reminds us of them by its likeness to them.
Thus to say that the predicate of every proposition is a general name,
expressed or implied, is the same as to say that every predication may
be taken as a reference to a class.
Ordinarily our notion or concept of the common features signified by
general names is vague and hazy. The business of Logic is to make them
clear. It is to this end that the individual objects of the class are
summoned before the mind. In ordinary thinking there is no definite
array or muster of objects: when we think of "dog" or "cat,"
"accident," "book," "beggar," "ratepayer," we do not stop to call
before the mind a host of representatives of the class, nor do we take
precise account of their common attributes. The concept of "house" is
what all houses have in common. To make this explicit would be no
easy matter, and yet we are constantly referring objects to the
class "house". We shall see presently that if we wish to make the
connotation or concept clear we must run over the denotation or class,
that is to say, the objects to which the general name is applied in
common usage. Try, for example, to conceive clearly what is meant
by house, tree, dog, walking-stick. You think of individual objects,
so-called, and of what they have in common.
A class may be constituted on one property or on many. There are
several points common to all houses, enclosing walls, a roof, a means
of exit and entrance. For the full concept of the natural kinds,
_men_, _dogs_, _mice_, etc., we should have to go to the natural
historian.
DEGREES OF GENERALITY. One class is said to be of higher generality
than another when it includes that other and more. Thus animal
includes man, dog, horse, etc.; man includes Aryan, Semite, etc.;
Aryan includes Hindoo, Teuton, Celt, etc.
The technical names for higher and lower classes are GENUS and
SPECIES. These terms are not fixed as in Natural History to certain
grades, but are purely relative one to another, and movable up and
down a scale of generality. A class may be a species relatively to one
class, which is above it, and a genus relatively to one below it. Thus
Aryan is a species of the genus man, Teuton a species of the genus
Aryan.
In the graded divisions of Natural History genus and species are fixed
names for certain grades. Thus: Vertebrates form a "division"; the
next subdivision, _e.g._, Mammals, Birds, Reptiles, etc., is called a
"class"; the next, _e.g_., Rodents, Carnivora, Ruminants, an "order";
the next, _e.g._, Rats, Squirrels, Beavers, a "genus"; the next,
_e.g._, Brown rats, Mice, a "species".
Vertebrates (division).
|
Mammals, Birds, Reptiles, etc. (class).
|
Rodents, Ruminants, Carnivors, etc. (order).
|
Rats, Squirrels, Beavers, etc. (genus).
|
Brown rats, Mice, etc. (species).
If we subdivide a large class into smaller classes, and, again,
subdivide these subdivisions, we come at last to single objects.
Men
|
------------
Europeans, Asiatics, etc.
|
-------------
Englishmen, Frenchmen, etc.
|
---------------------
John Doe, Richard Roe, etc.
A table of higher and lower classes arranged in order has been known
from of old as a _tree_ of division or classification. The following
is Porphyry's "tree":--
Being
/ \
Corporeal Incorporeal
\ /
(Body)
/ \
Animate Inanimate
\ /
(Living Being)
/ \
Sensible Insensible
\ /
(Animal)
/ \
Rational Irrational
\ /
(Man)
|
---------------------------------------
Socrates, Plato, and other individuals.
The single objects are called INDIVIDUALS, because the division cannot
be carried farther. The highest class is technically the SUMMUM GENUS,
or _Genus generalissimum_; the next highest class to any species is
the PROXIMUM GENUS; the lowest group before you descend to individuals
is the INFIMA SPECIES, or _Species specialissima_.
The attribute or attributes whereby a species is distinguished
from other species of the same genus, is called its DIFFERENTIA or
DIFFERENTIAE. The various species of houses are differentiated by their
several uses, dwelling-house, town-house, ware-house, public-house.
Poetry is a species of Fine Art, its differentia being the use of
metrical language as its instrument.
A lower class, indicated by the name of its higher class qualified by
adjectives or adjective phrases expressing its differential property
or properties, is said to be described PER GENUS ET DIFFERENTIAM.
Examples: "Black-bird," "note-book," "clever man," "man of Kent,"
"eminent British painter of marine subjects". By giving a combination
of attributes common to him with nobody else, we may narrow down the
application of a name to an individual: "The Commander-in-Chief of the
British forces at the battle of Waterloo".
Other attributes of classes as divided and defined, have received
technical names.
An attribute common to all the individuals of a class, found in that
class only, and following from the essential or defining attributes,
though not included among them, is called a PROPRIUM.
An attribute that belongs to some, but not to all, or that belongs to
all, but is not a necessary consequence of the essential attributes,
is called an ACCIDENT.
The clearest examples of Propria are found in mathematical figures.
Thus, the defining property of an equilateral triangle is the equality
of the sides: the equality of the angles is a proprium. That the
three angles of a triangle are together equal to two right angles is
a proprium, true of all triangles, and deducible from the essential
properties of a triangle.
Outside Mathematics, it is not easy to find _propria_ that satisfy
the three conditions of the definition. It is a useful exercise of
the wits to try for such. Educability--an example of the proprium
in mediaeval text-books--is common to men, and results from man's
essential constitution; but it is not peculiar; other animals are
educable. That man cooks his food is probably a genuine proprium.
That horses run wild in Thibet: that gold is found in California: that
clergymen wear white ties, are examples of Accidents. Learning is an
accident in man, though educability is a proprium.
What is known technically as an INSEPARABLE ACCIDENT, such as the
black colour of the crow or the Ethiopian, is not easy to distinguish
from the Proprium. It is distinguished only by the third character,
deducibility from the essence.[2]
Accidents that are both common and peculiar are often useful for
distinguishing members of a class. Distinctive dresses or badges, such
as the gown of a student, the hood of a D.D., are accidents, but mark
the class of the individual wearer. So with the colours of flowers.
_Genus_, _Species_, _Differentia_, _Proprium_, and _Accidens_ have
been known since the time of Porphyry as the FIVE PREDICABLES. They
are really only terms used in dividing and defining. We shall return
to them and endeavour to show that they have no significance except
with reference to fixed schemes, scientific or popular, of Division or
Classification.
Given such a fixed scheme, very nice questions may be raised as to
whether a particular attribute is a defining attribute, or a proprium,
or an accident, or an inseparable accident. Such questions afford
great scope for the exercise of the analytic intellect.
We shall deal more particularly with degrees of generality when
we come to Definition. This much has been necessary to explain an
unimportant but much discussed point in Logic, what is known as the
inverse variation of Connotation and Denotation.
Connotation and Denotation are often said to vary inversely in
quantity. The larger the connotation the smaller the denotation, and
_vice versa_. With certain qualifications the statement is correct
enough, but it is a rough compendious way of expressing the facts and
it needs qualification.
The main fact to be expressed is that the more general a name is, the
thinner is its meaning. The wider the scope, the shallower the ground.
As you rise in the scale of generality, your classes are wider but the
number of common attributes is less. Inversely, the name of a species
has a smaller denotation than the name of its genus, but a richer
connotation. _Fruit-tree_ applies to fewer objects than _tree_,
but the objects denoted have more in common: so with _apple_ and
_fruit-tree_, _Ribston Pippin_ and _apple_.
Again, as a rule, if you increase the connotation you contract the
area within which the name is applicable. Take any group of things
having certain attributes in common, say, _men of ability_: add
_courage_, _beauty_, _height of six feet_, _chest measurement of 40
inches_, and with each addition fewer individuals are to be found
possessing all the common attributes.
This is obvious enough, and yet the expression inverse variation is
open to objection. For the denotation may be increased in a sense
without affecting the connotation. The birth of an animal may be said
to increase the denotation: every year thousands of new houses are
built: there are swarms of flies in a hot summer and few in a cold.
But all the time the connotation of _animal_, _house_, or _fly_
remains the same: the word does not change its meaning.
It is obviously wrong to say that they vary in inverse proportion.
Double or treble the number of attributes, and you do not necessarily
reduce the denotation by one-half or one-third.
It is, in short, the meaning or connotation that is the main thing.
This determines the application of a word. As a rule if you increase
meaning, you restrict scope. Let your idea, notion, or concept of
_culture_ be a knowledge of Mathematics, Latin and Greek: your _men of
culture_ will be more numerous than if you require from each of them
these qualifications _plus_ a modern language, an acquaintance with
the Fine Arts, urbanity of manners, etc.
It is just possible to increase the connotation without decreasing the
denotation, to thicken or deepen the concept without diminishing
the class. This is possible only when two properties are exactly
co-extensive, as equilaterality and equiangularity in triangles.
SINGULAR and PROPER NAMES. A Proper or Singular name is a name used to
designate an individual. Its function, as distinguished from that of
the general name, is to be used purely for the purpose of distinctive
reference.
A man is not called Tom or Dick because he is like in certain respects
to other Toms or other Dicks. The Toms or the Dicks do not form a
logical class. The names are given purely for purposes of distinction,
to single out an individual subject. The Arabic equivalent for a
Proper name, _alam_, "a mark," "a sign-post," is a recognition of
this.
In the expressions "a Napoleon," "a Hotspur," "a Harry," the names
are not singular names logically, but general names logically, used to
signify the possession of certain attributes.
A man may be nicknamed on a ground, but if the name sticks and is
often used, the original meaning is forgotten. If it suggests
the individual in any one of his qualities, any point in which he
resembles other individuals, it is no longer a Proper or Singular name
logically, that is, in logical function. That function is fulfilled
when it has called to mind the individual intended.
To ask, as is sometimes done, whether Proper names are connotative or
denotative, is merely a confusion of language. The distinction between
connotation and denotation, extension and intension, applies only to
general names. Unless a name is general, it has neither extension nor
intension:[3] a Proper or Singular name is essentially the opposite of
a general name and has neither the one nor the other.
A nice distinction may be drawn between Proper and Singular names,
though they are strict synonyms for the same logical function. It is
not essential to the discharge of that function that the name should
be strictly appropriated to one object. There are many Toms and many
Dicks. It is enough that the word indicates the individual without
confusion in the particular circumstances.
This function may be discharged by words and combinations of words
that are not Proper in the grammatical sense. "This man," "the cover
of this book," "the Prime Minister of England," "the seer of Chelsea,"
may be Singular names as much as Honolulu or Lord Tennyson.
In common speech Singular names are often manufactured _ad hoc_
by taking a general name and narrowing it down by successive
qualifications till it applies only to one individual, as "The leading
subject of the Sovereign of England at the present time". If it so
happens that an individual has some attribute or combination peculiar
to himself, he may be suggested by the mention of that attribute
or combination:--"the inventor of the steam-engine," "the author of
Hudibras".
Have such names a connotation? The student may exercise his wits
on the question. It is a nice one, an excellent subject of debate.
Briefly, if we keep rigid hold of the meaning of connotation, this
Singular name has none. The combination is a singular name only
when it is the subject of a predication or an attribution, as in
the sentences, "The position of the leading subject of etc., is a
difficult one," or "The leading subject of etc., wears an eyeglass".
In such a sentence as "So-and-so is the leading subject of etc.," the
combined name has a connotation, but then it is a general and not a
singular name.
COLLECTIVE NAMES, as distinguished from General Names. A collective
name is a name for a number of similar units taken as a whole--a name
for a totality of similar units, as army, regiment, mob, mankind,
patrimony, personal estate.
A group or collection designated by a collective name is so far like
a class that the individual objects have something in common: they
are not heterogeneous but homogeneous. A mob is a collection of human
beings; a regiment of soldiers; a library of books.
The distinction lies in this, that whatever is said of a collective
name is said about the collection as a whole, and does not apply to
each individual; whatever is said of a general name applies to each
individual. Further, the collective name can be predicated only of
the whole group, as a whole; the general name is predicable of each,
distributively. "Mankind has been in existence for thousands of
years;" "The mob passed through the streets." In such expressions as
"An honest man's the noblest work of God," the subject is functionally
a collective name.
