Deductive Logic
Deductive LogicPREFACE.INTRODUCTION.PART I.—OF TERMS.CHAPTER 1.CHAPTER II.CHAPTER III.CHAPTER IV.PART II.—OF PROPOSITIONS.CHAPTER I.CHAPTER II.CHAPTER III.CHAPTER IV.CHAPTER V.CHAPTER VI.CHAPTER VII.CHAPTER VIII.PART III.—OF INFERENCES.CHAPTER I.CHAPTER II.CHAPTER III.CHAPTER IV.CHAPTER V.CHAPTER VI.CHAPTER VII.CHAPTER VIII.CHAPTER IX.CHAPTER X.CHAPTER XI.CHAPTER XII.CHAPTER XIII.CHAPTER XIVCHAPTER XV.CHAPTER XVI.CHAPTER XVII.CHAPTER XVIII.CHAPTER XIX.CHAPTER XX.CHAPTER XXI.CHAPTER XXII.CHAPTER XXIII.CHAPTER XXIV.CHAPTER XXV.CHAPTER XXVI.CHAPTER XXVII.CHAPTER XXVIII.CHAPTER XXIX.CHAPTER XXX.EXERCISES.PART I.CHAPTER I.CHAPTER II.CHAPTER III.CHAPTER IV.PART II.CHAPTER I.CHAPTER II.CHAPTER III.CHAPTER IV.CHAPTER V.CHAPTER VI.CHAPTER VII.CHAPTER VIII.PART III.CHAPTERS I-III.CHAPTER IV.CHAPTER V.CHAPTER VI.CHAPTER VII.CHAPTER VIII.CHAPTERS IX-XVIII.CHAPTER XIX.CHAPTERS XX-XXVIII.CHAPTER XXIX.CHAPTER XXX.Copyright
Deductive Logic
St. George William Joseph Stock
PREFACE.
One critic, who was kind enough to look at this book in
manuscript, recommended me to abandon the design of Publishing it,
on the ground that my logic was too like all other logics; another
suggested to me to cut out a considerable amount of new matter. The
latter advice I have followed; the former has encouraged me to hope
that I shall not be considered guilty of wanton innovation. The few
novelties which I have ventured to retain will, I trust, be
regarded as legitimate extensions of received lines of
teaching.My object has been to produce a work which should be as
thoroughly representative of the present state of the logic of the
Oxford Schools as any of the text-books of the past. The qualities
which I have aimed at before all others have been clearness and
consistency. For the task which I have taken upon myself I may
claim one qualification—that of experience; since more than
seventeen years have now elapsed since I took my first pupil in
logic for the Honour School of Moderations, and during that time I
have been pretty continuously engaged in studying and teaching the
subject.In acknowledging my obligations to previous writers I must
begin with Archbishop Whately, whose writings first gave me an
interest in the subject. The works of Mill and Hamilton have of
course been freely drawn upon. I have not followed either of those
two great writers exclusively, but have endeavoured to assimilate
what seemed best in both. To Professor Fowler I am under a special
debt. I had not the privilege of personal teaching from him in
logic,—as I had in some other subjects; but his book fell into my
hands at an early period in my mental training, and was so
thoroughly studied as to have become a permanent part of the
furniture of my mind. Much the same may be said of my relation to
the late Professor Jevons's Elementary Lessons in Logic. Two other
books, which I feel bound to mention with special emphasis, are
Hansel's edition of Aldrich and McCosh's Laws of Discursive
Thought. If there be added to the foregoing Watts's Logic,
Thomson's Outlines of the Laws of Thought, Bain's Deductive Logic,
Jevons's Studies in Deductive Logic and Principles of Science,
Bradley's Principles of Logic, Abbott's Elements of Logic, Walker's
edition of Murray, Ray's Text-book of Deductive Logic, and
Weatherley's Rudiments of Logic, I think the list will be exhausted
of modern works from which I am conscious of having borrowed. But,
not to forget the sun, while thanking the manufacturers of lamps
and candles, I should add that I have studied the works of
Aristotle according to the measure of my time and
ability.This work has had the great advantage of having been revised,
while still in manuscript, by Mr. Alfred Robinson, Fellow of New
College, to whom I cannot sufficiently express my obligation. I
have availed myself to the full of the series of criticisms which
he was kind enough to send me. As some additions have been made
since then, he cannot be held in anyway responsible for the faults
which less kindly critics may detect.For the examples at the end I am mainly indebted to others,
and to a large extent to my ingenious friend, the Rev. W. J. Priest
of Merton College.My thanks are due also to my friend and former pupil, Mr.
