Deductive Logic

-- 166. In a series of terms which fall under one another, as the extension decreases, the intension increases, and vice versa. Take for instance the following series--

Thing | Substance | Matter | Organism | Animal | Vertebrate | Mammal | Ruminant | Sheep | This sheep.

Here the term at the top possesses the widest possible extension, since it applies to everything. But at the same time it possesses the least possible amount of intension, implying nothing more than mere existence, whether in fact or thought. On the other hand, the term at the bottom possesses the greatest amount of intension, since it implies all the attributes of, an individual superadded to those of the cla.s.s to which it belongs: but its extension is the narrowest possible, being limited to one thing.

-- 167. At each step in the descent from the term at the top, which is called the 'Summum genus,' to the individual, we decrease the extension by increasing the intension. Thus by adding on to the bare notion of a thing the idea of independent existence, we descend to the term 'substance,' This process is known as Determination, or Specialisation.

-- 168. Again, by withdrawing our attention from the individual characteristics of a particular sheep, and fixing it upon those which are common to it with other animals of the same kind, we arrive at the common term, 'sheep.' Here we have increased the extension by decreasing the intension. This process is known as Generalisation.

-- 169. Generalisation implies abstraction, but we may have abstraction without generalisation.

-- 170. The following example is useful, as ill.u.s.trating to the eye how a decrease of extension is accompanied by an increase of intension. At each step of the descent here we visibly tack on a fresh attribute. [Footnote: This example is borrowed from Professor Jevons.]

s.h.i.+p | Steam-s.h.i.+p | Screw steam-s.h.i.+p | Iron screw steam-s.h.i.+p | British iron screw steam-s.h.i.+p.

Could we see the cla.s.ses denoted by the names the pyramid would be exactly inverted.

-- 171. The law of inverse variation of extension and intension must of course be confined to the inter-relations of a series of terms of which each can be predicated of the other until we arrive at the bottom of the

PART II.--OF PROPOSITIONS.

CHAPTER I.

_Of the Proposition as distinguished from Other Sentences_.

-- 172. As in considering the term, we found occasion to distinguish it from words generally, so now, in considering the proposition, it will be well to begin by distinguis.h.i.+ng it from other sentences.

-- 173. Every proposition is a sentence, but every sentence is not a proposition.

-- 174. The field of logic is far from being conterminous with that of language. Language is the mirror of man's whole nature, whereas logic deals with language only so far as it gives clothing to the products of thought in the narrow sense which we have a.s.signed to that term.

Language has materials of every sort lying strewn about, among which the logician has to seek for his proper implements.

-- 175. Sentences may be employed for a variety of purposes--

(1) To ask a question;

(2) To give an order;

(3) To express a feeling;

(4) To make a statement.

These various uses give rise respectively to

(1) The Interrogative Sentence;

(2) The Imperative Sentence;

(3) The Exclamatory Sentence;

(4) The Enunciative Sentence; Indicative Potential.

It is with the last of these only that logic is concerned.

-- 176. The proposition, therefore, corresponds to the Indicative and Potential, or Conditional, sentences of grammar. For it must be borne in mind that logic recognises no difference between a statement of fact and a supposition. 'It may rain to-morrow' is as much a proposition as 'It is raining now.'

-- 177. Leaving the grammatical aspect of the proposition, we must now consider it from the purely logical point of view.

-- 178. A proposition is a judgement expressed in words; and a judgement is a direct comparison between two concepts.

-- 179. The same thing may be expressed more briefly by saying that a proposition is a direct comparison between two terms.

-- 180. We say 'direct comparison,' because the syllogism also may be described as a comparison between two terms: but in the syllogism the two terms are compared indirectly, or by means of a third term.

-- 181. A proposition may be a.n.a.lysed into two terms and a Copula, which is nothing more than the sign of agreement or disagreement between them.

-- 182. The two terms are called the Subject and the Predicate (-- 58).

-- 183. The Subject is that of which something is stated.

-- 184. The Predicate is that which is stated of the subject.

-- 185. Hence the subject is thought of for its own sake, and the predicate for the sake of the subject.

CHAPTER II.

Of _the Copula_.

-- 186. There are two kinds of copula, one for affirmative and one for negative statements.

-- 187. Materially the copula is expressed by some part of the verb 'to be,' with or without the negative, or else is wrapped up in some inflexional form of a verb.

-- 188. The material form of the copula is an accident of language, and a matter of indifference to logic. 'The kettle boils' is as logical a form of expression as 'The kettle is boiling.' For it must be remembered that the word 'is' here is a mere sign of agreement between the two terms, and conveys no notion of actual existence. We may use it indeed with equal propriety to express non-existence, as when we say 'An idol is nothing.'

-- 189. When the verb 'to be' expresses existence in fact it is known in grammar as 'the substantive verb.' In this use it is predicate as well as copula, as when we say 'G.o.d is,' which may be a.n.a.lysed, if we please, into 'G.o.d is existent.'