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of lines and rectangles contained under those lines, as a corollary of the 5th Prop. of Euclid's Second Book.

Much might be said concerning the comparative advantages of the intuitive and symbolical methods. The latter is usually much the less laborious, and gives the most widely applicable answers; but the symbolical seldom or never gives the same command and comprehension of the subject as the intuitive method. Hence the study of geometry is always indispensable in education, although the same truths are often more readily proved by algebra. It is the peculiar glory of Newton that he was able to explain the motions of the heavenly bodies by the geometric or intuitive method; whereas the greatest of his successors, such as Lagrange or Laplace, have treated these motions by the aid of symbols.

What is true of mathematical subjects may be applied to all kinds of reasoning; for words are symbols as much as A, B, C, or x, y, z, and it is possible to argue with words without any consciousness of their meaning. Thus if I say that "selenium is a dyad element, and a dyad element is one capable of replacing two equivalents of hydrogen," no one ignorant of chemistry will be able to attach any meaning to these terms, and yet any one will be able to conclude that "selenium is capable of replacing two equivalents of hydrogen." Such a person argues in a purely symbolical manner. Similarly, whenever in common life we use words, without having in mind at the moment the full and precise meaning of the words, we possess symbolical knowledge only.

There is no worse habit for a student or reader to acquire than that of accepting words instead of a knowledge of things. It is perhaps worse than useless to read a work on natural history about Infusoria, Foraminifera, Rotifera and the like, if these names do not convey clear images to the mind. Nor can a student who has not

witnessed experiments, and examined the substances with his own eyes, derive any considerable advantage from works on chemistry and natural philosophy, where he will meet with hundreds of new terms which would be to him mere empty and confusing signs. On this account we should lose no opportunity of acquainting ourselves, by means of our senses, with the forms, properties and changes of things, in order that the language we employ may, as far as possible, be employed intuitively, and we may be saved from the absurdities and fallacies into which we might otherwise fall. We should observe, in short, the advice of Bacon-ipsis consuescere rebusto accustom ourselves to things themselves.

Hamilton's Lectures on Logic. Lect. IX.

Baynes' Port Royal Logic. Part I. Chap. 9, and Appendix.

LESSON VIII.

KINDS OF PROPOSITIONS.

A TERM standing alone is not capable of expressing truth; it merely refers the mind to some object or class of objects, about which something may be affirmed or denied, but about which the term itself does not affirm or deny anything. "Sun," "air," "table," suggest to every mind objects of thought, but we cannot say that “sun is true," or 'air is mistaken," or "table is false." We must join words or terms into sentences or propositions before they can express those reasoning actions of the mind to which

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truth or falsity may be attributed. "The sun is bright," "the air is fresh," ," "the table is unsteady," are statements which may be true or may be false, but we can certainly entertain the question of their truth in any circumstances. Now as the logical term was defined to be any combination of words expressing an act of simple apprehension, so a logical proposition is any combination of words expressing an act of judgment. The proposition is in short the result of an act of judgment reduced to the form of language.

What the logician calls a proposition the grammarian calls a sentence. But though every proposition is a sentence, it is not to be supposed that every sentence is a proposition. There are in fact several kinds of sentences more or less distinct from a proposition, such as a Sentence Interrogative or Question, a Sentence Imperative or a Command, a Sentence Optative, which expresses a wish, and an Exclamatory Sentence, which expresses an emotion of wonder or surprise. These kinds of sentence may possibly be reduced, by a more or less indirect mode of expression, to the form of a Sentence Indicative, which is the grammatical name for a proposition; but until this be done they have no proper place in Logic, or at least no place which logicians have hitherto sufficiently explained.

The name proposition is derived from the Latin words pro, before, and pono, I place, and means the laying or placing before any person the result of an act of judgment. Now every act of judgment or comparison must involve the two things brought into comparison, and every proposition will naturally consist of three partsthe two terms or names denoting the things compared, and the copula or verb indicating the connection between them, as it was ascertained in the act of judgment. Thus the proposition, "Gold is a yellow substance," expresses

an agreement between gold and certain other substances previously called yellow in regard to their colour. Gold and yellow substance are evidently the two terms, and is the copula.

It is always usual to call the first term of a proposition the subject, since it denotes the underlying matter, as it were (Latin, sub, under, and jactum, laid) about which something is asserted. The second term is called the predicate, which simply means that which is affirmed or asserted. This name is derived from the Latin prædicare, to assert, whence comes the French name prédicateur, corrupted into our preacher. This Latin verb is not to be confused with the somewhat similar one predicere, which has the entirely different meaning to predict or foretell. I much suspect that newspaper writers and others, who pedantically use the verb "to predicate," sometimes fall into this confusion, and really mean to predict, but it is in any case desirable that a purely technical term like predicate should not be needlessly introduced into common language, when there are so many other good words which might be used. This and all other technical scientific terms should be kept to their proper scientific use, and the neglect of this rule injures at once the language of common life and the language of science.

Propositions are distinguished into two kinds, according as they make a statement conditionally or unconditionally. Thus the proposition, "If metals are heated they are softened," is conditional, since it does not make an assertion concerning metals generally, but only in the circumstances when they become heated. Any circumstance which must be granted or supposed before the assertion becomes applicable is a condition. Conditional propositions are of two kinds, Hypothetical and Disjunctive, but their consideration will be best deferred to a

subsequent Lesson (XIX). Unconditional propositions are those with which we shall for some time be solely concerned, and these are usually called Categorical Propositions, from the Greek verb Karnуopéw (kategoreo, to assert or affirm).

The following diagram will conveniently represent the classification of sentences and propositions as far as we have yet proceeded :

Indicative

Proposition Conditional Disjunctive.
[Categorical
Hypothetical.

Interrogative

Sentence

Imperative

Optative

Exclamatory

It is now necessary to consider carefully the several kinds of categorical propositions. They are classified according to quality and according to quantity. As regards quality they are either affirmative or negative; as regards quantity they are either universal or particular.

An affirmative proposition is one which asserts a certain agreement between the subject and predicate, so that the qualities or attributes of the predicate belong to the subject. The proposition, "gold is a yellow substance," states such an agreement of gold with other yellow substances, that we know it to have the colour yellow, as well as whatever qualities are implied in the name substance. A negative proposition, on the other hand, asserts a difference or discrepancy, so that some at least of the qualities of the predicate do not belong to the subject. "Gold is not easily fusible" denies that the quality of being easily fused belongs to gold.

Propositions are again divided according to quantity into universal and particular propositions. If the propo sition affirms the predicate to belong to the whole of the subject, it is an universal proposition, as in the example

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