Gilbert Grindle, Scholar of Corpus, who has been at the pains to
compose an index, and to revise the proofs as they passed through
the press.And last, but not least, I must set on record my gratitude to
Commander R. A. Stock, R.N., one of Her Majesty's Knights of
Windsor, without whose brotherly aid this work might never have
been written, and would certainly not have assumed exactly its
present shape.
INTRODUCTION.
§ 1. LOGIC is divided into two branches, namely—(1) Inductive,(2) Deductive.§ 2. The problem of inductive logic is to determine the
actual truth or falsity of propositions: the problem of deductive
logic is to determine their relative truth or falsity, that is to
say, given such and such propositions as true, what others will
follow from them.§ 3. Hence in the natural order of treatment inductive logic
precedes deductive, since it is induction which supplies us with
the general truths, from which we reason down in our deductive
inferences.§ 4. It is not, however, with logic as a whole that we are
here concerned, but only with deductive logic, which may be defined
as The Science of the Formal Laws of Thought.§ 5. In order fully to understand this definition we must
know exactly what is meant by 'thought,' by a 'law of thought,' by
the term 'formal,' and by 'science.'§ 6. Thought, as here used, is confined to the faculty of
comparison. All thought involves comparison, that is to say, a
recognition of likeness or unlikeness.§ 7. The laws of thought are the conditions of correct
thinking. The term 'law,' however, is so ambiguous that it will be
well to determine more precisely in what sense it is here
used.§ 8. We talk of the 'laws of the land' and of the 'laws of
nature,' and it is evident that we mean very different things by
these expressions. By a law in the political sense is meant a
command imposed by a superior upon an inferior and sanctioned by a
penalty for disobedience. But by the 'laws of nature' are meant
merely certain uniformities among natural phenomena; for instance,
the 'law of gravitation' means that every particle of matter does
invariably attract every other particle of matter in the
universe.§ 9. The word 'law' is transferred by a metaphor from one of
these senses to the other. The effect of such a command as that
described above is to produce a certain amount of uniformity in the
conduct of men, and so, where we observe uniformity in nature, we
assume that it is the result of such a command, whereas the only
thing really known to us is the fact of uniformity
itself.§ 10. Now in which of these two senses are we using the term
'laws of thought'? The laws of the land, it is plain, are often
violated, whereas the laws of nature never can be so [Footnote:
There is a sense in which people frequently speak of the laws of
nature being violated, as when one says that intemperance or
celibacy is a violation of the laws of nature, but here by 'nature'
is meant an ideal perfection in the conditions of existence.]. Can
the laws of thought be violated in like manner with the laws of the
land? Or are they inviolable like the laws of nature?§ 11. In appearance they can be, and manifestly often are
violated-for how else could error be possible? But in reality they
can not. No man ever accepts a contradiction when it presents
itself to the mind as such: but when reasoning is at all
complicated what does really involve a contradiction is not seen to
do so; and this sort of error is further assisted by the infinite
perplexities of language.§ 12. The laws of thought then in their ultimate expression
are certain uniformities which invariably hold among mental
phenomena, and so far they resemble the laws of nature: but in
their complex applications they may be violated owing to error, as
the laws of the land may be violated by crime.§ 13. We have now to determine the meaning of the expression
'formal laws of thought.'§ 14. The distinction between form and matter is one which
pervades all nature. We are familiar with it in the case of
concrete things. A cup, for instance, with precisely the same form,
may be composed of very different matter-gold, silver, pewter, horn
or what not?§ 15. Similarly in every act of thought we may distinguish
two things—(1) the object thought about,(2) the way in which the mind thinks of it.The first is called the Matter; the second the Form of
Thought.§ 16. Now Formal, which is another name for Deductive Logic,
is concerned only with the way in which the mind thinks, and has
nothing to do with the particular objects thought
about.§ 17. Since the form may be the same, whilst the matter is
different, we may say that formal logic is concerned with the
essential and necessary elements of thought as opposed to such as
are accidental and contingent. By 'contingent' is meant what holds
true in some cases, but not in others. For instance, in the
particular case of equilateral triangles it is true to say, not
only that 'all equilateral triangles are equiangular,' but also
that 'all equiangular triangles are equilateral.' But the evidence
for these two propositions is independent. The one is not a formal
consequence of the other. If it were, we should be able to apply
the same inference to all matter, and assert generally that if all
A is B, all B is A, which it is notorious that we cannot