A collective name may be used as a general name when it is extended on
the ground of what is common to all such totalities as it designates.
"An excited mob is dangerous;" "An army without discipline is
useless." The collective name is then "connotative" of the common
characters of the collection.
MATERIAL OR SUBSTANTIAL NAMES. The question has been raised whether
names of material, gold, water, snow, coal, are general or collective
singular. In the case of pieces or bits of a material, it is true that
any predicate made concerning the material, such as "Sugar is sweet,"
or "Water quenches thirst," applies to any and every portion. But
the separate portions are not individuals in the whole signified by
a material name as individuals are in a class. Further, the name of
material cannot be predicated of a portion as a class name can be of
an individual. We cannot say, "This is a sugar". When we say, "This is
a piece of sugar," sugar is a collective name for the whole material.
There are probably words on the borderland between general names and
collective names. In such expressions as "This is a _coal_," "The
bonnie _water_ o' Urie," the material name is used as a general
name. The real distinction is between the distributive use and the
collective use of a name; as a matter of grammatical usage, the same
word may be used either way, but logically in any actual proposition
it must be either one or the other.
ABSTRACT NAMES are names for the common attributes or concepts on
which classes are constituted. A concrete name is a name directly
applicable to an individual in all his attributes, that is, as he
exists in the concrete. It may be written on a ticket and pinned to
him. When we have occasion to speak of the point or points in which a
number of individuals resemble one another, we use what is called an
abstract name. "Generous man," "clever man," "timid man," are concrete
names; "generosity," "cleverness," "timidity," are abstract names.
It is disputed whether abstract names are connotative. The question
is a confused one: it is like asking whether the name of a town is
municipal. An abstract name is the name of a connotation as a separate
object of thought or reference, conceived or spoken of in abstraction
from individual accidents. Strictly speaking it is notative rather
than _con_notative: it cannot be said to have a connotation because
it is itself the symbol of what is called the connotation of a general
name.[4]
The distinction between abstract names and concrete names is
virtually a grammatical distinction, that is, a distinction in mode
of predication. We may use concrete names or abstract names at our
pleasure to express the same meaning. To say that "John is a timid
man" is the same thing as saying that "Timidity is one of the
properties or characteristics or attributes of John". "Pride and
cruelty generally go together;" "Proud men are generally cruel men."
General names are predicable of individuals because they possess
certain attributes: to predicate the possession of those attributes is
the same thing as to predicate the general name.
Abstract forms of predication are employed in common speech quite as
frequently as concrete, and are, as we shall see, a great source of
ambiguity and confusion.
[Footnote 1: It has been somewhat too hastily assumed on the
authority of Mansel (Note to Aldrich, pp. 16, 17) that Mill
inverted the scholastic tradition in his use of the word
_Connotative_. Mansel puts his statement doubtfully, and
admits that there was some licence in the use of the word
Connotative, but holds that in Scholastic Logic an adjective
was said to "signify _primarily_ the attribute, and to
_connote_ or _signify secondarily_ ([Greek: prossemainein])
the subject of inhesion". The truth is that Mansel's view was
a theory of usage not a statement of actual usage, and he had
good reason for putting it doubtfully.
As a matter of fact, the history of the distinction follows
the simple type of increasing precision and complexity, and
Mill was in strict accord with standard tradition. By the
Nominalist commentators on the _Summulae_ of Petrus Hispanus
certain names, adjectives grammatically, are called
_Connotativa_ as opposed to _Absoluta_, simply because they
have a double function. White is connotative as signifying
both a subject, such as Socrates, of whom "whiteness" is an
attribute, and an attribute "whiteness": the names "Socrates"
and "whiteness" are Absolute, as having but a single
signification. Occam himself speaks of the subject as the
primary signification, and the attribute as the secondary,
because the answer to "What is white?" is "Something informed
with whiteness," and the subject is in the nominative case
while the attribute is in an oblique case (_Logic_, part I.
chap. x.). Later on we find that Tataretus (_Expositio in
Summulas_, A.D. 1501), while mentioning (Tract. Sept. _De
Appellationibus_) that it is a matter of dispute among
Doctores whether a connotative name _connotat_ the subject or
the attribute, is perfectly explicit in his own definition,
"Terminus connotativus est qui praeter illud pro quo supponit
connotat aliquid adjacere vel non adjacere rei pro qua
supponit" (Tract. Sept. _De Suppositionibus_). And this
remained the standard usage as long as the distinction
remained in logical text-books. We find it very clearly
expressed by Clichtoveus, a Nominalist, quoted as an authority
by Guthutius in his _Gymnasium Speculativum_, Paris, 1607 (_De
Terminorum Cognitione_, pp. 78-9). "Terminus absolutus est,
qui solum illud pro quo in propositione supponit, significat.
Connotativus autem, qui ultra idipsum, aliud importat." Thus
_man_ and _animal_ are absolute terms, which simply stand
for (supponunt pro) the things they signify. _White_ is a
connotative name, because "it stands for (supponit pro) a
subject in which it is an accident: and beyond this, still
signifies an accident, which is in that subject, and is
expressed by an abstract name". Only Clichtoveus drops the
verb _connotat_, perhaps as a disputable term, and says simply
_ultra importat_.
So in the Port Royal Logic (1662), from which possibly Mill
took the distinction: "Les noms qui signifient les choses
comme modifiees, marquant premierement et directement la
chose, quoique plus confusement, et indirectement le mode,
quoique plus distinctement, sont appeles _adjectifs_ ou
_connotatifs_; comme rond, dur, juste, prudent" (part i. chap
ii.).
What Mill did was not to invert Scholastic usage but to revive
the distinction, and extend the word connotative to general
names on the ground that they also imported the possession
of attributes. The word has been as fruitful of meticulous
discussion as it was in the Renaissance of Logic, though
the ground has changed. The point of Mill's innovation was,
premising that general names are not absolute but are applied
in virtue of a meaning, to put emphasis on this meaning as
the cardinal consideration. What he called the connotation had
dropped out of sight as not being required in the Syllogistic
Forms. This was as it were the point at which he put in his
horn to toss the prevalent conception of Logic as Syllogistic.
The real drift of Mill's innovation has been obscured by
the fact that it was introduced among the preliminaries
of Syllogism, whereas its real usefulness and significance
belongs not to Syllogism in the strict sense but to
Definition. He added to the confusion by trying to devise
forms of Syllogism based on connotation, and by discussing
the Axiom of the Syllogism from this point of view. For
syllogistic purposes, as we shall see, Aristotle's forms are
perfect, and his conception of the proposition in extension
the only correct conception. Whether the centre of gravity in
Consistency Logic should not be shifted back from Syllogism to
Definition, the latter being the true centre of consistency,
is another question. The tendency of Mill's polemic was to
make this change. And possibly the secret of the support it
has recently received from Mr. Bradley and Mr. Bosanquet is
that they, following Hegel, are moving in the same direction.
In effect, Mill's doctrine of Connotation helped to fix
a conception of the general name first dimly suggested by
Aristotle when he recognised that names of genera and species
signify Quality, in showing what sort a thing is. Occam
carried this a step farther towards clear light by including
among Connotative Terms such general names as "monk," name of
classes that at once suggest a definite attribute. The third
step was made by Mill in extending the term Connotation to
such words as "man," "horse," the _Infimae Species_ of the
Schoolmen, the Species of modern science.
Whether connotation was the best term to use for this purpose,
rather than extension, may be questioned: but at least it was
in the line of tradition through Occam.]
[Footnote 2: The history of the definition of the _Proprium_
is an example of the tendency of distinctions to become more
minute and at the same time more purposeless. Aristotle's
[Greek: idion] was an attribute, such as the laugh of the man
or the bark of the dog, common to all of a class and peculiar
to the class (_quod convenit omni soli et semper_) yet not
comprised in the definition of the class. Porphyry recognised
three varieties of [Greek: idia] besides this, four in all,
as follows:--(1) an attribute peculiar to a species but not
possessed by all, as knowledge of medicine or geometry; (2)
possessed by a whole species but not peculiar to it, as being
a biped in man; (3) peculiar to a species, and possessed
by all at a certain time, as turning grey in old age; (4)
Aristotle's "proprium," peculiar and possessed by all, as
risibility. The idea of the Proprium as deducible from or
consequent on the essence would seem to have originated in
the desire to find something common to all Poryphyry's four
varieties.]
[Footnote 3: It is a plausible contention that in the case
of the Singular name the extension is at a minimum and the
intension at a maximum, the extension being one individual,
and the intension the totality of his attributes. But this is
an inexact and confused use of words. A name does not _extend_
beyond the individual except when it is used to signify one
or more of his prominent qualities, that is, is used with the
function of a general name. The _ex_tension of a Singular name
is zero: it has no extension. On the other hand, it suggests,
in its function as a Singular name, no properties or
qualities; it suggests only a subject; _i.e._, it has no
intension. The ambiguity of the term Denotation helps the
confusion in the case of Singular names. "Denote" in common
speech means to indicate, to distinguish. But when in Logic
we say that a general name denotes individuals, we have no
thought of indicating or distinguishing: we mean only that
it is applicable to any one, without respect of individuals,
either in predication or epithetic description.]
[Footnote 4: Strictly speaking, as I have tried to indicate
all along, the words Connotation and Denotation, or Extension
and Intension, apply only to general names. Outside general
names, they have no significance. An adjective with its noun
is a general name, of which the adjective gives part of the
Connotation. If we apply the word connotation to signify
merely the suggestion of an attribute in whatever grammatical
connexion, then an abstract name is undoubtedly as much
connotative as an adjective. The word _Sweetness_ has the same
meaning as _Sweet_: it indicates or signifies, conveys to the
mind of the reader the same attribute: the only difference is
that it does not at the same time indicate a subject in which
the attribute is found, as _sweet apple_. The meaning is not
_con_noted.]
CHAPTER II.
THE SYLLOGISTIC ANALYSIS OF PROPOSITIONS INTO TERMS.
I.--THE BARE ANALYTIC FORMS.
The word "term" is loosely used as a mere synonym for a name: strictly
speaking, a term ([Greek: horos], a boundary) is one of the parts of
a proposition as analysed into Subject and Predicate. In Logic, a term
is a technical word in an analysis made for a special purpose, that
purpose being to test the mutual consistency of propositions.
For this purpose, the propositions of common speech may be viewed as
consisting of two TERMS, a linkword called the copula (positive or
negative) expressing a relation between them, and certain symbols of
quantity used to express that relation more precisely.
Let us indicate the Subject term by S, and the Predicate term by P.
All propositions may be analysed into one or other of four forms:--
All S is P,
No S is P,
Some S is P,
Some S is not P.
All S is P is called the UNIVERSAL AFFIRMATIVE, and is indicated by
the symbol A (the first vowel of Affirmo).
No S is P is called the UNIVERSAL NEGATIVE, symbol E (the first vowel
of Nego).
Some S is P is called the PARTICULAR AFFIRMATIVE, symbol I (the second
vowel of _aff_Irmo).
Some S is not P is called the PARTICULAR NEGATIVE, symbol O (the
second vowel of _neg_O).
The distinction between Universal and Particular is called a
distinction in QUANTITY; between Affirmative and Negative, a
distinction in QUALITY. A and E, I and O, are of the same quantity,
but of different quality: A and I, E and O, same in quality, different
in quantity.
In this symbolism, no provision is made for expressing degrees of
particular quantity. _Some_ stands for any number short of all: it may
be one, few, most, or all but one. The debates in which Aristotle's
pupils were interested turned mainly on the proof or disproof of
general propositions; if only a proposition could be shown to be not
universal, it did not matter how far or how little short it came. In
the Logic of Probability, the degree becomes of importance.
