Sec. 4.  But now, returning to the definition of a Proposition given in Sec. 2, that it is ‘a sentence in which one term is predicated of another,’ we must consider what is the import of such predication.  For the definition, as it stands, seems to be purely Nominalist.  Is a proposition nothing more than a certain synthesis of words; or, is it meant to correspond with something further, a synthesis of ideas, or a relation of facts?

Conceptualist logicians, who speak of judgments instead of propositions, of course define the judgment in their own language.  According to Hamilton, it is “a recognition of the relation of congruence or confliction in which two concepts stand to each other.”  To lighten the sentence, I have omitted one or two qualifications (Hamilton’s Lectures on Logic, xiii.).  “Thus,” he goes on “if we compare the thoughts water, iron, and rusting, we find them congruent, and connect them into a single thought, thus:  water rusts iron—­in that case we form a judgment.”  When a judgment is expressed in words, he says, it is called a proposition.

But has a proposition no meaning beyond the judgment it expresses?  Mill, who defines it as “a portion of discourse in which a predicate is affirmed or denied of a subject” (Logic, Book 1., chap. iv.  Sec. 1.), proceeds to inquire into the import of propositions (Book 1., chap. v.), and finds three classes of them:  (a) those in which one proper name is predicated of another; and of these Hobbes’s Nominalist definition is adequate, namely, that a proposition asserts or denies that the predicate is a name for the same thing as the subject, as Tully is Cicero.

(b) Propositions in which the predicate means a part (or the whole) of what the subject means, as Horses are animals, Man is a rational animal.  These are Verbal Propositions (see below:  chap. v.  Sec. 6), and their import consists in affirming or denying a coincidence between the meanings of names, as The meaning of ‘animal’ is part of the meaning of ’horse.’ They are partial or complete definitions.

But (c) there are also Real Propositions, whose predicates do not mean the same as their subjects, and whose import consists in affirming or denying one of five different kinds of matter of fact:  (1) That the subject exists, or does not; as if we say The bison exists, The great auk is extinct. (2) Co-existence, as Man is mortal; that is, the being subject to death coinheres with the qualities on account of which we call certain objects men. (3) Succession, as Night follows day. (4) Causation (a particular kind of Succession), as Water rusts iron. (5) Resemblance, as The colour of this geranium is like that of a soldier’s coat, or A = B.

On comparing this list of real predications with the list of logical relations given above (chap. i.  Sec. 5 (a)), it will be seen that the two differ only in this, that I have there omitted simple Existence.  Nothing simply exists, unrelated either in Nature or in knowledge.  Such a proposition as The bison exists may, no doubt, be used in Logic (subject to interpretation) for the sake of custom or for the sake of brevity; but it means that some specimens are still to be found in N. America, or in Zoological gardens.