do.§ 18. It remains now for the full elucidation of our
definition to determine what is meant by 'science.'§ 19. The question has often been discussed whether logic is
a science or an art. The answer to it must depend upon the meaning
we assign to these terms.§ 20. Broadly speaking, there is the same difference between
Science and Art as there is between knowing and doing.Science is systematized knowledge; Art is systematized action. Science is acquired by study; Art is acquired by practice.§ 21. Now logic is manifestly a branch of knowledge, and does
not necessarily confer any practical skill. It is only the right
use of its rules in thinking which can make men think better. It is
therefore, in the broad sense of the terms, wholly a science and
not at all an art.§ 22. But this word 'art,' like most others, is ambiguous,
and is often used, not for skill displayed in practice, but for the
knowledge necessary thereto. This meaning is better conveyed by the
term 'practical science.'§ 23. Science is either speculative or practical. In the
first case we study merely that we may know; in the latter that we
may do.Anatomy is a speculative science; Surgery is a practical science.In the first case we study the human frame in order that we
may understand its structure; in the second that we may assist its
needs. Whether logic is a speculative or a practical science
depends entirely upon the way in which it is treated. If we study
the laws of thought merely that we may know what they are, we are
making it a speculative science; if we study the same laws with a
view to deducing rules for the guidance of thought, we are making
it a practical science.§ 24. Hence logic may be declared to be both the science and
the art of thinking. It is the art of thinking in the same sense in
which grammar is the art of speaking. Grammar is not in itself the
right use of words, but a knowledge of it enables men to use words
correctly. In the same way a knowledge of logic enables men to
think correctly, or at least to avoid incorrect thoughts. As an art
logic may be called the navigation of the sea of
thought.§ 25. The laws of thought are all reducible to the three
following axioms, which are known as The Three Fundamental Laws of
Thought.(1) The Law of Identity—Whatever is, is;or, in a more precise form,Every A is A.(2) The Law of Contradiction—Nothing can both be and not
be; Nothing can be A and not
A.(3) The Law of Excluded Middle—Everything must either be or not
be; Everything is either A or not
A.§ 26. Each of these principles is independent and
self-evident.§ 27. If it were possible for the law of identity to be
violated, no violation of the law of contradiction would
necessarily ensue: for a thing might then be something else,
without being itself at the same time, which latter is what the law
of contradiction militates against. Neither would the law of
excluded middle be infringed. For, on the supposition, a thing
would be something else, whereas all that the law of excluded
middle demands is that it should either be itself or not. A would
in this case adopt the alternative of being not A.§ 28. Again, the violation of the law of contradiction does
not involve any violation of the law of identity: for a thing might
in that case be still itself, so that the law of identity would be
observed, even though, owing to the law of contradiction not
holding, it were not itself at the same time. Neither would the law
of excluded middle be infringed. For a thing would, on the
supposition, be both itself and not itself, which is the very
reverse of being neither.§ 29. Lastly, the law of excluded middle might be violated
without a violation of the law of contradiction: for we should then
have a thing which was neither A nor not A, but not a thing which
was both at the same time. Neither would the law of identity be
infringed. For we should in this case have a thing which neither
was nor was not, so that the conditions of the law of identity
could not exist to be broken. That law postulates that whatever is,
is: here we have a thing which never was to begin
with.§ 30. These principles are of so simple a character that the
discussion of them is apt to be regarded as puerile. Especially is
this the case with regard to the law of identity. This principle in
fact is one of those things which are more honoured in the breach
than in the observance. Suppose for a moment that this law did not
hold—then what would become of all our reasoning? Where would be
the use of establishing conclusions about things, if they were
liable to evade us by a Protean change of identity?§ 31. The remaining two laws supplement each other in the
following way. The law of contradiction enables us to affirm of two
exhaustive and mutually exclusive alternatives, that it is
impossible for both to be true; the law of excluded middle entitles
us to add, that it is equally impossible for both to be false. Or,
to put the same thing in a different form, the law of contradiction
lays down that one of two such alternatives must be false; the law
of excluded middle adds that one must be true.§32. There are three processes of thought(1) Conception.(2) Judgement.(3) Inference or Reasoning.§ 33. Conception, which is otherwise known as Simple
Apprehension, is the act of forming in the mind the idea of
