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time with reference to the terms themselves (or, to speak more accurately, the things signified by them), but it is also divested of the notion of existence. In other words, it is employed simply as a connecting particle, not as a substantive verb. Where the substantive verb is used in a logical proposition, it must be expressed in the predicate. Thus 'I am,' 'The king is not,' become 'I am existent,' 'The king is non-existent.' That the copula implies no notion of existence is evident from the fact that we can use such propositions as these: 'The labours of Hercules are a myth,' 'He is a nonentity.'

Can we modify the copula so as to express certainty, probability, possibility, or other modes of connection between the subject and predicate? This is the celebrated question of Modality, a question which has been the source of much difference of opinion amongst logicians. Even though it were granted that the proposition simply expresses our present judgment on the compatibility or incompatibility of two terms, it might be maintained that it should express the nature of our judgment and the degree of our assent or dissent, whether it be certain, approximating to certainty, or faltering. Thus it might be maintained that the following should be accepted as instances of the ultimate analysis of a logical proposition: 'This is certainly the man I saw yesterday,' 'This is probably the man I saw yesterday,' 'This is possibly the man I saw yesterday.' That we use these forms in conversation and discussion is unquestionable, but it is one main object of Logic

to analyse our abbreviated inferences and statements into their full logical equivalents. Instead therefore of admitting various descriptions of copulæ (other than the affirmative and negative), in order to conform Logic to ordinary language, it seems simpler, as well as more scientific, to insist on the uniform character of the copula, and to represent propositions like the foregoing as predicating our degree of assent to or dissent from the sentence in question. Thus, after asking myself the question 'Is this the man I saw yesterday?' I may either answer simply 'This is the man I saw yesterday,' or I may describe the degree of my assent by stating 'That this is the man I saw yesterday is certain, probable, possible,' &c. In fact, such propositions seem to be the result of an act of reflection on the degree of our own conviction.

We shall therefore regard the form A is or is not B as the ultimate and uniform logical analysis of all propositions, though we shall occasionally, for the sake of brevity, avail ourselves of the forms sanctioned by popular language.

CHAPTER III.

Division of Propositions according to their Quantity and Quality.

WE have already seen that propositions are either affirmative or negative, according as the copula used is of the form 'is' or 'is not.' This is called a division of propositions according to their Quality.

They are further divided, according to their Quantity, into Universal and Particular. For, in affirming or denying a predicate of a subject, it is obvious that I may either affirm or deny the predicate of all the individuals denoted by the subject, or of part only. Thus in affirming mortality of man, I may say 'All men are mortal,' or 'Some men are mortal;' in denying wisdom of man, I may deny it of all men or only of some men, i. e. I may say 'No men are wise,' or 'Some men are not wise.' When the predicate is affirmed or denied of all the individuals denoted by the subject, the proposition is called an Universal Proposition; when of part only, a Particular Proposition. A Singular Proposition, i. e. a proposition of which the subject is a singular term, ranks as an Universal, because the predicate is affirmed or denied of everything (i. e. in this

case, the one thing) denoted by the subject. The same holds good of a proposition in which the subject is a collective term. An attributive, as we have already seen, cannot, by itself, be used as the subject of a proposition. Abstract terms which have come to be used as common terms, and admit of plurals, as figure, triangle, virtue, pleasure, &c., have a denotative power, and may, like common terms, form the subjects of either universal or particular propositions. But those abstract terms, like humanity, wisdom, &c., which retain their original characteristic of being connotative only, and admit of no plurals, simply express an attribute or group of attributes with which, as a whole, it is asserted or denied that the predicate is compatible; consequently, a proposition, of which such a term is the subject, ranks as an universal.

Thus such propositions as 'Ambition is aggressive,' 'Wisdom is a virtue,' 'The fourteenth legion is disbanded,' 'Socrates is an Athenian citizen,' are, on the very face of them, universals. But propositions in which the subject is a common term or an abstract term used as a common term, must be quantified; that is, we must attach to the subject either an universal or a particular designation. It is not sufficient to say, 'triangles are figures,' 'horses are black;' we must state whether we mean that all triangles' or 'some triangles' are 'figures,' whether we mean that 'all horses' or 'some horses' are black. Indefinite' or 'indesignate' propositions, as they are called, i. e. propositions in which the subject, being

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a common term, is not quantified, are inadmissible in Logic.

By combining the division of propositions into universal and particular with that into affirmative and negative we obtain four forms, viz.

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We shall in future designate these forms of proposition respectively as A, E, I, O1.

Note. Sir W. Hamilton, followed by several other logicians, maintains that in thought the predicate is always quantified as well as the subject. He proposes to reform the logical theory of the proposition accord

1 It sometimes requires a little ingenuity to state a given proposition in one of the above forms. Thus the propositions None but the brave deserve the fair,' 'The wise alone are good,' 'Not every historian is worthy of credit,'' All his acts are not defensible,' when stated in strictly logical form, become respectively, No not - brave (or None who are not brave) are deserving of the fair, No not- wise (or None who are not wise) are good, Some historians are not worthy of credit, Some of his acts are not defensible. The simplest equivalents of the two former propositions are, All who deserve the fair are brave, All good men are wise, but these are gained by permutation and conversion, two forms of inference which have not yet been explained.

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