Distinguish, in this Analysis, to avoid subsequent confusion, between
the Subject and the Subject Term, the Predicate and the Predicate
Term. The Subject is the Subject Term quantified: in A and E,[1] "All
S"; in I and O, "Some S". The Predicate is the Predicate Term with the
Copula, positive or negative: in A and I, "is P"; in E and O, "is not
P".
It is important also, in the interest of exactness, to note that S and
P, with one exception, represent general names. They are symbols
for classes. P is so always: S also except when the Subject is an
individual object. In the machinery of the Syllogism, predications
about a Singular term are treated as Universal Affirmatives. "Socrates
is a wise man" is of the form All S is P.
S and P being general names, the signification of the symbol "is" is
not the same as the "is" of common speech, whether the substantive
verb or the verb of incomplete predication. In the syllogistic form,
"is" means _is contained in_, "is not," _is not contained in_.
The relations between the terms in the four forms are represented by
simple diagrams known as Euler's circles.
[Illustration:
1 concentric circles of P and S - S in centre A
2 S and P in the same circle A
3 S and P each in a circle, overlapping circle. I & O
4 S in one circle and P in another circle. E
5 concentric circles of S and P - P in centre I?
]
Diagram 5 is a purely artificial form, having no representative in
common speech. In the affirmations of common speech, P is always a
term of greater extent than S.
No. 2 represents the special case where S and P are coextensive, as in
All equiangular triangles are equilateral.
S and P being general names, they are said to be DISTRIBUTED when the
proposition applies to them in their whole extent, that is, when the
assertion covers every individual in the class.
In E, the Universal Negative, both terms are distributed: "No S is P"
wholly excludes the two classes one from the other, imports that not
one individual of either is in the other.
In A, S is distributed, but not P. S is wholly in P, but nothing is
said about the extent of P beyond S.
In O, S is undistributed, P is distributed. A part of S is declared to
be wholly excluded from P.
In I, neither S nor P is distributed.
It will be seen that the Predicate term of a Negative proposition is
always distributed, of an Affirmative, always undistributed.
A little indistinctness in the signification of P crept into mediaeval
text-books, and has tended to confuse modern disputation about the
import of Predication. Unless P is a class name, the ordinary doctrine
of distribution is nonsense; and Euler's diagrams are meaningless. Yet
many writers who adopt both follow mediaeval usage in treating P as the
equivalent of an adjective, and consequently "is" as identical with
the verb of incomplete predication in common speech.
It should be recognised that these syllogistic forms are purely
artificial, invented for a purpose, namely, the simplification of
syllogising. Aristotle indicated the precise usage on which his
syllogism is based (_Prior Analytics_, i. 1 and 4). His form[2] for
All S is P, is S is wholly in P; for No S is P, S is wholly not in P.
His copula is not "is," but "is in," and it is a pity that this usage
was not kept. "All S is in P" would have saved much confusion. But,
doubtless for the sake of simplicity, the besetting sin of tutorial
handbooks, All S is P crept in instead, illustrated by such examples
as "All men are mortal".
Thus the "is" of the syllogistic form became confused with the "is"
of common speech, and the syllogistic view of predication as
being equivalent to inclusion in, or exclusion from a class, was
misunderstood. The true Aristotelian doctrine is not that predication
consists in referring subjects to classes, but only that for certain
logical purposes it may be so regarded. The syllogistic forms are
artificial forms. They were not originally intended to represent the
actual processes of thought expressed in common speech. To argue
that when I say "All crows are black," I do not form a class of
black things, and contemplate crows within it as one circle is within
another, is to contradict no intelligent logical doctrine.
The root of the confusion lies in quoting sentences from common speech
as examples of the logical forms, forgetting that those forms are
purely artificial. "Omnis homo est mortalis," "All men are mortal," is
not an example formally of All S is P. P is a symbol for a substantive
word or combination of words, and mortal is an adjective. Strictly
speaking, there is no formal equivalent in common speech, that is,
in the forms of ordinary use--no strict grammatical formal
equivalent--for the syllogistic propositional symbols. We can make
an equivalent, but it is not a form that men would use in ordinary
intercourse. "All man is in mortal being" would be a strict
equivalent, but it is not English grammar.
Instead of disputing confusedly whether All S is P should be
interpreted in extension or in comprehension, it would be better to
recognise the original and traditional use of the symbols S and P
as class names, and employ other symbols for the expression in
comprehension or connotation. Thus, let _s_ and _p_ stand for the
connotation. Then the equivalent for All S is P would be All S has
_p_, or _p_ always accompanies _s_, or _p_ belongs to all S.
It may be said that if predication is treated in this way, Logic is
simplified to the extent of childishness. And indeed, the manipulation
of the bare forms with the help of diagrams and mnemonics is a very
humble exercise. The real discipline of Syllogistic Logic lies in the
reduction of common speech to these forms.
This exercise is valuable because it promotes clear ideas about the
use of general names in predication, their ground in thought and
reality, and the liabilities to error that lurk in this fundamental
instrument of speech.
[Footnote 1: For perfect symmetry, the form of E should be
All S is not P. "No S is P" is adopted for E to avoid conflict
with a form of common speech, in which All S is not P conveys
the meaning of the Particular Negative. "All advices are not
safe" does not mean that safeness is denied of all advices,
but that safeness cannot be affirmed of all, _i.e._, Not all
advices are safe, _i.e._, some are not.]
[Footnote 2: His most precise form, I should say, for in "P is
predicated of every S" he virtually follows common speech.]
II.--THE PRACTICE OF SYLLOGISTIC ANALYSIS.
The basis of the analysis is the use of general names in predication.
To say that in predication a subject is referred to a class, is only
another way of saying that in every categorical sentence the predicate
is a general name express or implied: that it is by means of general
names that we convey our thoughts about things to others.
"Milton is a great poet." "Quoth Hudibras, _I smell a rat_." _Great
poet_ is a general name: it means certain qualities, and applies to
anybody possessing them. _Quoth_ implies a general name, a name for
persons _speaking_, connoting or meaning a certain act and applicable
to anybody in the performance of it. _Quoth_ expresses also past time:
thus it implies another general name, a name for persons _in past
time_, connoting a quality which differentiates a species in the genus
persons speaking, and making the predicate term "persons speaking in
past time". Thus the proposition _Quoth Hudibras_, analysed into the
syllogistic form S is in P, becomes S (Hudibras) is in P (persons
speaking in past time). The Predicate term P is a class constituted on
those properties. _Smell a rat_ also implies a general name, meaning
an act or state predicable of many individuals.
Even if we add the grammatical object of _Quoth_ to the analysis, the
Predicate term is still a general name. Hudibras is only one of the
persons speaking in past time who have spoken of themselves as being
in a certain mood of suspicion.[1]
The learner may well ask what is the use of twisting plain speech into
these uncouth forms. The use is certainly not obvious. The analysis
may be directly useful, as Aristotle claimed for it, when we wish
to ascertain exactly whether one proposition contradicts another, or
forms with another or others a valid link in an argument. This is
to admit that it is only in perplexing cases that the analysis is of
direct use. The indirect use is to familiarise us with what the
forms of common speech imply, and thus strengthen the intellect for
interpreting the condensed and elliptical expression in which common
speech abounds.
There are certain technical names applied to the components of
many-worded general names, CATEGOREMATIC and SYNCATEGOREMATIC, SUBJECT
and ATTRIBUTIVE. The distinctions are really grammatical rather than
logical, and of little practical value.
A word that can stand by itself as a term is said to be Categorematic.
_Man_, _poet_, or any other common noun.
A word that can only form part of a term is Syncategorematic. Under
this definition come all adjectives and adverbs.
The student's ingenuity may be exercised in applying the
distinction to the various parts of speech. A verb may be said to be
_Hypercategorematic_, implying, as it does, not only a term, but also
a copula.
A nice point is whether the Adjective is categorematic or
syncategorematic. The question depends on the definition of "term"
in Logic. In common speech an adjective may stand by itself as a
predicate, and so might be said to be Categorematic. "This heart is
merry." But if a term is a class, or the name of a class, it is not
Categorematic in the above definition. It can only help to specify a
class when attached to the name of a higher genus.
Mr. Fowler's words SUBJECT and ATTRIBUTIVE express practically the
same distinction, except that Attributive is of narrower extent than
syncategorematic. An Attributive is a word that connotes an attribute
or property, as _hot_, _valorous_, and is always grammatically an
adjective.
The EXPRESSION OF QUANTITY, that is, of Universality or
non-universality, is all-important in syllogistic formulae. In them
universality is expressed by _All_ or _None_. In ordinary speech
universality is expressed in various forms, concrete and abstract,
plain and figurative, without the use of "all" or "none".
Uneasy lies the head that wears a crown.
He can't be wrong whose life is in the right.
What cat's averse to fish?
Can the leopard change his spots?
The longest road has an end.
Suspicion ever haunts the guilty mind.
Irresolution is always a sign of weakness.
Treason never prospers.
A proposition in which the quantity is not expressed is called by
Aristotle INDEFINITE ([Greek: adioristos]). For "indefinite"[2]
Hamilton suggests PREINDESIGNATE, undesignated, that is, before being
received from common speech for the syllogistic mill. A proposition is
PREDESIGNATE when the quantity is definitely indicated. All the above
propositions are "Predesignate" universals, and reducible to the form
All S is P, or No S is P.
The following propositions are no less definitely particular,
reducible to the form I or O. In them as in the preceding quantity
is formally expressed, though the forms used are not the artificial
syllogistic forms:--
Afflictions are often salutary.
Not every advice is a safe one.
All that glitters is not gold.
Rivers generally[3] run into the sea.
Often, however, it is really uncertain from the form of common speech
whether it is intended to express a universal or a particular. The
quantity is not formally expressed. This is especially the case
with proverbs and loose floating sayings of a general tendency. For
example:--
Haste makes waste.
Knowledge is power.
Light come, light go.
Left-handed men are awkward antagonists.
Veteran soldiers are the steadiest in fight.
Such sayings are in actual speech for the most part delivered as
universals.[4] It is a useful exercise of the Socratic kind to decide
whether they are really so. This can only be determined by a survey of
facts. The best method of conducting such a survey is probably (1)
to pick out the concrete subject, "hasty actions," "men possessed of
knowledge," "things lightly acquired"; (2) to fix the attribute or
attributes predicated; (3) to run over the individuals of the subject
class and settle whether the attribute is as a matter of fact meant to
be predicated of each and every one.
This is the operation of INDUCTION. If one individual can be found of
whom the attribute is not meant to be predicated, the proposition is
not intended as Universal.
Mark the difference between settling what is intended and settling
what is true. The conditions of truth and the errors incident to the
attempt to determine it, are the business of the Logic of Rational
Belief, commonly entitled Inductive Logic. The kind of "induction"
here contemplated has for its aim merely to determine the quantity of
a proposition in common acceptation, which can be done by considering
in what cases the proposition would generally be alleged. This
corresponds nearly as we shall see to Aristotelian Induction, the
acceptance of a universal statement when no instance to the contrary
is alleged.
It is to be observed that for this operation we do not practically use
the syllogistic form All S is P. We do not raise the question Is All
S, P? That is, we do not constitute in thought a class P: the class in
our minds is S, and what we ask is whether an attribute predicated of
this class is truly predicated of every individual of it.
Suppose we indicate by _p_ the attribute, knot of attributes, or
concept on which the class P is constituted, then All S is P is
equivalent to "All S has _p_": and Has All S _p_? is the form of a
question that we have in our minds when we make an inductive survey on
the above method. I point this out to emphasise the fact that there is
no prerogative in the form All S is P except for syllogistic purposes.