anything, e.g. when we form in the mind the idea of a cup, we are
performing the process of conception.§ 34. Judgement, in the sense in which it is here used
[Footnote: Sometimes the term 'judgement' is extended to the
comparison of nameless sense-impressions, which underlies the
formation of concepts. But this amounts to identifying judgement
with thought in general.] may be resolved into putting two ideas
together in the mind, and pronouncing as to their agreement or
disagreement, e.g. we have in our minds the idea of a cup and the
idea of a thing made of porcelain, and we combine them in the
judgement—'This cup is made of porcelain.'§ 35. Inference, or Reasoning, is the passage of the mind
from one or more judgements to another, e.g. from the two
judgements 'Whatever is made of porcelain is brittle,' and 'This
cup is made of porcelain,' we elicit a third judgement, 'This cup
is brittle.'§ 36. Corresponding to these three processes there are three
products of thought, viz.(1) The Concept.(2) The Judgement.(3) The Inference.§ 37. Since our language has a tendency to confuse the
distinction between processes and products, [Footnote: E.g. We have
to speak quite indiscriminately of Sensation, Imagination,
Reflexion, Sight, Thought, Division, Definition, and so on, whether
we mean in any case a process or a product.] it is the more
necessary to keep them distinct in thought. Strictly we ought to
speak of conceiving, judging and inferring on the one hand, and, on
the other, of the concept, the judgement and the
inference.The direct object of logic is the study of the products
rather than of the processes of thought. But, at the same time, in
studying the products we are studying the processes in the only way
in which it is possible to do so. For the human mind cannot be both
actor and spectator at once; we must wait until a thought is formed
in our minds before we can examine it. Thought must be already dead
in order to be dissected: there is no vivisection of consciousness.
Thus we can never know more of the processes of thought than what
is revealed to us in their products.§ 38. When the three products of thought are expressed in
language, they are called respectively(1) The Term.(2) The Proposition.(3) The Inference.§ 39. Such is the ambiguity of language that we have already
used the term 'inference' in three different senses—first, for the
act or process of inferring; secondly, for the result of that act
as it exists in the mind; and, thirdly, for the same thing as
expressed in language. Later on we shall have to notice a further
ambiguity in its use.§ 40. It has been declared that thought in general is the
faculty of comparison, and we have now seen that there are three
products of thought. It follows that each of these products of
thought must be the result of a comparison of some kind or
other.The concept is the result of comparing
attributes. The judgement is the result of comparing
concepts. The inference is the result of comparing
judgements.§ 41. In what follows we shall, for convenience, adopt the
phraseology which regards the products of thought as clothed in
language in preference to that which regards the same products as
they exist in the mind of the individual. For although the object
of logic is to examine thought pure and simple, it is obviously
impossible to discuss it except as clothed in language. Accordingly
the three statements above made may be expressed as
follows—The term is the result of comparing
attributes. The proposition is the result of comparing
terms. The inference is the result of comparing
propositions.§ 42. There is an advantage attending the change of language
in the fact that the word 'concept' is not an adequate expression
for the first of the three products of thought, whereas the word
'term' is. By a concept is meant a general notion, or the idea of a
class, which corresponds only to a common term. Now not only are
common terms the results of comparison, but singular terms, or the
names of individuals, are so too.§ 43. The earliest result of thought is the recognition of an
individual object as such, that is to say as distinguished and
marked off from the mass of its surroundings. No doubt the first
impression produced Upon the nascent intelligence of an infant is
that of a confused whole. It requires much exercise of thought to
distinguish this whole into its parts. The completeness of the
recognition of an individual object is announced by attaching a
name to it. Hence even an individual name, or singular term,
implies thought or comparison. Before thechildcan attach a meaning to the word
'mother,' which to it is a
singular term, it must have distinguished between the set of
impressions produced in it by one object from those which are
produced in it by others. Thus, when Vergil saysIncipe, parve puer, risu cognoscere matrem,he is exhorting the beatific infant to the exercise of the
faculty of comparison.§ 44. That a common term implies comparison does not need to
be insisted upon. It is because things resemble each other in
certain of their attributes that we call them by a common name, and
this resemblance could not be ascertained except by comparison, at
some time and by some one. Thus a common term, or concept, is the
compressed result of an indefinite number of comparisons, which lie
