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mean “no metals are denser than water,” or “not all the metals,” &c., the last of course being the true sense. The little adjective few is very subject to a subtle ambiguity of this kind; for if I say “ few books are at once learned and amusing,” I may fairly be taken to assert that a few books certainly are so, but what I really mean to draw attention to is my belief that “the greater number of books are not at once learned and amusing." A proposition of this kind is generally to be classed rather as 0 than I. The word some is subject to an exactly similar ambiguity between some but not all, and some at least, it may be all; the latter appears to be the correct interpretation, as shewn in the following lesson (p 79).

As propositions are met with in ordinary language they are subject to various inversions and changes of the simple logical form,

(1) It is not uncommon, especially in poetry, to find the predicate placed first, for the sake of emphasis or variety; as in “Blessed are the merciful ;" “ Comes something down with eventide ;” “Great is Diana of the Ephesians.” There is usually no difficulty in detecting such an inversion of the terms, and the sentence must then be reduced to the regular order before being treated in logic.

(2) The subject may sometimes be mistaken for the predicate when it is described by a relative clause, stand- : ing at the end of the sentence, as in “no one is free who is enslaved by his appetites.” Here free is evidently the predicate, although it stands in the middle of the sentence, and “one who is enslaved by his appetites” is the real subject. This proposition is evidently of the form E.

Propositions are also expressed in various modes differing from the simple logical order, and some of the different kinds which arise must be noticed.

Exclusive propositions contain some words, such as only, alone, none but, which limit the predicate to the subject. Thus, in “elements alone are metals,” we are informed that the predicate “metal” cannot be applied to anything except“elements,” but we are not to understand that “all elements are metals.” The same meaning is expressed by “none but elements are metals ;" or, again, by “ all that are not elements are not metals;" and this we shall see in the next lesson is really equivalent to "all metals are elements.” Arguments which appear fallacious at first sight will often be found correct when they contain exclusive propositions and these are properly interpreted.

Exceptive propositions affirm a predicate of all the subject with the exception of certain defined cases, to which, as is implied, the predicate does not belong. Thus, “ all the planets, except Venus and Mercury, are beyond the earth's orbit,” is a proposition evidently equivalent to two, viz. that Venus and Mercury are not beyond the earth's orbit, but that the rest are. If the exceptions are not actually specified by name an exceptive proposition must often be treated as a particular one. For if I say “all the planets in our system except one agree with Bode's law," and do not give the name of that one exception, the reader cannot, on the ground of the proposition, assert of any planet positively that it does agree with Bode's law.

Some propositions are distinguished as explicative or essential, because they merely affirm of their subject a predicate which is known to belong to it by all who can define the subject. Such propositions merely unfold what is already contained in the subject. “A parallelogram has four sides and four angles,” is an explicative or essential proposition. “ London, which is the capital of England, is the largest city of Europe,” contains two pro

positions; of which one merely directs our attention to a fact which all may be supposed to know, viz. that London is the capital of England.

Ampliative propositions, on the other hand, join a new predicate to the subject. Thus to those who do not know the comparative sizes of cities in Europe, the last example contains an ampliative proposition. The greater number of propositions are of this kind.

Tautologous or Truistic propositions are those which merely affirm the subject of itself, and give no information whatever; as in, “whatever is, is;" " what I have written, I have written."

It is no part of formal Logic to teach us how to interpret the meanings of sentences as we meet them in writings; this is rather the work of the grammarian and philologist. Logic treats of the relations of the different propositions, and the inferences which can be drawn from them; but it is nevertheless desirable that the reader should acquire some familiarity with the real logical meaning of conventional or peculiar forms of expression, and a number of examples will be found at the end of the book, which the reader is requested to classify and treat as directed.

In addition to the distinctions already noticed it has long been usual to distinguish propositions as they are pure or modal. The pure proposition simply asserts that the predicate does or does not belong to the subject, while the modal proposition states this cum modo, or with an intimation of the mode or manner in which the predicate belongs to the subject. The presence of any adverb of time, place, manner, degree, &c., or any expression equivalent to an adverb, confers modality on a proposition. “ Error is always in haste;" "justice is ever equal;” “ perfect man ought always to be conquering himself,” are examples of modal propositions in this acceptation of

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the name. Other logicians, however, have adopted a different view, and treat modality as consisting in the degree of certainty or probability with which a judgment is made and asserted. Thus, we may say, “an equilateral triangle is necessarily equiangular;" "men are generally trustworthy;" “a falling barometer probably indicates a coming storm;" “Aristotle's lost treatises may possibly be recovered;" and all these assertions are made with a different degree of certainty or modality. Dr Thomson is no doubt right in holding that the modality does not affect the copula of the proposition, and the subject could only be properly treated in a work on Probable Reasoning

Many logicians have also divided propositions according as they are true or false, and it might well seem to be a distinction of importance. Nevertheless, it is wholly beyond the province of the logician to consider whether a proposition is true or not in itself; all that he has to determine is the comparative truth of propositions

-that is, whether one proposition is true when another is. Strictly speaking, logic has nothing to do with a proposition by itself; it is only in converting or transmuting certain propositions into certain others that the work of reasoning consists, and the truth of the conclusion is only so far in question as it follows from the truth of what we shall call the premises. It is the duty of the special sciences each in its own sphere to determine what are true propositions and what are false, and logic would be but another name for the whole of knowledge could it take this duty on itself.

See Mr Mill's System of Logic, Book I. Chap. IV. which generally agrees with what is given above. Chapters V. and vi. contain Mr Mill's views on the Nature and Import of Propositions, which subject may be further

studied in Mr Mill's Examination of Sir W. Hamilton's Philosophy, Chap. XVIII. ; Hamilton's Lectures on Logic, No. XIII.; and Mansel's Prolegomena Logica, Chap. II. ; but the subject is too metaphysical in character to be treated in this work.

LESSON 1X.

THE OPPOSITION OF PROPOSITIONS.

We have ascertained that four distinct kinds of propositions are recognized by logicians,—the Universal affirmative, the Particular affirmative, the Universal negative, and the Particular negative, commonly indicated by the symbols A, I, E, 0. It is now desirable to compare together somewhat minutely the meaning and use of propositions of these various kinds, so that we may clearly learn how the truth of one will affect the truth of others, or how the same truth may be thrown into various forms of expression.

The proposition A expresses the fact that the thing or class of things denoted by the subject is included in, and forms part of the class of things denoted by the predicate. Thus “ all metals are elements" means that metals form a part of the class of elements, but not the whole. As there are altogether 63 known elements, of which 48 are metals, we cannot say that all elements are metals. The proposition itself does not tell us anything about elements in general; it is not in fact concerned with elements, metals being the subject about which it gives us informa

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