This inductive survey may be made a useful COLLATERAL DISCIPLINE. The
bare forms of Syllogistic are a useless item of knowledge unless they
are applied to concrete thought. And determining the quantity of a
common aphorism or saw, the limits within which it is meant to hold
good, is a valuable discipline in exactness of understanding. In
trying to penetrate to the inner intention of a loose general maxim,
we discover that what it is really intended to assert is a general
connexion of attributes, and a survey of concrete cases leads to
a more exact apprehension of those attributes. Thus in considering
whether _Knowledge is power_ is meant to be asserted of all knowledge,
we encounter along with such examples as the sailor's knowledge that
wetting a rope shortens it, which enabled some masons to raise a stone
to its desired position, or the knowledge of French roads possessed by
the German invaders,--along with such examples as these we encounter
cases where a knowledge of difficulties without a knowledge of the
means of overcoming them is paralysing to action. Samuel Daniel
says:--
Where timid knowledge stands considering
Audacious ignorance has done the deed.
Studying numerous cases where "Knowledge is power" is alleged or
denied, we find that what is meant is that a knowledge of the right
means of doing anything is power--in short, that the predicate is not
made of all knowledge, but only of a species of knowledge.
Take, again, _Custom blunts sensibility_. Putting this in the
concrete, and inquiring what predicate is made about "men accustomed
to anything" (S), we have no difficulty in finding examples where such
men are said to become indifferent to it. We find such illustrations
as Lovelace's famous "Paradox":--
Through foul we follow fair
For had the world one face
And earth been bright as air
We had known neither place.
Indians smell not their nest
The Swiss and Finn taste best
The spices of the East.
So men accustomed to riches are not acutely sensible of their
advantages: dwellers in noisy streets cease to be distracted by the
din: the watchmaker ceases to hear the multitudinous ticking in his
shop: the neighbours of chemical works are not annoyed by the smells
like the casual passenger. But we find also that wine-tasters
acquire by practice an unusual delicacy of sense; that the eyes once
accustomed to a dim light begin to distinguish objects that were at
first indistinguishable; and so on. What meanings of "custom" and of
"sensibility" will reconcile these apparently conflicting examples?
What are the exact attributes signified by the names? We should
probably find that by sensibility is meant emotional sensibility as
distinguished from intellectual discrimination, and that by custom is
meant familiarity with impressions whose variations are not attended
to, or subjection to one unvarying impression.
To verify the meaning of abstract proverbs in this way is to travel
over the road by which the Greek dialecticians were led to feel the
importance of definition. Of this more will be said presently. If
it is contended that such excursions are beyond the bounds of Formal
Logic, the answer is that the exercise is a useful one and that it
starts naturally and conveniently from the formulae of Logic. It is the
practice and discipline that historically preceded the Aristotelian
Logic, and in the absence of which the Aristotelian formulae would have
a narrowing and cramping effect.
CAN ALL PROPOSITIONS BE REDUCED TO THE SYLLOGISTIC FORM? Probably: but
this is a purely scientific inquiry, collateral to Practical Logic.
The concern of Practical Logic is chiefly with forms of proposition
that favour inaccuracy or inexactness of thought. When there is no
room for ambiguity or other error, there is no virtue in artificial
syllogistic form. The attempt so to reduce any and every proposition
may lead, however, to the study of what Mr. Bosanquet happily calls
the "Morphology" of Judgment, Judgment being the technical name for
the mental act that accompanies the utterance of a proposition. Even
in such sentences as "How hot it is!" or "It rains," the rudiment of
subject and predicate may be detected. When a man says "How hot it
is," he conveys the meaning, though there is no definitely formed
subject in his mind, that the outer world at the moment of his
speaking has a certain quality or attribute. So with "It rains". The
study of such examples in their context, however, reveals the fact
that the same form of Common speech may cover different subjects and
predicates in different connexions. Thus in the argument:--
"Whatever is, is best.
It rains!"--
the Subject is _Rain_ and the Predicate _is now_, "is at the present
time," "is in the class of present events".
[Footnote 1: Remember that when we speak of a general name,
we do not necessarily mean a single word. A general name,
logically viewed, is simply the name of a _genus_, kind, or
class: and whether this is single-worded or many-worded
is, strictly speaking, a grammatical question. "Man,"
"man-of-ability," "man-of-ability-and-courage,"
"man-of-ability-and-courage-and-gigantic-stature,"
"man-who-fought-at-Marathon"--these are all general names
in their logical function. No matter how the constitutive
properties of the class are indicated, by one word or in
combination, that word or combination is a general name. In
actual speech we can seldom indicate by a single word the
meaning predicated.]
[Footnote 2: The objection taken to the word "indefinite,"
that the quantity of particular propositions is indefinite,
_some_ meaning any quantity less than all, is an example of
the misplaced and frivolous subtlety that has done so much
to disorder the tradition of Logic. By "indefinite" is
simply meant not definitely expressed as either Universal
or Particular, Total or Partial. The same objection might be
taken to any word used to express the distinction: the degree
of quantity in Some S is not "designate" any more than it is
"definite" or "dioristic".]
[Footnote 3: _Generally._ In this word we have an instance of
the frequent conflict between the words of common speech and
logical terminology. How it arises shall be explained in next
chapter. A General proposition is a synonym for a Universal
proposition (if the forms A and E are so termed): but
"generally" in common speech means "for the most part," and is
represented by the symbol of particular quantity, _Some_.]
[Footnote 4: With some logicians it is a mechanical rule in
reducing to syllogistic form to treat as I or O all sentences
in which there is no formal expression of quantity. This is to
err on the safe side, but common speakers are not so guarded,
and it is to be presumed rather that they have a universal
application in their minds when they do not expressly
qualify.]
III.--SOME TECHNICAL DIFFICULTIES.
_The formula for_ EXCLUSIVE PROPOSITIONS. "None but the brave deserve
the fair": "No admittance except on business": "Only Protestants can
sit on the throne of England".
These propositions exemplify different ways in common speech of naming
a subject _exclusively_, the predication being made of all outside a
certain term. "None that are not brave, etc.;" "none that are not on
business, etc.;" "none that are not Protestants, etc.". No not-S is
P. It is only about all outside the given term that the universal
assertion is made: we say nothing universally about the individuals
within the term: we do not say that all Protestants are eligible, nor
that all persons on business are admitted, nor that every one of the
brave deserves the fair. All that we say is that the possession of the
attribute named is an indispensable condition: a person may possess
the attribute, and yet on other grounds may not be entitled to the
predicate.
The justification for taking special note of this form in Logic is
that we are apt by inadvertence to make an inclusive inference from
it. Let it be said that None but those who work hard can reasonably
expect to pass, and we are apt to take this as meaning that all who
work hard may reasonably expect to pass. But what is denied of every
Not-S is not necessarily affirmed of every S.
_The expression of_ TENSE or TIME _in the Syllogistic Forms_. Seeing
that the Copula in S is P or S is in P does not express time, but only
a certain relation between S and P, the question arises Where are we
to put time in the analytic formula? "Wheat is dear;" "All had fled;"
time is expressed in these propositions, and our formula should
render the whole content of what is given. Are we to include it in
the Predicate term or in the Subject term? If it must not be left out
altogether, and we cannot put it with the copula, we have a choice
between the two terms.
It is a purely scholastic question. The common technical treatment is
to view the tense as part of the predicate. "All had fled," All S is
P, _i.e._, the whole subject is included in a class constituted on the
attributes of flight at a given time. It may be that the Predicate is
solely a predicate of time. "The Board met yesterday at noon." S is P,
_i.e._, the meeting of the Board is one of the events characterised by
having happened at a certain time, agreeing with other events in that
respect.
But in some cases the time is more properly regarded as part of the
subject. _E.g._, "Wheat is dear". S does not here stand for wheat
collectively, but for the wheat now in the market, the wheat of the
present time: it is concerning this that the attribute of dearness is
predicated; it is this that is in the class of dear things.
_The expression of_ MODALITY _in the Syllogistic Forms_. Propositions
in which the predicate is qualified by an expression of necessity,
contingency, possibility or impossibility [_i.e._, in English by
_must_, _may_, _can_, or _cannot_], were called in Mediaeval Logic
_Modal_ Propositions. "Two and two _must_ make four." "Grubs _may_
become butterflies." "Z _can_ paint." "Y _cannot_ fly."
There are two recognised ways of reducing such propositions to the
form S is P. One is to distinguish between the _Dictum_ and the
_Mode_, the proposition and the qualification of its certainty, and
to treat the _Dictum_ as the Subject and the _Mode_ as the Predicate.
Thus: "That two and two make four is necessary"; "That Y can fly is
impossible".
The other way is to treat the Mode as part of the predicate.
The propriety of this is not obvious in the case of Necessary
propositions, but it is unobjectionable in the case of the other three
modes. Thus: "Grubs are things that have the potentiality of becoming
butterflies"; "Z has the faculty of painting"; "Y has not the faculty
of flying".
The chief risk of error is in determining the quantity of the subject
about which the Contingent or Possible predicate is made. When it is
said that "Victories may be gained by accident," is the predicate made
concerning All victories or Some only? Here we are apt to confuse the
meaning of the contingent assertion with the matter of fact on which
in common belief it rests. It is true only that some victories have
been gained by accident, and it is on this ground that we assert in
the absence of certain knowledge concerning any victory that it
may have been so gained. The latter is the effect of the contingent
assertion: it is made about any victory in the absence of certain
knowledge, that is to say, formally about all.
The history of Modals in Logic is a good illustration of intricate
confusion arising from disregard of a clear traditional definition.
The treatment of them by Aristotle was simple, and had direct
reference to tricks of disputation practised in his time. He specified
four "modes," the four that descended to mediaeval logic, and he
concerned himself chiefly with the import of contradicting these
modals. What is the true contradictory of such propositions as, "It
is possible to be" ([Greek: dynaton einai]), "It admits of being"
([Greek: endechetai einai]), "It must be" ([Greek: anankaion einai]),
"It is impossible to be" ([Greek: adynaton einai])? What is implied in
saying "No" to such propositions put interrogatively? "Is it possible
for Socrates to fly?" "No." Does this mean that it is not possible for
Socrates to fly, or that it is possible for Socrates not to fly?
A disputant who had trapped a respondent into admitting that it is
possible for Socrates not to fly, might have pushed the concession
farther in some such way as this: "Is it possible for Socrates not to
walk?" "Certainly." "Is it possible for him to walk?" "Yes." "When you
say that it is possible for a man to do anything do you not believe
that it is possible for him to do it?" "Yes." "But you have admitted
that it is possible for Socrates not to fly?"
It was in view of such perplexities as these that Aristotle set forth
the true contradictories of his four Modals. We may laugh at such
quibbles now and wonder that a grave logician should have thought them
worth guarding against. But historically this is the origin of the
Modals of Formal Logic, and to divert the names of them to signify
other distinctions than those between modes of qualifying the
certainty of a statement is to introduce confusion.
Thus we find "Alexander was a great general," given as an example of
a Contingent Modal, on the ground that though as a matter of fact
Alexander was so he might have been otherwise. It was not _necessary_
that Alexander should be a great general: therefore the proposition
is _contingent_. Now the distinction between Necessary truth and
Contingent truth may be important philosophically: but it is merely
confusing to call the character of propositions as one or the other by
the name of Modality. The original Modality is a mode of expression:
to apply the name to this character is to shift its meaning.
A more simple and obviously unwarrantable departure from tradition
is to extend the name Modality to any grammatical qualification of
a single verb in common speech. On this understanding "Alexander
conquered Darius" is given by Hamilton as a _Pure_ proposition, and
"Alexander conquered Darius honourably" as a _Modal_. This is a merely
grammatical distinction, a distinction in the mode of composing the
predicate term in common speech. In logical tradition Modality is a
mode of qualifying the certainty of an affirmation. "The conquest
of Darius by Alexander was honourable," or "Alexander in conquering
Darius was an honourable conqueror," is the syllogistic form of the
proposition: it is simply assertory, not qualified in any "mode".