wrapped up in it like so many fossils, witnessing to prior ages of
thought.§ 45. In the next product of thought, namely, the
proposition, we have the result of a single act of comparison
between two terms; and this is why the proposition is called the
unit of thought, as being the simplest and most direct result of
comparison.§ 46. In the third product of thought, namely, the inference,
we have a comparison of propositions either directly or by means of
a third. This will be explained later on. For the present we return
to the first product of thought.§ 47. The nature of singular terms has not given rise to much
dispute; but the nature of common terms has been the great
battle-ground of logicians. What corresponds to a singular term is
easy to determine, for the thing of which it is a name is there to
point to: but the meaning of a common term, like 'man' or 'horse,'
is not so obvious as people are apt to think on first hearing of
the question.§ 48. A common term or class-name was known to mediæval
logicians under the title of a Universal; and it was on the
question 'What is a Universal 7' that they split into the three
schools of Realists, Nominalists, and Conceptualists. Here are the
answers of the three schools to this question in their most
exaggerated form—§ 49. Universals, said the Realists, are substances having an
independent existence in nature.§ 50. Universals, said the Nominalists, are a mere matter of
words, the members of what we call a class having nothing in common
but the name.§ 51. Universals, said the Conceptualists, exist in the mind
alone, They are the conceptions under which the mind regards
external objects.§ 52. The origin of pure Realism is due to Plato and his
doctrine of 'ideas'; for Idealism, in this sense, is not opposed to
Realism, but identical with it. Plato seems to have imagined that,
as there was a really existing thing corresponding to a singular
term, such as Socrates, so there must be a really existing thing
corresponding to the common term 'man.' But when once the existence
of these general objects is admitted, they swamp all other
existences. For individual men are fleeting and transitory—subject
to growth, decay and death—whereas the idea of man is imperishable
and eternal. It is only by partaking in the nature of these ideas
that individual objects exist at all.§ 53. Pure Nominalism was the swing of the pendulum of
thought to the very opposite extreme; while Conceptualism was an
attempt to hit the happy mean between the two.§ 54. Roughly it may be said that the Realists sought for the
answer to the question 'What is a Universal?' in the matter of
thought, the Conceptualists in the form, and the Nominalists in the
expression.§ 55. A full answer to the question 'What is a Universal?'
will bring in something of the three views above given, while
avoiding the exaggeration of each. A Universal is a number of
things that are called by the same name; but they would not be
called by the same name unless they fell under the same conception
in the mind; nor would they fall under the same conception in the
mind unless there actually existed similar attributes in the
several members of a class, causing us to regard them under the
same conception and to give them the same name. Universals
therefore do exist in nature, and not merely in the mind of man:
but their existence is dependent upon individual objects, instead
of individual objects depending for their existence upon them.
Aristotle saw this very clearly, and marked the distinction between
the objects corresponding to the singular and to the common term by
calling the former Primary and the latter Secondary Existences.
Rosinante and Excalibur are primary, but 'horse' and 'sword'
secondary existences.§ 56. We have seen that the three products of thought are
each one stage in advance of the other, the inference being built
upon the proposition, as the proposition is built upon the term.
Logic therefore naturally divides itself into three
parts.The First Part of Logic deals with the
Term; The Second Part deals with the
Proposition; The Third Part deals with the
Inference.
PART I.—OF TERMS.
CHAPTER 1.
Of the Term as distinguished from other
words.
§ 57. The word 'term' means a boundary.
§ 58. The subject and predicate are the two terms, or
boundaries, of a proposition. In a proposition we start from a
subject and end in a predicate (§§ 182-4), there being nothing
intermediate between the two except the act of pronouncing as to
their agreement or disagreement, which is registered externally
under the sign of the copula. Thus the subject is the 'terminus a
quo,' and the predicate is the 'terminus ad quem.'
§ 59. Hence it appears that the term by its very name
indicates that it is arrived at by an analysis of the proposition.
It is the judgement or proposition that is the true unit of thought
and speech. The proposition as a whole is prior in conception to
the terms which are its parts: but the parts must come before the
whole in the synthetic order of treatment.
§ 60. A term is the same thing as a name or noun.
§ 61. A name is a word, or collection of words, which serves
as a mark to recall or transmit the idea of a thing, either in
itself or through some of its attributes.
§ 62. Nouns, or names, are either Substantive or
Adjective.
