Deductive Logic
S >>
St. George Stock >> Deductive Logic
Pages:
1 | 2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18
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.
101. Since things are divided exhaustively into substances and
attributes, it follows that any term which is not the name of a thing
capable of being conceived to exist by itself, must be an abstract
term. Individual substances can alone be conceived to exist by
themselves: all their qualities, actions, passions, and
inter-relations, all their states, and all events with regard to them,
presuppose the existence of these individual substances. All names
therefore of such things as those just enumerated are abstract
terms. The term 'action,' for instance, is an abstract term. For how
could there be action without an agent? The term 'act' also is equally
abstract for the same reason. The difference between 'action' and
'act' is not the difference between abstract and concrete, but the
difference between the name of a process and the name of the
corresponding product. Unless acts can be conceived to exist without
agents they are as abstract as the action from which they result.
102. Since every term must be either abstract or concrete, it may be
asked--Are attributives abstract or concrete? The answer of course
depends upon whether they are names of substances or names of
attributes. But attributives, it must be remembered, are never
directly names of anything, in the way that subject-terms are; they
are only names of things in virtue of being predicated of
them. Whether an attributive is abstract or concrete, depends on the
nature of the subject of which it is asserted or denied. When we say
'This man is noble,' the term 'noble' is concrete, as being the name
of a substance: but when we say 'This act is noble,' the term 'noble'
is abstract, as being the name of an attribute.
103. The division of terms into Abstract and Concrete is based upon
the kind of thing signified. It involves no reference to actual
existence. There are imaginary as well as real substances. Logically a
centaur is as much a substance as a horse.
_Terms._
104. A Singular Term is a name which can be applied, in the same
sense, to one thing only, e.g. 'John,' 'Paris,' 'the capital of
France,' 'this pen.'
105. A Common Term is a name which can be applied, in the same
sense, to a class of things, e.g. 'man,' 'metropolis,' 'pen.'
In order that a term may be applied in the same sense to a number of
things, it is evident that it must indicate attributes which are
common to all of them. The term 'John' is applicable to a number of
things, but not in the same sense, as it does not indicate attributes.
106. Common terms are formed, as we have seen already ( 99), by
abstraction, i. e. by withdrawing the attention from the attributes in
which individuals differ, and concentrating it upon those which they
have in common.
107. A class need not necessarily consist of more than two
things. If the sun and moon were the only heavenly bodies in the
universe, the word 'heavenly body' would still be a common term, as
indicating the attributes which are possessed alike by each.
108. This being so, it follows that the division of terms into
singular and common is as exhaustive as the preceding ones, since a
singular term is the name of one thing and a common term of more than
one. It is indifferent whether the thing in question be a substance or
an attribute; nor does it matter how complex it may be, so long as it
is regarded by the mind as one.
109. Since every term must thus be either singular or common, the
members of the preceding divisions must find their place under one or
both heads of this one. Subject-terms may plainly fall under either
head of singular or common: but attributives are essentially common
terms. Such names as 'green,' 'gentle,' 'incongruous' are applicable,
strictly in the same sense, to all the things which possess the
attributes which they imply.
110. Are abstract terms then, it may be asked, singular or common?
To this question we reply--That depends upon how they are used. The
term 'virtue,' for instance, in one sense, namely, as signifying moral
excellence in general, without distinction of kind, is strictly a
singular term, as being the name of one attribute: but as applied to
different varieties of moral excellence--justice, generosity,
gentleness and so on--it is a common term, as being a name which is
applicable, in the same sense, to a class of attributes. Similarly the
term 'colour,' in a certain sense, signifies one unvarying attribute
possessed by bodies, namely, the power of affecting the eye, and in
this sense it is a singular term: but as applied to the various ways
in which the eye may be affected, it is evidently a common term, being
equally applicable to red, blue, green, and every other colour. As
soon as we begin to abstract from attributes, the higher notion
becomes a common term in reference to the lower. By a 'higher notion'
is meant one which is formed by a further process of abstraction. The
terms 'red,' 'blue,' 'green,' etc., are arrived at by abstraction from
physical objects; 'colour' is arrived at by abstraction from them, and
contains nothing, but what is common to all. It therefore applies in
the same sense to each, and is a common term in relation to them.
111. A practical test as to whether an abstract term, in any given
case, is being used as a singular or common term, is to try whether
the indefinite article or the sign of the plural can be attached to
it. The term 'number,' as the name of a single attribute of things,
admits of neither of these adjuncts: but to talk of 'a number' or 'the
numbers, two, three, four,' etc., at once marks it as a common
term. Similarly the term 'unity' denotes a single attribute, admitting
of no shades of distinction: but when a writer begins to speak of 'the
unities' he is evidently using the word for a class of things of some
kind or other, namely, certain dramatical proprieties of composition.
Proper _Names_ and _Designations_.
112. Singular terms may be subdivided into Proper Names and
Designations.
113. A Proper Name is a permanent singular term applicable to a
thing in itself; a Designation is a singular term devised for the
occasion, or applicable to a thing only in so far as it possesses some
attribute.
114. 'Homer' is a proper name; 'this man,' 'the author of the Iliad'
are designations.
115. The number of things, it is clear, is infinite. For, granting
that the physical universe consists of a definite number of
atoms--neither one more nor one less--still we are far from having
exhausted the possible number of things. All the manifold material
objects, which are made up by the various combinations of these atoms,
constitute separate objects of thought, or things, and the mind has
further an indefinite power of conjoining and dividing these objects,
so as to furnish itself with materials of thought, and also of fixing
its attention by abstraction upon attributes, so as to regard them as
things, apart from the substances to which they belong.
116. This being so, it is only a very small number of things, which
are constantly obtruding themselves upon the mind, that have singular
terms permanently set apart to denote them. Human beings, some
domestic animals, and divisions of time and place, have proper names
assigned to them in most languages, e.g. 'John,' 'Mary,' 'Grip,'
'January,' 'Easter,' 'Belgium,' 'Brussels,' 'the Thames,' 'Ben-Nevis.'
Besides these, all abstract terms, when used without reference to
lower notions, are of the nature of proper names, being permanently
set apart to denote certain special attributes, e.g. 'benevolence,'
'veracity,' 'imagination,' 'indigestibility, 'retrenchment.'
Pages:
1 | 2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18