Deductive Logic

by George William Joseph Stock, M.A.

Part 1: Chapter 1

Additional Information
  • Year Published: 1888
  • Language: English
  • Country of Origin: England
  • Source: Stock, G. W. J. (1888). Deductive Logic. Oxford, England; Pembroke College.
  • Readability:
    • Flesch–Kincaid Level: 11.0
  • Word Count: 1,285
  • Genre: Informational
  • Keywords: math, math history
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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.