A Noun Substantive is the name of a thing in itself, that is
to say, without reference to any special attribute.
§ 63. A Noun Adjective is a name which we are entitled to add
to a thing, when we know it to possess a given attribute.
§ 64. The Verb, as such, is not recognised by logic, but is
resolved into predicate and copula, that is to say, into a noun
which is affirmed or denied of another, plus the sign of that
affirmation or denial. 'The kettle boils' is logically equivalent
to 'The kettle is boiling,' though it is by no means necessary to
express the proposition in the latter shape. Here we see that
'boils' is equivalent to the noun 'boiling' together with the
copula 'is,' which declares its agreement with the noun 'kettle.'
'Boiling' here is a noun adjective, which we are entitled to add to
'kettle,' in virtue of certain knowledge which we have about the
latter. Being a verbal noun, it is called in grammar a participle,
rather than a mere adjective. The word 'attributive' in logic
embraces both the adjective and participle of grammar.
§ 65. In grammar every noun is a separate word: but to logic,
which is concerned with the thought rather than with the
expression, it is indifferent whether a noun, or term, consists of
one word or many. The latter are known as 'many-worded names.' In
the following passage, taken at random from Butler's Analogy—'These
several observations, concerning the active principle of virtue and
obedience to God's commands, are applicable to passive submission
or resignation to his will'—we find the subject consisting of
fourteen words, and the predicate of nine. It is the exception
rather than the rule to find a predicate which consists of a single
word. Many-worded names in English often consist of clauses
introduced by the conjunction 'that,' as 'That letters should be
written in strict conformity with nature is true': often also of a
grammatical subject with one or more dependent clauses attached to
it, as
'He who fights and runs away, Will live to fight another
day.'
§ 66. Every term then is not a word, since a term may consist
of a collection of words. Neither is every word a term. 'Over,' for
instance, and 'swiftly,' and, generally, what are called particles
in grammar, do not by themselves constitute terms, though they may
be employed along with other words to make up a term.
§ 67. The notions with which thought deals involve many
subtle relations and require many nice modifications. Language has
instruments, more or less perfect, whereby such relations and
modifications may be expressed. But these subsidiary aids to
expression do not form a notion which can either have something
asserted of it or be asserted itself of something else.
§ 68. Hence words are divided into three classes—
(1) Categorematic;
(2) Syncategorematic;
(3) Acategorematic.
§ 69. A Categorematic word is one which can be used by itself
as a term.
§ 70. A Syncategorematic word is one which can help to form a
term.
§ 71. An Acategorematic word is one which can neither form,
nor help to form, a term [Footnote: Comparatively few of the parts
of speech are categorematic. Nouns, whether substantive or
adjective, including of course pronouns and participles, are so,
but only in their nominative cases, except when an oblique case is
so used as to be equivalent to an attributive. Verbs also are
categorematic, but only in three of their moods, the Indicative,
the Infinitive, and the Potential. The Imperative and Optative
moods clearly do not convey assertions at all, while the
Subjunctive can only figure as a subordinate member of some
assertion. We may notice, too, that the relative pronoun, unlike
the rest, is necessarily syncategorematic, for the same reason as
the subjunctive mood. Of the remaining parts of speech the article,
adverb, preposition, and conjunction can never be anything but
syncategorematic, while the interjection is acategorematic, like
the vocative case of nouns and the imperative and optative moods of
verbs, which do not enter at all into the form of sentence known as
the proposition.].
§ 72. Categorematic literally means 'predicable.' 'Horse,'
'swift,' 'galloping' are categorematic. Thus we can say, 'The horse
is swift,' or 'The horse is galloping.' Each of these words forms a
term by itself, but 'over' and 'swiftly' can only help to form a
term, as in the proposition, 'The horse is galloping swiftly over
the plain.'
§ 73. A term then may be said to be a categorematic word or
collection of words, that is to say, one which can be used by
itself as a predicate.
§ 74. To entitle a word or collection of words to be called a
term, it is not necessary that it should be capable of standing by
itself as a subject. Many terms which can be used as predicates are
incapable of being used as subjects: but every term which can be
used as a subject (with the doubtful exception of proper names) can
be used also as a predicate. The attributives 'swift' and
'galloping' are terms, quite as much as the subject 'horse,' but
they cannot themselves be used as subjects.
