That general was defeated; This man is occasionally intemperate; or (4) when the subject consists of a number of nouns collectively understood; so that they may be viewed as one single thing or body; as, Cæsar, Pompey, and Crassus constituted the first trium virate. All the books in Ptolemy's library consisted of 200,000 volumes, i. e., all together. The king, lords, and commons form a British parliament. The syncategorem all, when used distributively, is a sign of a universal proposition; when it is applied in a collective sense, the proposition is singular; when it is distributive, its place may be correctly supplied by every or each; as, All the colleges are governed by their respective statutes, i, e., each of the colleges. All the primary planets revolve in elliptic orbits about our sun as their centre. When it is collective, it admits of the introduction of the word together; as, All the colleges constitute an university, i. e., collectively taken. All the primary planets are eleven. In all singular propositions the predicate is asserted of the whole of the subject. Hence the subject is distributed, and singular propositions are considered as universals. 5. An indefinite proposition has a common term for its subject; but it has no sign expressed to indicate whether its subject is to be taken in a universal or particular sense; as, Beasts have four feet, i. e., all beasts. A planet is ever changing its place, i. e., all planets. The stars appear to us when the twilight is gone, i. e., those stars only which are above the horizon. Every indefinite proposition will admit either of an universal or a particular sign, for the predicate must be asserted either universally or partially of the subject. But to determine this, we must look to the matter of the proposition, as it is in this way alone we can ascertain the natural connection between the subject and the predicate. The mattera of a proposition is the extent of connection which naturally exists between the extremes, and it is of three kinds―necessary, impossible, and contingent. When the terms of a proposition agree essentially and invariably with each other, it is said to be in necessary matter, e. g. All moral agents are responsible. a Those who hold logic to be a formal science must of course discard from its domain all consideration of real existence, and of the relations of real existence. Of the truth or falsehood of propositions in themselves, it is supposed to know nothing, and can take no account of it. If this view of logic be correct, the matter and modality of propositions must be excluded from its province as extralogical. If truth or falsehood,' remarks Sir W. Hamilton, as a material quality of propositions and syllogisms is extralogical, so also is their modality. Necessity, possibility, &c., are circumstances which do not affect the logical copula or the logical inference. They do not relate to the connection of the subject and the predicate, of the antecedent and consequent, as terms in thought, but as realities in existence; they are metaphysical, not logical conditions. The syllogistic inference is always necessary; it is modified by no extraformal condition; is equally apodictic in contingent as in necessary matter.'-— Ed. Rev., Vol. LVII. Kant sanctions the modality of propositions and syllogisms as necessary to be taken into account by the logician. Whateley's views of the province of logic are so contradictory that his authority on either side of the question goes for nothing. b There are three ways in which a predicate may be conceived of as necessary to its subject:—First, if it is an essential or formal quality—this is formal necessity;-secondly, as being an inseparable deduction from some essential or When the terms of a proposition differ from each other essentially and invariably, it is said to be in impossible matter, e. g. No triangles are squares. When the terms of a proposition partly agree with each other, and partly differ, it is said to be in contingent matter, e. g. Legal enactments are beneficial to society. Of propositions implying necessary matter, affirmatives are true, and negatives false; of those expressing impossible matter, negatives are true, and affirmatives false; of those expressing contingent matter, universals are false and particulars true. In necessary and impossible matter indefinite propositions are reduced to the class of universals, and in contingent matter to the class of particulars. In the following example, Angels are incorporeal, the subject angels is not accompanied by any sign of universality or particularity; but as we cannot conceive of 'angels' as not being incorporeal, we affirm this predicate of all angels; and hence the proposition is universal, the predicate being asserted of the whole subject. In the following proposition, Human inventions are beneficial to society, there is no sign indicative either of universal or particular quantity prefixed to the subject; but on examining the mat formal quality-this is natural necessity;-thirdly, as being incapable of being denied to it henceforward-this is necessity of fact. The first necessity is expressed, when we say that a quality is generic or specific-the second, when we call it a proprium-the third, when we say that a fact has become an inseparable accident.-Moberly, p. 30. ter of the proposition, we ascertain that the predicate cannot be affirmed of the whole subject, because the matter of the proposition is contingent; and hence we can only assert, Some human inventions are beneficial to society. Since singular propositions may be considered as universals, and since indefinite propositions can be reduced to universals, if their matter is necessary or impossible, and to particulars, if their matter is contingent, it is unnecessary to consider either as a separate class of propositions; for, strictly speaking, propositions, when viewed according to their quantity, may be divided into two kinds, viz., universal and particular. All pure categorical propositions, therefore, considered according to their quality and quantity, may be regarded as of four kinds, viz., universal affirmative, universal negative, particular affirmative, and particular negative. These four classes of propositions are marked by the first four vowels, called symbols. Thus A. Universal affirmative. The following scheme exhibits the relations of quantity and quality : PROPOSITIONS. SUBJECTS. PREDICATES. Universal affirmatives,.........Universal,........Particular. Universal negatives, ....... Universal,........Universal. Particular affirmatives, ........Particular,.......Particular. Particular negatives,...........Particular,.......Universal. In reference to the universality and particularity of the predicates of propositions, the following maxims will be found in all cases to apply:-In negative propositions the predicate is universal by necessity. In affirmative propositions the pre 2 dicate is particular when it is only an attribute of the subject; but it is universal when it can be substituted for, or reciprocate with the subject. The following scheme presents the division of propositions, with their sub-divisions : Modal propositions have been already cursorily noticed in the manner in which they are generally treated, viz., that of considering any proposition to be modal in which the copula is affected by some modifying word, e. g.– Men are necessarily mortal. |