There is a similar misunderstanding in Mr. Shedden's treatment of
"generally" as constituting a Modal in such sentences, as "Rivers
_generally_ flow into the sea". He argues that as _generally_ is not
part either of the Subject term or of the Predicate term, it must
belong to the Copula, and is therefore a _modal_ qualification of the
whole assertion. He overlooked the fact that the word "generally" is
an expression of Quantity: it determines the quantity of the Subject
term.
Finally it is sometimes held (_e.g._, by Mr. Venn) that the question
of Modality belongs properly to Scientific or Inductive Logic, and is
out of place in Formal Logic. This is so far accurate that it is
for Inductive Logic to expound the conditions of various degrees of
certainty. The consideration of Modality is pertinent to Formal Logic
only in so far as concerns special perplexities in the expression of
it. The treatment of it by Logicians has been rendered intricate by
torturing the old tradition to suit different conceptions of the end
and aim of Logic.
PART II.
DEFINITION.
CHAPTER I.
IMPERFECT UNDERSTANDING OF WORDS AND THE REMEDIES
THEREFOR.--DIALECTIC.--DEFINITION.
We cannot inquire far into the meaning of proverbs or traditional
sayings without discovering that the common understanding of general
and abstract names is loose and uncertain. Common speech is a
quicksand.
Consider how we acquire our vocabulary, how we pick up the words that
we use from our neighbours and from books, and why this is so soon
becomes apparent. Theoretically we know the full meaning of a name
when we know all the attributes that it connotes, and we are not
justified in extending it except to objects that possess all the
attributes. This is the logical ideal, but between the _ought to be_
of Logic and the _is_ of practical life, there is a vast difference.
How seldom do we conceive words in their full meaning! And who is to
instruct us in the full meaning? It is not as in the exact sciences,
where we start with a knowledge of the full meaning. In Geometry, for
example, we learn the definitions of the words used, _point_, _line_,
_parallel_, etc., before we proceed to use them. But in common speech,
we learn words first in their application to individual cases. Nobody
ever defined _good_ to us, or _fair_, or _kind_, or _highly educated_.
We hear the words applied to individual objects: we utter them in the
same connexion: we extend them to other objects that strike us as like
without knowing the precise points of likeness that the convention
of common speech includes. The more exact meaning we learn by
gradual induction from individual cases. _Ugly_, _beautiful_, _good_,
_bad_--we learn the words first as applicable to things and persons:
gradually there arises a more or less definite sense of what the
objects so designated have in common. The individual's extension of
the name proceeds upon what in the objects has most impressed him
when he caught the word: this may differ in different individuals; the
usage of neighbours corrects individual eccentricities. The child
in arms shouts _Da_ at the passing stranger who reminds him of his
father: for him at first it is a general name applicable to every man:
by degrees he learns that for him it is a singular name.
The mode in which words are learnt and extended may be studied most
simply in the nursery. A child, say, has learnt to say _mambro_ when
it sees its nurse. The nurse works a hand-turned sewing machine,
and sings to it as she works. In the street the child sees an
organ-grinder singing as he turns his handle: it calls _mambro_:
the nurse catches the meaning and the child is overjoyed. The
organ-grinder has a monkey: the child has an india-rubber monkey toy:
it calls this also _mambro_. The name is extended to a monkey in
a picture-book. It has a toy musical box with a handle: this also
becomes _mambro_, the word being extended along another line of
resemblance. A stroller with a French fiddle comes within the
denotation of the word: a towel-rail is also called _mambro_ from some
fancied resemblance to the fiddle. A very swarthy hunch-back _mambro_
frightens the child: this leads to the transference of the word to a
terrific coalman with a bag of coals on his back. In a short time
the word has become a name for a great variety of objects that have
nothing whatever common to all of them, though each is strikingly like
in some point to a predecessor in the series. When the application
becomes too heterogeneous, the word ceases to be of use as a sign and
is gradually abandoned, the most impressive meaning being the last
to go. In a child's vocabulary where the word _mambro_ had a run of
nearly two years, its last use was as an adjective signifying ugly or
horrible.
The history of such a word in a child's language is a type of what
goes on in the language of men. In the larger history we see similar
extensions under similar motives, checked and controlled in the same
way by surrounding usage.
It is obvious that to avoid error and confusion, the meaning or
connotation of names, the concepts, should somehow be fixed: names
cannot otherwise have an identical reference in human intercourse. We
may call this ideal fixed concept the LOGICAL CONCEPT: or we may call
it the SCIENTIFIC CONCEPT, inasmuch as one of the main objects of the
sciences is to attain such ideals in different departments of study.
But in actual speech we have also the PERSONAL CONCEPT, which varies
more or less with the individual user, and the POPULAR or VERNACULAR
CONCEPT, which, though roughly fixed, varies from social sect to
social sect and from generation to generation.
The variations in Popular Concepts may be traced in linguistic
history. Words change with things and with the aspects of things,
as these change in public interest and importance. As long as the
attributes that govern the application of words are simple, sensible
attributes, little confusion need arise: the variations are matters of
curious research for the philologist, but are logically insignificant.
Murray's Dictionary, or such books as Trench's _English Past and
Present_, supply endless examples, as many, indeed as there are
words in the language. _Clerk_ has almost as many connotations as
our typical _mambro_: clerk in holy orders, church clerk, town clerk,
clerk of assize, grocer's clerk. In Early English, the word meant "man
in a religious order, cleric, clergyman"; ability to read, write, and
keep accounts being a prominent attribute of the class, the word was
extended on this simple ground till it has ceased altogether to cover
its original field except as a formal designation. But no confusion is
caused by the variation, because the property connoted is simple.[1]
So with any common noun: street, carriage, ship, house, merchant,
lawyer, professor. We might be puzzled to give an exact definition of
such words, to say precisely what they connote in common usage; but
the risk of error in the use of them is small.
When we come to words of which the logical concept is a complex
relation, an obscure or intangible attribute, the defects of the
popular conception and its tendencies to change and confusion, are
of the greatest practical importance. Take such words as _Monarchy_,
_tyranny_, _civil freedom_, _freedom of contract_, _landlord_,
_gentleman_, _prig_, _culture_, _education_, _temperance_,
_generosity_. Not merely should we find it difficult to give an
analytic definition of such words: we might be unable to do so, and
yet flatter ourselves that we had a clear understanding of their
meaning. But let two men begin to discuss any proposition in which any
such word is involved, and it will often be found that they take the
word in different senses. If the relation expressed is complex, they
have different sides or lines of it in their minds; if the meaning
is an obscure quality, they are guided in their application of it by
different outward signs.
Monarchy, in its original meaning, is applied to a form of government
in which the will of one man is supreme, to make laws or break them,
to appoint or dismiss officers of state and justice, to determine
peace or war, without control of statute or custom. But supreme power
is never thus uncontrolled in reality; and the word has been extended
to cover governments in which the power of the titular head is
controlled in many different modes and degrees. The existence of a
head, with the title of King or Emperor, is the simplest and most
salient fact: and wherever this exists, the popular concept of a
monarchy is realised. The President of the United States has more real
power than the Sovereign of Great Britain; but the one government
is called a Republic and the other a Monarchy. People discuss the
advantages and disadvantages of monarchy without first deciding
whether they take the word in its etymological sense of unlimited
power, or its popular sense of titular kingship, or its logical sense
of power definitely limited in certain ways. And often in debate,
monarchy is really a singular term for the government of Great
Britain.
_Culture_, _religious_, _generous_, are names for inward states or
qualities: with most individuals some simple outward sign directs
the application of the word--it may be manner, or bearing, or routine
observances, or even nothing more significant than the cut of the
clothes or of the hair. Small things undoubtedly are significant, and
we must judge by small things when we have nothing else to go by: but
instead of trying to get definite conceptions for our moral epithets,
and suspending judgment till we know that the use of the epithet is
justified, the trifling superficial sign becomes for us practically
the whole meaning of the word. We feel that we must have a judgment of
some sort at once: only simple signs are suited to our impatience.
It was with reference to this state of things that Hegel formulated
his paradox that the true abstract thinker is the plain man who laughs
at philosophy as what he calls abstract and unpractical. He holds
decided opinions for or against this or the other abstraction,
_freedom_, _tyranny_, _revolution_, _reform_, _socialism_, but what
these words mean and within what limits the things signified are
desirable or undesirable, he is in too great a hurry to pause and
consider.
The disadvantages of this kind of "abstract" thinking are obvious.
The accumulated wisdom of mankind is stored in language. Until we have
cleared our conceptions, and penetrated to the full meaning of words,
that wisdom is a sealed book to us. Wise maxims are interpreted by
us hastily in accordance with our own narrow conceptions. All the
vocables of a language may be more or less familiar to us, and yet we
may not have learnt it as an instrument of thought. Outside the very
limited range of names for what we see and use in the daily routine of
life, food and clothes and the common occupations of men, words
have little meaning for us, and are the vehicles merely of thin
preconceptions and raw prejudices.
The remedy for "abstract" thinking is more thinking, and in pursuing
this two aims may be specified for the sake of clearness, though they
are closely allied, and progress towards both may often be made by
one and the same operation. (1) We want to reach a clear and full
conception of the meaning of names as used now or at a given time.
Let us call this the _Verification of the Meaning_. (2) We want to fix
such conceptions, and if necessary readjust their boundaries. This is
the province of _Definition_, which cannot be effectually performed
without _Scientific Classification_ or _Division_.
I.--VERIFICATION OF THE MEANING--DIALECTIC.
This can only be done by assembling the objects to which the words are
applied, and considering what they have in common. To ascertain the
actual connotation we must run over the actual denotation. And since
in such an operation two or more minds are better than one, discussion
or dialectic is both more fruitful and more stimulating than solitary
reflection or reading.
The first to practise this process on a memorable scale, and with
a distinct method and purpose, was Socrates. To insist upon the
necessity of clear conceptions, and to assist by his dialectic
procedure in forming them, was his contribution to philosophy.
His plan was to take a common name, profess ignorance of its meaning,
and ask his interlocutor whether he would apply it in such and such
an instance, producing one after another. According to Xenophon's
_Memorabilia_ he habitually chose the commonest names, _good_,
_unjust_, _fitting_, and so forth, and tried to set men thinking
about them, and helped them by his questions to form an intelligent
conception of the meaning.
For example, what is the meaning of injustice? Would you say that
the man who cheats or deceives is unjust? Suppose a man deceives his
enemies, is there any injustice in that? Can the definition be that
a man who deceives his friends is unjust? But there are cases where
friends are deceived for their own good: are these cases of injustice?
A general may inspirit his soldiers by a falsehood. A man may cajole
a weapon out of his friend's hand when he sees him about to commit
suicide. A father may deceive his son into taking medicine. Would you
call these men unjust? By some such process of interrogation we
are brought to the definition that a man is unjust who deceives his
friends to their hurt.
Observe that in much of his dialectic the aim of Socrates was merely
to bring out the meaning lying vague and latent, as it were, in
the common mind. His object was simply what we have called the
verification of the meaning. And a dialectic that confines itself to
the consideration of what is ordinarily meant as distinct from what
ought to be meant may often serve a useful purpose. Disputes about
words are not always as idle as is sometimes supposed. Mr. H. Sidgwick
truly remarks (_a propos_ of the terms of Political Economy) that
there is often more profit in seeking a definition than in finding it.
Conceptions are not merely cleared but deepened by the process. Mr.