§ 75. When an attributive appears to be used as a subject, it
is owing to a grammatical ellipse. Thus in Latin we say 'Boni
sapientes sunt,' and in English 'The good are wise,' because it is
sufficiently declared by the inflexional form in the one case, and
by the usage of the language in the other, that men are signified.
It is an accident of language how far adjectives can be used as
subjects. They cease to be logical attributives the moment they are
so used.
§ 76. There is a sense in which every word may become
categorematic, namely, when it is used simply as a word, to the
neglect of its proper meaning. Thus we can say—'"Swiftly" is an
adverb.' 'Swiftly' in this sense is really no more than the proper
name for a particular word. This sense is technically known as the
'suppositio materialis' of a word.
CHAPTER II.
Of the Division of Things.
§ 77. Before entering on the divisions of terms it is
necessary to advert for a moment to a division of the things
whereof they are names.
§ 78. By a 'thing' is meant simply an object of
thought—whatever one can think about.
§ 79. Things are either Substances or Attributes. Attributes
may be sub-divided into Qualities and Relations.
Thing _______________|_______________ | | Substance Attribute _____________|____________ |
| Quality
Relation
§ 80. A Substance is a thing which can be conceived to exist
by itself. All bodies are material substances. The soul, as a
thinking subject, is an immaterial substance.
§ 81. An Attribute is a thing which depends for its existence
upon a substance, e.g. greenness, hardness, weight, which cannot be
conceived to exist apart from green, hard, and heavy
substances.
§ 82. A Quality is an attribute which does not require more
than one substance for its existence. The attributes just mentioned
are qualities. There might be greenness, hardness, and weight, if
there were only one green, hard and heavy substance in the
universe.
§ 83. A Relation is an attribute which requires two or more
substances for its existence, e.g. nearness, fatherhood,
introduction.
§ 84. When we say that a substance can be conceived to exist
by itself, what is meant is that it can be conceived to exist
independently of other substances. We do not mean that substances
can be conceived to exist independently of attributes, nor yet out
of relation to a mind perceiving them. Substances, so far as we can
know them, are only collections of attributes. When therefore we
say that substances can be conceived to exist by themselves,
whereas attributes are dependent for their existence upon
substances, the real meaning of the assertion reduces itself to
this, that it is only certain collections of attributes which can
be conceived to exist independently; whereas single attributes
depend for their existence upon others. The colour, smoothness or
solidity of a table cannot be conceived apart from the extension,
whereas the whole cluster of attributes which constitutes the table
can be conceived to exist altogether independently of other 'such
clusters. We can imagine a table to exist, if the whole material
universe were annihilated, and but one mind left to perceive it.
Apart from mind, however, we cannot imagine it: since what we call
the attributes of a material substance are no more than the various
modes in which we find our minds affected.
§ 85. The above division of things belongs rather to the
domain of metaphysics than of logic: but it is the indispensable
basis of the division of terms, to which we now proceed.
CHAPTER III.
Of the Division of Terms.
§ 86. The following scheme presents to the eye the chief
divisions of terms.
Term Division of terms according to their
place in thought. Subject-Term Attributive
according to the kind of thing
signified. Abstract Concrete
according to Quantity in
Extension. Singular Common
according to Quality. Positive Privative Negative
according to number of
meanings. Univocal Equivocal
according to number of things
involved in the name. Absolute Relative
according to number of
quantities. Connotative Non-connotative
Subject-term and Attributive.
§ 87. By a Subject-term is meant any term which is capable of
standing by itself as a subject, e.g. 'ribbon,' 'horse.'
§ 88. Attributives can only be used as predicates, not as
subjects, e.g. 'cherry-coloured,' 'galloping.' These can only be
used in conjunction with other words (syncategorematically) to make
up a subject. Thus we can say 'A cherry-coloured ribbon is
becoming,' or 'A galloping horse is dangerous.'
§ 89. Attributives are contrivances of language whereby we
indicate that a subject has a certain attribute. Thus, when we say
'This paper is white,' we indicate that the subject 'paper'
possesses the attribute whiteness. Logic, however, also recognises
as attributives terms which signify the non-possession of
attributes. 'Not-white' is an attributive equally with
'white.'
§ 90. An Attributive then may be defined as a term which
signifies the possession, or non-possession, of an attribute by a
subject.
