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 pre.dicere, 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 karŋyopéw (kategoreo, to assert or affirm).

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

Sentence

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 proposition affirms the predicate to belong to the whole of the subject, it is an universal proposition, as in the example

"all metals are elements," which affirms that the quality of being undecomposable or of being simple in nature is true of all metals. But if we say 66 some metals are brittle," the quality of brittleness is affirmed only of some indefinite portion of the metals, and there is nothing in the proposition to make us sure that any certain metal is brittle. The name particular being derived from the diminutive of the Latin pars would naturally signify a small part, but in logic it must be carefully interpreted as signifying any part, from the smallest fraction up to nearly the whole. Particular propositions do not include cases where a predicate is affirmed of the whole or of none of the subject, but they include any between these limits. We may accordingly count among particular propositions all such as the following:

A very few metals are less dense than water.

Most elements are metals.

Many of the planets are comparatively small bodies.
Not a few distinguished men have had distinguished

sons.

The reader must carefully notice the somewhat subtle point explained further on, that the particular proposition though asserting the predicate only of a part of the subject, does not deny it to be true of the whole.

Aristotle, indeed, considered that there were altogether four kinds of proposition as regards quantity, namely—

The singular proposition is one which has a singular

term for its subject, as in—

Socrates was very wise.
London is a vast city.

But we may fairly consider that a singular proposition is an universal one; for it clearly refers to the whole of the subject, which in this case is a single individual thing.

Indefinite or indesignate propositions are those which are devoid of any mark of quantity whatever, so that the form of words gives us no mode of judging whether the predicate is applicable to the whole or only part of the subject. Metals are useful, Comets are subject to the law of gravitation, are indefinite propositions. In reality, however, such propositions have no distinct place in logic at all, and the logician cannot properly treat them until the true and precise meaning is made apparent. The predicate must be true either of the whole or of part of the subject, so that the proposition, as it stands, is clearly incomplete; but if we attempt to remedy this and supply the marks of quantity, we overstep the proper boundaries of logic and assume ourselves to be acquainted with the subject matter or science of which the proposition treats. We may safely take the preceding examples to mean some metals are useful" and "all comets are subject to the law of gravitation," but not on logical grounds. Hence we may strike out of logic altogether the class of indefinite propositions, on the understanding that they must be rendered definite before we treat them. I may observe, however, that in the following lessons I shall frequently use propositions in the indefinite form as examples, on the understanding that where no sign of quantity appears, the universal quantity is to be assumed. It is probable that wherever a term is used alone, it ought to be interpreted as meaning the whole of its class. But however this may be, we need not recognize the indefinite proposition as a distinct kind; and singular propositions having been resolved into universals, there remain only the two kinds, Universal and Particular.

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Remembering now that there are two kinds of propo

sition as regards quality, and two as regards quantity, we shall be able to form altogether four varieties, thus :

The vowel letters placed at the right hand are symbols or abbreviated names, which are always used to denote the four kinds of proposition; and there will be no difficulty in remembering their meaning if we observe that A and I occur in the Latin verb affirmo, I affirm, and E and O in nego, I deny.

There will not generally be any difficulty in referring to its proper class any proposition that we meet with in writings. The mark of universality usually consists of some adjective of quantity, such as all, every, each, any, the whole; but whenever the predicate is clearly intended to apply to the whole of the subject we may treat the proposition as universal. The signs of a particular proposition are the adjectives of quantity, some, certain, a few, many, most, or such others as clearly indicate part at least.

The negative proposition is known by the adverbial particle not being joined to the copula; but in the proposition E, that is the universal negative, we frequently use the particle no or none prefixed to the subject. Thus, 99 66 no metals are compound," none of the ancients were acquainted with the laws of motion," are familiar forms of the universal negative.

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The student must always be prepared too to meet with misleading or ambiguous forms of expression. Thus the proposition, "all the metals are not denser than water," might be taken as E or 0, according as we interpret it to