Sidgwick's remarks are so happy that I must take leave to quote them:
they apply not merely to the verification of ordinary meaning but also
to the study of special uses by authorities, and the reasons for those
special uses.
"The truth is--as most readers of Plato know, only it is a
truth difficult to retain and apply--that what we gain by
discussing a definition is often but slightly represented in
the superior fitness of the formula that we ultimately adopt;
it consists chiefly in the greater clearness and fulness in
which the characteristics of the matter to which the formula
refers have been brought before the mind in the process of
seeking for it. While we are apparently aiming at definitions
of terms, our attention should be really fixed on distinctions
and relations of fact. These latter are what we are concerned
to know, contemplate, and as far as possible arrange and
systematise; and in subjects where we cannot present them to
the mind in ordinary fulness by the exercise of the organs of
sense, there is no way of surveying them so convenient as
that of reflecting on our use of common terms.... In comparing
different definitions our aim should be far less to decide
which we ought to adopt, than to apprehend and duly consider
the grounds on which each has commended itself to reflective
minds. We shall generally find that each writer has noted some
relation, some resemblance or difference, which others have
overlooked; and we shall gain in completeness, and often
in precision, of view by following him in his observations,
whether or not we follow him in his conclusions."[2]
Mr. Sidgwick's own discussions of _Wealth_, _Value_, and _Money_ are
models. A clue is often found to the meaning in examining startlingly
discrepant statements connected with the same leading word. Thus
we find some authorities declaring that "style" cannot be taught or
learnt, while others declare that it can. But on trying to ascertain
what they mean by "style," we find that those who say it cannot be
taught mean either a certain marked individual character or manner of
writing--as in Buffon's saying, _Le style c'est l'homme meme_--or a
certain felicity and dignity of expression, while those who say style
can be taught mean lucid method in the structure of sentences or in
the arrangement of a discourse. Again in discussions on the rank of
poets, we find different conceptions of what constitutes greatness in
poetry lying at the root of the inclusion of this or the other poet
among great poets. We find one poet excluded from the first rank of
greatness because his poetry was not serious; another because his
poetry was not widely popular; another because he wrote comparatively
little; another because he wrote only songs or odes and never
attempted drama or epic. These various opinions point to different
conceptions of what constitutes greatness in poets, different
connotations of "great poet". Comparing different opinions concerning
"education" we may be led to ask whether it means more than
instruction in the details of certain subjects, whether it does not
also import the formation of a disposition to learn or an interest in
learning or instruction in a certain method of learning.
Historically, dialectic turning on the use of words preceded the
attempt to formulate principles of Definition, and attempts at precise
definition led to Division and Classification, that is to systematic
arrangement of the objects to be defined. Attempt to define any such
word as "education," and you gradually become sensible of the needs in
respect of method that forced themselves upon mankind in the history
of thought. You soon become aware that you cannot define it by itself
alone; that you are beset by a swarm of more or less synonymous words,
_instruction_, _discipline_, _culture_, _training_, and so on; that
these various words represent distinctions and relations among things
more or less allied; and that, if each must be fixed to a definite
meaning, this must be done with reference to one another and to the
whole department of things that they cover.
The first memorable attempts at scientific arrangement were
Aristotle's treatises on Ethics and Politics, which had been the
subjects of active dialectic for at least a century before. That
these the most difficult of all departments to subject to scientific
treatment should have been the first chosen was due simply to their
preponderating interest: "The proper study of mankind is man". The
systems of what are known as the Natural Sciences are of modern
origin: the first, that of Botany, dates from Cesalpinus in the
sixteenth century. But the principles on which Aristotle proceeded in
dividing and defining, principles which have gradually themselves been
more precisely formulated, are principles applicable to all systematic
arrangements for purposes of orderly study. I give them in the precise
formulae which they have gradually assumed in the tradition of Logic.
The principles of Division are often given in Formal Logic, and the
principles of Classification in Inductive Logic, but there is no
valid reason for the separation. The classification of objects in the
Natural Sciences, of animals, plants, and stones, with a view to
the thorough study of them in form, structure, and function, is
more complex than classifications for more limited purposes, and the
tendency is to restrict the word classification to these elaborate
systems. But really they are only a series of divisions and
subdivisions, and the same principles apply to each of the subordinate
divisions as well as to the division of the whole department of study.
II.--PRINCIPLES OF DIVISION OR CLASSIFICATION AND DEFINITION.
Confusion in the boundaries of names arises from confused ideas
regarding the resemblances and differences of things. As a protective
against this confusion, things must be clearly distinguished in their
points of likeness and difference, and this leads to their arrangement
in systems, that is, to division and classification. A name is not
secure against variation until it has a distinct place in such a
system as a symbol for clearly distinguished attributes. Nor must we
forget, further, that systems have their day, that the best system
attainable is only temporary, and may have to be recast to correspond
with changes of things and of man's way of looking at them.
The leading principles of DIVISION may be stated as follows:--
I. Every division is made on the ground of differences in
some attribute common to all the members of the whole to be
divided.
This is merely a way of stating what a logical division is. It is
a division of a generic whole or _genus_, an indefinite number of
objects thought of together as possessing some common character or
attribute. All have this attribute, which is technically called the
_fundamentum divisionis_, or generic attribute. But the whole is
divisible into smaller groups (_species_), each of which possesses the
common character with a difference (_differentia_). Thus, mankind may
be divided into White men, Black men, Yellow men, on ground of the
differences in the colour of their skins: all have skins of some
colour: this is the _fundamentum divisionis_: but each subdivision or
species has a different colour: this is the _differentia_. Rectilineal
figures are divided into triangles, quadrangles, pentagons, etc., on
the ground of differences in the number of angles.
Unless there is a _fund. div._, _i.e._, unless the differences are
differences in a common character, the division is not a logical
division. To divide men into Europeans, opticians, tailors, blondes,
brunettes, and dyspeptics is not to make a logical division. This is
seen more clearly in connexion with the second condition of a perfect
division.
II. In a perfect division, the subdivisions or species are
mutually exclusive.
Every object possessing the common character should be in one or other
of the groups, and none should be in more than one.
Confusion between classes, or overlapping, may arise from two
causes. It may be due (1) to faulty division, to want of unity in
the _fundamentum divisionis_; (2) to the indistinct character of the
objects to be defined.
(1) Unless the division is based upon a single ground, unless each
species is based upon some mode of the generic character, confusion is
almost certain to arise. Suppose the field to be divided, the objects
to be classified, are three-sided rectilineal plane figures, each
group must be based upon some modification of the three sides. Divide
them into equilateral, isosceles, and scalene according as the three
sides are all of equal length, or two of equal length, or each of
different length, and you have a perfect division. Similarly you can
divide them perfectly according to the character of the angles into
acute-angled, right-angled and obtuse-angled. But if you do not keep
to a single basis, as in dividing them into equilateral, isosceles,
scalene, and right-angled, you have a cross-division. The same
triangle might be both right-angled and isosceles.
(2) Overlapping, however, may be unavoidable in practice owing to
the nature of the objects. There may be objects in which the dividing
characters are not distinctly marked, objects that possess the
differentiae of more than one group in a greater or less degree. Things
are not always marked off from one another by hard and fast lines.
They shade into one another by imperceptible gradations. A clear
separation of them may be impossible. In that case you must allow a
certain indeterminate margin between your classes, and sometimes it
may be necessary to put an object into more than one class.
To insist that there is no essential difference unless a clear
demarcation can be made is a fallacy. A sophistical trick called the
_Sorites_ or Heap from the classical example of it was based upon this
difficulty of drawing sharp lines of definition. Assuming that it is
possible to say how many stones constitute a heap, you begin by asking
whether three stones form a heap. If your respondent says No, you
ask whether four stones form a heap, then five, and so on and he is
puzzled to say when the addition of a single stone makes that a heap
which was not a heap before. Or you may begin by asking whether twenty
stones form a heap, then nineteen, then eighteen, and so on, the
difficulty being to say when what was a heap ceases to be so.
Where the objects classified are mixed states or affections, the
products of interacting factors, or differently interlaced or
interfused growths from common roots, as in the case of virtues, or
emotions, or literary qualities, sharp demarcations are impossible.
To distinguish between wit and humour, or humour and pathos, or pathos
and sublimity is difficult because the same composition may partake
of more than one character. The specific characters cannot be made
rigidly exclusive one of another.
Even in the natural sciences, where the individuals are concrete
objects of perception, it may be difficult to decide in which of
two opposed groups an object should be included. Sydney Smith has
commemorated the perplexities of Naturalists over the newly
discovered animals and plants of Botany Bay, in especial with the
_Ornithorynchus_,--"a quadruped as big as a large cat, with the
eyes, colour, and skin of a mole, and the bill and web-feet of a
duck--puzzling Dr. Shaw, and rendering the latter half of his life
miserable, from his utter inability to determine whether it was a bird
or a beast".
III. The classes in any scheme of division should be of
co-ordinate rank.
The classes may be mutually exclusive, and yet the division imperfect,
owing to their not being of equal rank. Thus in the ordinary division
of the Parts of Speech, parts, that is, of a sentence, Prepositions
and Conjunctions are not co-ordinate in respect of function, which is
the basis of the division, with Nouns, Adjectives, Verbs, and Adverbs.
The preposition is a part of a phrase which serves the same function
as an adjective, _e.g._, _royal_ army, army _of the king_; it is thus
functionally part of a part, or a particle. So with the conjunction:
it also is a part of a part, _i.e._, part of a clause serving the
function of adjective or adverb.
IV. The basis of division (_fundamentum divisionis_) should be
an attribute admitting of important differences.
The importance of the attribute chosen as basis may vary with the
purpose of the division. An attribute that is of no importance in one
division, may be important enough to be the basis of another division.
Thus in a division of houses according to their architectural
attributes, the number of windows or the rent is of little importance;
but if houses are taxed or rated according to the number of windows
or the rent, these attributes become important enough to be a basis
of division for purposes of taxation or rating. They then admit of
important differences.
That the importance is relative to the purpose of the division should
be borne in mind because there is a tendency to regard attributes that
are of importance in any familiar or pre-eminent division as if they
had an absolute importance. In short, disregard of this relativity is
a fallacy to be guarded against.
In the sciences, the purpose being the attainment and preservation
of knowledge, the objects of study are divided so as to serve that
purpose. Groups must be formed so as to bring together the objects
that have most in common. The question, Who are to be placed together?
in any arrangement for purposes of study, receives the same answer
for individuals and for classes that have to be grouped into higher
classes, namely, Those that have most in common. This is what Dr. Bain
happily calls "the golden rule" of scientific classification: "Of the
various groupings of resembling things, preference is given to such as
have the greatest number of attributes in common". I slightly
modify Dr. Bain's statement: he says "the most numerous and the most
important attributes in common". But for scientific purposes number of
attributes constitutes importance, as is well recognised by Dr. Fowler
when he says that the test of importance in an attribute proposed as a
basis of classification is the number of other attributes of which it
is an index or invariable accompaniment. Thus in Zoology the
squirrel, the rat, and the beaver are classed together as Rodents, the
difference between their teeth and the teeth of other Mammalia being
the basis of division, because the difference in teeth is accompanied
by differences in many other properties. So the hedge-hog, the
shrew-mouse, and the mole, though very unlike in outward appearance
and habits, are classed together as Insectivora, the difference in
what they feed on being accompanied by a number of other differences.
_The Principles of_ DEFINITION. The word "definition" as used in Logic
shows the usual tendency of words to wander from a strict meaning and
become ambiguous. Throughout most of its uses it retains this much of
a common signification, the fixing or determining of the boundaries
of a class[3] by making clear its constituent attributes. Now in this
making clear two processes may be distinguished, a material process
and a verbal process. We have (1) the clearing up of the common
attributes by a careful examination of the objects included in the
class: and we have (2) the statement of these common attributes in
language. The rules of definition given by Dr. Bain, who devotes a
separate Book in his Logic to the subject of Definition, concern the
first of these processes: the rules more commonly given concern mainly
the second.