§ 91. It must be carefully noticed that attributives are not
names of attributes, but names of the things which possess the
attributes, in virtue of our knowledge that they possess them. Thus
'white' is the name of all the things which possess the attribute
whiteness, and 'virtuous' is a name; not of the abstract quality,
virtue, itself, but of the men and actions which possess it. It is
clear that a term can only properly be said to be a name of those
things whereof it can be predicated. Now, we cannot intelligibly
predicate an attributive of the abstract quality, or qualities, the
possession of which it implies. We cannot, for instance, predicate
the term 'learned' of the abstract quality of learning: but we may
predicate it of the individuals, Varro and Vergil. Attributives,
then, are to be regarded as names, not of the attributes which they
imply, but of the things in which those attributes are
found.
§ 92. Attributives, however, are names of things in a less
direct way than that in which subject-terms may be the names of the
same things. Attributives are names of things only in predication,
whereas subject-terms are names of things in or out of predication.
The terms 'horse' and 'Bucephalus' are names of certain things, in
this case animals, whether we make any statement about them or not:
but the terms 'swift' and 'fiery' only become names of the same
things in virtue of being predicable of them. When we say 'Horses
are swift' or 'Bucephalus was fiery,' the terms 'swift' and 'fiery'
become names respectively of the same things as 'horse' and
'Bucephalus.' This function of attributives as names in a secondary
sense is exactly expressed by the grammatical term 'noun
adjective.' An attributive is not directly the name of anything. It
is a name added on in virtue of the possession by a given thing of
a certain attribute, or, in some cases, the non-possession.
§ 93. Although attributives cannot be used as subjects, there
is nothing to prevent a subject-term from being used as a
predicate, and so assuming for the time being the functions of an
attributive. When we say 'Socrates was a man,' we convey to the
mind the idea of the same attributes which are implied by the
attributive 'human.' But those terms only are called attributives
which can never be used except as predicates.
§ 94. This division into Subject-terms and Attributives may
be regarded as a division of terms according to their place in
thought. Attributives, as we have seen, are essentially predicates,
and can only be thought of in relation to the subject, whereas the
subject is thought of for its own sake.
Abstract and Concrete Terms.
§ 95. An Abstract Term is the name of an attribute, e.g.
whiteness [Footnote: Since things cannot be spoken of except by
their names, there is a constantly recurring source of confusion
between the thing itself and the name of it. Take for instance
'whiteness.' The attribute whiteness is a thing, the word
'whiteness' is a term.], multiplication, act, purpose,
explosion.
§ 96. A Concrete Term is the name of a substance, e.g. a man,
this chair, the soul, God.
§ 97. Abstract terms are so called as being arrived at by a
process of Abstraction. What is meant by Abstraction will be clear
from a single instance. The mind, in contemplating a number of
substances, may draw off, or abstract, its attention from all their
other characteristics, and fix it only on some point, or points,
which they have in common. Thus, in contemplating a number of
three-cornered objects, we may draw away our attention from all
their other qualities, and fix it exclusively upon their
three-corneredness, thus constituting the abstract notion of
'triangle.' Abstraction may be performed equally well in the case
of a single object: but the mind would not originally have known on
what points to fix its attention except by a comparison of
individuals.
§ 98. Abstraction too may be performed upon attributes as
well as substances. Thus, having by abstraction already arrived at
the notion of triangle, square, and so on, we may fix our attention
upon what these have in common, and so rise to the higher
abstraction of 'figure.' As thought becomes more complex, we may
have abstraction on abstraction and attributes of attributes. But,
however many steps may intervene, attributes may always be traced
back to substances at last. For attributes of attributes can mean
at bottom nothing but the co-existence of attributes in, or in
connection with, the same substances.
§ 99. We have said that abstract terms are so called, as
being arrived at by abstraction: but it must not be inferred from
this statement that all terms which are arrived at by abstraction
are abstract. If this were so, all names would be abstract except
proper names of individual substances. All common terms, including
attributives, are arrived at by abstraction, but they are not
therefore abstract terms. Those terms only are called abstract,
which cannot be applied to substances at all. The terms 'man' and
'human' are names of the same substance of which Socrates is a
name. Humanity is a name only of certain attributes of that
substance, namely those which are shared by others. All names of
concrete things then are concrete, whether they denote them
individually or according to classes, and whether directly and in
themselves, or indirectly, as possessing some given
attribute.
§ 100. By a 'concrete thing' is meant an individual Substance
conceived of with all its attributes about it. The term is not
confined to material substances. A spirit conceived of under
personal attributes is as concrete as plum-pudding.