One eminent merit in Dr. Bain's treatment is that it recognises the
close connexion between Definition and Classification. His cardinal
rules are reduced to two.
I. _Assemble for comparison representative individuals of the
class._
II. _Assemble for comparison representative individuals of the
contrasted class or classes._
Seeing that the contrasted classes are contrasted on some basis of
division, this is in effect to recognise that you cannot clearly
define any class except in a scheme of classification. You must have
a wide _genus_ with its _fundamentum divisionis_, and, within this,
_species_ distinguished by their several _differentiae_.
Next, as to the verbal process, rules are commonly laid down mostly
of a trifling and obvious character. That "a definition should state
neither more nor less than the common attributes of the class," or
than the attributes signified by the class-name, is sometimes given
as a rule of definition. This is really an explanation of what a
definition is, a definition of a definition. And as far as mere
statement goes it is not strictly accurate, for when the attributes
of a genus are known it is not necessary to give all the attributes of
the species, which include the generic attributes as well, but it is
sufficient to give the generic name and the differentia. Thus
Poetry may be defined as "a Fine Art having metrical language as its
instrument". This is technically known as definition _per genus
et differentiam_. This mode of statement is a recognition of the
connexion between Definition and Division.
The rule that "a definition should not be a synonymous repetition of
the name of the class to be defined," is too obvious to require formal
statement. To describe a Viceroy as a man who exercises viceregal
functions, may have point as an epigram in the case of a _faineant_
viceroy, but it is not a definition.
So with the rule that "a definition should not be couched in ambiguous
unfamiliar, or figurative language". To call the camel "the ship of
the desert" is a suggestive and luminous description of a property,
but it is not a definition. So with the noble description of Faith as
"the substance of things hoped for, the evidence of things not seen".
But if one wonders why so obvious a "rule" should be laid down, the
answer is that it has its historical origin in the caprices of
two classes of offenders, mystical philosophers and pompous
lexicographers.[4]
That "the definition should be simply convertible with the term for
the class defined," so that we may say, for example, either: "Wine is
the juice of the grape," or, "The juice of the grape is wine," is an
obvious corollary from the nature of definition, but should hardly be
dignified with the name of a "rule".
_The Principles of_ NAMING. Rules have been formulated for the choice
of names in scientific definition and classification, but it may be
doubted whether such choice can be reduced to precise rule. It is
enough to draw attention to certain considerations obvious enough on
reflection.
We may take for granted that there should be distinct names for every
defining attribute (a _Terminology_) and for every group or class (a
_Nomenclature_). What about the selection of the names? Suppose an
investigator is struck with likenesses and differences that seem to
him important enough to be the basis of a new division, how should he
be guided in his choice of names for the new groups that he proposes?
Should he coin new names, or should he take old names and try to fit
them with new definitions?
The balance of advantages is probably in favour of Dr. Whewell's
dictum that "in framing scientific terms, the appropriation of old
words is preferable to the invention of new ones". Only care must be
taken to keep as close as possible to the current meaning of the
old word, and not to run counter to strong associations. This is
an obvious precept with a view to avoiding confusion. Suppose, for
example, that in dividing Governments you take the distribution of
political power as your basis of division and come to the conclusion
that the most important differences are whether this power is vested
in a few or in the majority of the community. You want names to
fix this broad division. You decide instead of coining the new word
_Pollarchy_ to express the opposite of _Oligarchy_ to use the old
words _Republic_ and _Oligarchy_. You would find, as Sir George
Cornewall Lewis found, that however carefully you defined the word
Republic, a division under which the British Government had to be
ranked among Republics would not be generally understood and accepted.
Using the word in the sense explained above, Mr. Bagehot maintained
that the constitution of Great Britain was more Republican than that
of the United States, but his meaning was not taken except by a few.
The difficulty in choosing between new words and old words to express
new meanings is hardly felt in the exact sciences. It is at least at
a minimum. The innovator may encounter violent prejudice, but, arguing
with experts, he can at least make sure of being understood, if his
new division is based upon real and important differences. But in
other subjects the difficulty of transmitting truth or of expressing
it in language suited for precise transmission, is almost greater than
the difficulty of arriving at truth. Between new names and old
names redefined, the possessor of fresh knowledge, assuming it to be
perfectly verified, is in a quandary. The objects with which he deals
are already named in accordance with loose divisions resting on strong
prejudices. The names in current use are absolutely incapable of
conveying his meaning. He must redefine them if he is to use them. But
in that case he runs the risk of being misunderstood from people being
too impatient to master his redefinition. His right to redefine may
even be challenged without any reference to the facts to be expressed:
he may simply be accused of circulating false linguistic coin, of
debasing the verbal currency. The other alternative open to him is
to coin new words. In that case he runs the risk of not being read at
all. His contribution to verified knowledge is passed by as pedantic
and unintelligible. There is no simple rule of safety: between Scylla
and Charybdis the mariner must steer as best he may. Practically the
advantage lies with old words redefined, because thereby discussion is
provoked and discussion clears the air.
Whether it is best to attempt a formal definition or to use words in a
private, peculiar, or esoteric sense, and leave this to be gathered by
the reader from the general tenor of your utterances, is a question of
policy outside the limits of Logic. It is for the logician to expound
the method of Definition and the conditions of its application: how
far there are subjects that do not admit of its application profitably
must be decided on other grounds. But it is probably true that no
man who declines to be bound by a formal definition of his terms is
capable of carrying them in a clear unambiguous sense through a heated
controversy.
[Footnote 1: Except, perhaps, in new offices to which the
name is extended, such as _Clerk_ of School Board. The name,
bearing its most simple and common meaning, may cause popular
misapprehension of the nature of the duties. Any uncertainty
in meaning may be dangerous in practice: elections have been
affected by the ambiguity of this word.]
[Footnote 2: Sidgwick's _Political Economy_, pp. 52-3. Ed.
1883.]
[Footnote 3: Some logicians, however, speak of defining a
thing, and illustrate this as if by a thing they meant a
concrete individual, the realistic treatment of Universals
lending itself to such expressions. But though the authority
of Aristotle might be claimed for this, it is better to
confine the name in strictness to the main process of defining
a class. Since, however, the method is the same whether it is
an individual or a class that we want to make distinct, there
is no harm in the extension of the word definition to both
varieties. See Davidson's _Logic of Definition_, chap. ii.]
[Footnote 4: See Davidson's _Logic of Definition_, chap. iii.]
CHAPTER II.
THE FIVE PREDICABLES.--VERBAL AND REAL PREDICATION.
We give a separate chapter to this topic out of respect for the space
that it occupies in the history of Logic. But except as an exercise in
subtle distinction for its own sake, all that falls to be said about
the Predicables might be given as a simple appendix to the chapter on
Definition.
Primarily, the Five Predicables or Heads of Predicables--Genus,
Species, Differentia, Proprium, and Accidens--are not predicables at
all, but merely a list or enumeration of terms used in dividing and
defining on the basis of attributes. They have no meaning except in
connexion with a fixed scheme of division. Given such a scheme, and
we can distinguish in it the whole to be divided (the _genus_), the
subordinate divisions (the _species_), the attribute or combination of
attributes on which each species is constituted (the _differentia_),
and other attributes, which belong to some or all of the individuals
but are not reckoned for purposes of division and definition
(_Propria_ and _Accidentia_). The list is not itself a logical
division: it is heterogeneous, not homogeneous; the two first are
names of classes, the three last of attributes. But corresponding to
it we might make a homogeneous division of attributes, as follows:--
Attributes
___________|____________
| |
Defining Non-defining
_____|______ ____|__________
| | | |
Generic Specific Proprium Accidens
(Differentia)
The origin of the title Predicables as applied to these five terms is
curious, and may be worth noting as an instance of the difficulty of
keeping names precise, and of the confusion arising from forgetting
the purpose of a name. Porphyry in his [Greek: eisagoge] or
Introduction explains the five words ([Greek: phonai]) simply as terms
that it is useful for various purposes to know, expressly mentioning
definition and division. But he casually remarks that Singular names,
"This man," "Socrates," can be predicated only of one individual,
whereas _Genera_, _Species_, _Differentiae_, etc., are predicables
of many. That is to say he describes them as Predicables simply by
contradistinction from Singular names. A name, however, was wanted for
the five terms taken all together, and since they are not a logical
division, but merely a list of terms used in dividing and defining,
there was no apt general designation for them such as would occur
spontaneously. Thus it became the custom to refer to them as
the Predicables, a means of reference to them collectively being
desiderated, while the meaning of this descriptive title was
forgotten.
To call the five divisional elements or _Divisoria_ Predicables is to
present them as a division of Predicate Terms on the basis of their
relation to the Subject Term: to suggest that every Predicate Term
must be either a Genus or a Species, or a Differentia, or a Proprium,
or an Accidens of the Subject Term. They are sometimes criticised
as such, and it is rightly pointed out that the Predicate is never a
species of or with reference to the Subject. But, in truth, the five
so-called Predicables were never meant as a division of predicates
in relation to the subject: it is only the title that makes this
misleading suggestion.
To complete the confusion it so happens that Aristotle used three of
the Five terms in what was virtually a division of Predicates inasmuch
as it was a division of Problems or Questions. In expounding the
methods of Dialectic in the Topica he divided Problems into four
classes according to the relation of the Predicate to the Subject. The
Predicate must either be simply convertible with the subject or not.
If simply convertible, the two must be coextensive, and the
Predicate must be either a Proprium or the Definition. If not simply
convertible, the Predicate must either be part of the Definition or
not. If part of the Definition it must be either a Generic Property
or a Differentia (both of which in this connexion Aristotle includes
under Genus): if not part of the Definition, it is an Accident.
Aristotle thus arrives at a fourfold division of Problems or
Predicates:--[Greek: genos] (_Genus_, including _Differentia_,
[Greek: diaphora]); [Greek: horos] (Definition); [Greek: to idion]
(_Proprium_); and [Greek: to symbebekos] (_Accidens_). The object of
it was to provide a basis for his systematic exposition; each of the
four kinds admitted of differences in dialectic method. For us it is
a matter of simple curiosity and ingenuity. It serves as a monument
of how much Greek dialectic turned on Definition, and it corresponds
exactly to the division of attributes into Defining and Non-defining
given above. It is sometimes said that Aristotle showed a more
scientific mind than Porphyry in making the Predicables four instead
of five. This is true if Porphyry's list had been meant as a division
of attributes: but it was not so meant.
The distinction between VERBAL or ANALYTIC and REAL or SYNTHETIC
Predication corresponds to the distinction between Defining and
Non-defining attributes, and also has no significance except with
reference to some scheme of Division, scientific and precise or loose
and popular.
When a proposition predicates of a subject something contained in the
full notion, concept, or definition of the subject term, it is called
Verbal, Analytic, or Explicative: _verbal_, inasmuch as it merely
explains the meaning of a name; _explicative_ for the same reason;
_analytic_, inasmuch as it unties the bundle of attributes held
together in the concept and pays out one, or all one by one.
When the attributes of the Predicate are not contained in the concept
of the Subject, the proposition is called _Real_, _Synthetic_, or
_Ampliative_, for parallel reasons.
Thus: "A triangle is a three-sided rectilinear figure" is Verbal or
Analytic; "Triangles have three angles together equal to two right
angles," or "Triangles are studied in schools," is Real or Synthetic.
According to this distinction, predications of the whole Definition
or of a Generic attribute or of a Specific attribute are Verbal;
predications of Accident are Real. A nice point is whether Propria are
Verbal or Real. They can hardly be classed with Verbal, inasmuch as
one may know the full meaning of the name without knowing them: but
it might be argued that they are Analytic, inasmuch as they are
implicitly contained in the defining attributes as being deducible
from them.
Observe, however, that the whole distinction is really valid only
in relation to some fixed or accepted scheme of classification or
division. Otherwise, what is Verbal or Analytic to one man may be
Real or Synthetic to another. It might even be argued that every
proposition is Analytic to the man who utters it and Synthetic to the
man who receives it. We must make some analysis of a whole of thought
before paying it out in words: and in the process of apprehending the
meaning of what we hear or read we must add the other members of the
sentence on to the subject. Whether or not this is super-subtle, it
clearly holds good that what is Verbal (in the sense defined) to the
learned man of science may be Real to the learner. That the horse has
six incisors in each jaw or that the domestic dog has a curly tail,
is a Verbal Proposition to the Natural Historian, a mere exposition
of defining marks; but the plain man has a notion of horse or dog into
which this defining attribute does not enter, and to him accordingly
the proposition is Real.
But what of propositions that the plain man would at once recognise as
Verbal? Charles Lamb, for example, remarks that the statement that "a
good name shows the estimation in which a man is held in the world" is
a verbal proposition. Where is the fixed scheme of division there?
The answer is that by a fixed scheme of division we do not necessarily
mean a scheme that is rigidly, definitely and precisely fixed. To make
such schemes is the business of Science. But the ordinary vocabulary
of common intercourse as a matter of fact proceeds upon schemes
of division, though the names used in common speech are not always
scientifically accurate, not always the best that could be devised for
the easy acquisition and sure transmission of thorough knowledge. The
plain man's vocabulary, though often twisted aside by such causes
as we have specified, is roughly moulded on the most marked
distinguishing attributes of things. This was practically recognised
by Aristotle when he made one of his modes of definition consist in
something like what we have called verifying the meaning of a name,
ascertaining the attributes that it signifies in common speech or in
the speech of sensible men. This is to ascertain the essence, [Greek:
ousia], or _Substantia_, of things, the most salient attributes that
strike the common eye either at once or after the closer inspection
that comes of long companionship, and form the basis of the ordinary
vocabulary. "Properly speaking," Mansel says,[1] "All Definition is an
inquiry into _Attributes_. Our complex notions of Substances can only
be resolved into various Attributes, with the addition of an unknown
_substratum_: a something to which we are compelled to regard
these attributes as belonging. _Man_, for example, is analysed
into Animality, Rationality, and the something which exhibits these
phenomena. Pursue the analysis and the result is the same. We have a
something corporeal, animated, sensible, rational. An unknown constant
must always be added to complete the integration." This "unknown
constant" was what Locke called the _Real_ Essence, as distinguished
from the _Nominal_ Essence, or complex of attributes. It is upon this
nominal essence, upon divisions of things according to attributes,
that common speech rests, and if it involves many cross-divisions,
this is because the divisions have been made for limited and
conflicting purposes.
[Footnote 1: Aldrich's Compendium, Appendix, Note C. The
reader may be referred to Mansel's Notes A and C for valuable
historical notices of the Predicables and Definition.]
CHAPTER III.
ARISTOTLE'S CATEGORIES.
In deference to tradition a place must be found in every logical
treatise for Aristotle's Categories. No writing of the same length
has exercised a tithe of its influence on human thought. It governed
scholastic thought and expression for many centuries, being from its
shortness and consequent easiness of transcription one of the
few books in every educated man's library. It still regulates the
subdivisions of Parts of Speech in our grammars. Its universality of
acceptance is shown in the fact that the words _category_ ([Greek:
kategoria]) and _predicament_, its Latin translation, have passed into
common speech.
The Categories have been much criticised and often condemned as a
division, but, strange to say, few have inquired what they originally
professed to be a division of, or what was the original author's
basis of division. Whether the basis is itself important, is another
question: but to call the division imperfect, without reference to the
author's intention, is merely confusing, and serves only to illustrate
the fact that the same objects may be differently divided on different
principles of division. Ramus was right in saying that the Categories
had no logical significance, inasmuch as they could not be made a
basis for departments of logical method; and Kant and Mill in saying
that they had no philosophical significance, inasmuch as they are
founded upon no theory of Knowing and Being: but this is to condemn
them for not being what they were never intended to be.
The sentence in which Aristotle states the objects to be divided, and
his division of them is so brief and bold that bearing in mind the
subsequent history of the Categories, one first comes upon it with a
certain surprise. He says simply:--
"Of things expressed without syntax (_i.e._, single words), each
signifies either substance, or quantity, or quality, or relation,
or place, or time, or disposition (_i.e._, attitude or internal
arrangement), or appurtenance, or action (doing), or suffering (being
done to)."[1]
The objects, then, that Aristotle proposed to classify were single
words (the _themata simplicia_ of the Schoolmen). He explains that by
"out of syntax" ([Greek: aneu symplokes]) he means without reference
to truth or falsehood: there can be no declaration of truth or
falsehood without a sentence, a combination, or syntax: "man runs" is
either true or false, "man" by itself, "runs" by itself, is neither.
His division, therefore, was a division of single words according to
their differences of signification, and without reference to the truth
or falsehood of their predication.[2]
Signification was thus the basis of division. But according to what
differences? The Categories themselves are so abstract that this
question might be discussed on their bare titles interminably. But
often when abstract terms are doubtful, an author's intention may be
gathered from his examples. And when Aristotle's examples are ranged
in a table, certain principles of subdivision leap to the eyes.
Thus:--
Substance Man } COMMON { Substance
([Greek: ousia]) ([Greek: anthropos]) } NOUN {
(_Substantia_)
--------------------------------------------------------------
Quantity Five-feet-five } {
([Greek: poson]) ([Greek: tripechu]) } {
(_Quantitas_) } {
Quality Scholarly } { Permanent
([Greek: poion]) ([Greek: grammatikon])} ADJECTIVE { Attribute
(_Qualitas_) } {
Relation Bigger } {
([Greek: pros ti]) ([Greek: meizon]) } {
(_Relatio_) } {
--------------------------------------------------------------
Place In-the-Lyceum } {
([Greek: pou]) ([Greek: en Lykeio]) } {
(_Ubi_) } ADVERB { Temporary
Time Yesterday } { Attribute
([Greek: pote]) ([Greek: chthes]) } {
(_Quando_) } {
--------------------------------------------------------------
Disposition Reclines } {
([Greek: keisthai]) ([Greek: anakeitai]) } {
(_Positio_) } {
Appurtenance Has-shoes-on } {
([Greek: echein]) ([Greek: hypodedetai])} {
(_Habitus_) } VERB {
Action Cuts } { Temporary
([Greek: poiein]) ([Greek: temnei]) } { Attribute
(_Actio_) } {
Passion Is cut } {
([Greek: paschein]) ([Greek: temnetai]) } {
(_Passio_) } {
In looking at the examples, our first impression is that Aristotle has
fallen into a confusion. He professes to classify words out of syntax,
yet he gives words with the marks of syntax on them. Thus his division
is accidentally grammatical, a division of parts of speech, parts of
a sentence, into Nouns, Adjectives, Adverbs, and Verbs. And his
subdivisions of these parts are still followed in our grammars. But
really it is not the grammatical function that he attends to, but
the signification: and looking further at the examples, we see what
differences of signification he had in his mind. It is differences
relative to a concrete individual, differences in the words applied to
him according as they signify the substance of him or his attributes,
permanent or temporary.
Take any concrete thing, Socrates, this book, this table. It must
be some kind of a thing, a man, a book. It must have some size
or quantity, six feet high, three inches broad. It must have some
quality, white, learned, hard. It must have relations with other
things, half this, double that, the son of a father. It must be
somewhere, at some time, in some attitude, with some "havings,"
appendages, appurtenances, or belongings, doing something, or having
something done to it. Can you conceive any name (simple or composite)
applicable to any object of perception, whose signification does not
fall into one or other of these classes? If you cannot, the categories
are justified as an exhaustive division of significations. They are
a complete list of the most general resemblances among individual
things, in other words, of the _summa genera_, the _genera
generalissima_ of predicates concerning this, that or the other
concrete individual. No individual thing is _sui generis_: everything
is like other things: the categories are the most general likenesses.
The categories are exhaustive, but do they fulfil another requisite of
a good division--are they mutually exclusive? Aristotle himself
raised this question, and some of his answers to difficulties are
instructive. Particularly his discussion of the distinction between
Second Substances or Essences and Qualities. Here he approximates to
the modern doctrine of the distinction between Substance and Attribute
as set forth in our quotation from Mansel at p. 110. Aristotle's
Second Essences ([Greek: deuterai ousiai]) are common nouns or general
names, Species and Genera, _man_, _horse_, _animal_, as distinguished
from Singular names, _this man_, _this horse_, which he calls First
Substances ([Greek: protai ousiai]), essences _par excellence_, to
which real existence in the highest sense is attributed. Common nouns
are put in the First Category because they are predicated in answer to
the question, What is this? But he raises the difficulty whether they
may not rather be regarded as being in the Third Category, that of
Quality ([Greek: to poion]). When we say, "This is a man," do we not
declare what sort of a thing he is? do we not declare his Quality? If
Aristotle had gone farther along this line, he would have arrived
at the modern point of view that a man is a man in virtue of his
possessing certain attributes, that general names are applied in
virtue of their connotation. This would have been to make the line
of distinction between the First Category and the Third pass between
First Essence and Second, ranking the Second Essences with Qualities.
But Aristotle did not get out of the difficulty in this way. He solved
it by falling back on the differences in common speech. "Man" does not
signify the quality simply, as "whiteness" does. "Whiteness" signifies
nothing but the quality. That is to say, there is no separate name in
common speech for the common attributes of man. His further obscure
remark that general names "define quality round essence" [Greek: peri
ousian], inasmuch as they signify what sort a certain essence is, and
that genera make this definition more widely than species, bore fruit
in the mediaeval discussions between Realists and Nominalists by which
the signification of general names was cleared up.
Another difficulty about the mutual exclusiveness of the Categories
was started by Aristotle in connexion with the Fourth Category,
Relation ([Greek: pros ti] _Ad aliquid_, _To something_). Mill remarks
that "that could not be a very comprehensive view of the nature of
Relation which would exclude action, passivity, and local situation
from that Category," and many commentators, from Simplicius down to
Hamilton, have remarked that all the last six Categories might be
included under Relation. This is so far correct that the word Relation
is one of the vaguest and most extensive of words; but the criticism
ignores the strictness with which Aristotle confined himself in
his Categories to the forms of common speech. It is clear from
his examples that in his Fourth Category he was thinking only of
"relation" as definitely expressed in common speech. In his meaning,
any word is a relative which is joined with another in a sentence by
means of a preposition or a case-inflection. Thus "disposition" is a
relative: it is the disposition _of_ something. This kind of relation
is perfect when the related terms reciprocate grammatically; thus
"master," "servant," since we can say either "the master of the
servant," or "the servant of the master". In mediaeval logic the term
_Relata_ was confined to these perfect cases, but the Category had
a wider scope with Aristotle. And he expressly raised the question
whether a word might not have as much right to be put in another
Category as in this. Indeed, he went further than his critics in his
suggestions of what Relation might be made to include. Thus: "big"
signifies Quality; yet a thing is big with reference to something
else, and is so far a Relative. Knowledge must be knowledge of
something, and is a relative: why then should we put "knowing"
(_i.e._, learned) in the Category of Quality. "Hope" is a relative,
as being the hope _of_ a man and the hope of something. Yet we say,
"I have hope," and there hope would be in the category of Having,
Appurtenance. For the solution of all such difficulties, Aristotle
falls back
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