§ 4. But now, returning to the definition of a Proposition given in [§ 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. § 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. § 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. § 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.
Controversy as to the Import of Propositions really turns upon a difference of opinion as to the scope of Logic and the foundations of knowledge. Mill was dissatisfied with the "congruity" of concepts as the basis of a judgment. Clearly, mere congruity does not justify belief. In the proposition Water rusts iron, the concepts water, rust and iron may be congruous, but does any one assert their connection on that ground? In the proposition Murderers are haunted by the ghosts of their victims, the concepts victim, murderer, ghost have a high degree of congruity; yet, unfortunately, I cannot believe it: there seems to be no such cheap defence of innocence. Now, Mill held that Logic is concerned with the grounds of belief, and that the scope of Logic includes Induction as well as Deduction; whereas, according to Hamilton, Induction is only Modified Logic, a mere appendix to the theory of the "forms of thought as thought." Indeed, Mill endeavoured in his Logic to probe the grounds of belief deeper than usual, and introduced a good deal of Metaphysics—either too much or not enough—concerning the ground of axioms. But, at any rate, his great point was that belief, and therefore (for the most part) the Real Proposition, is concerned not merely with the relations of words, or even of ideas, but with matters of fact; that is, both propositions and judgments point to something further, to the relations of things which we can examine, not merely by thinking about them (comparing them in thought), but by observing them with the united powers of thought and perception. This is what convinces us that water rusts iron: and the difficulty of doing this is what prevents our feeling sure that murderers are haunted by the ghosts of their victims. Hence, although Mill's definition of a proposition, given above, is adequate for propositions in general; yet that kind of proposition (the Real) with regard to which Logic (in Mill's view) investigates the conditions of proof, may be more explicitly and pertinently defined as 'a predication concerning the relation of matters of fact.'
§ 5. This leads to a very important distinction to which we shall often have to refer in subsequent pages—namely, the distinction between the Form and the Matter of a proposition or of an argument. The distinction between Form and Matter, as it is ordinarily employed, is easily understood. An apple growing in the orchard and a waxen apple on the table may have the same shape or form, but they consist of different materials; two real apples may have the same shape, but contain distinct ounces of apple-stuff, so that after one is eaten the other remains to be eaten. Similarly, tables may have the same shape, though one be made of marble, another of oak, another of iron. The form is common to several things, the matter is peculiar to each. Metaphysicians have carried the distinction further: apples, they say, may have not only the same outward shape, but the same inward constitution, which, therefore, may be called the Form of apple-stuff itself—namely, a certain pulpiness, juiciness, sweetness, etc.; qualities common to all dessert apples: yet their Matter is different, one being here, another there—differing in place or time, if in nothing else. The definition of a species is the form of every specimen of it.
To apply this distinction to the things of Logic: it is easy to see how two propositions may have the same Form but different Matter: not using 'Form' in the sense of 'shape,' but for that which is common to many things, in contrast with that which is peculiar to each. Thus, All male lions are tawny and All water is liquid at 50° Fahrenheit, are two propositions that have the same form, though their matter is entirely different. They both predicate something of the whole of their subjects, though their subjects are different, and so are the things predicated of them. Again, All male lions have tufted tails and All male lions have manes, are two propositions having the same form and, in their subjects, the same matter, but different matter in their predicates. If, however, we take two such propositions as these: All male lions have manes and Some male lions have manes, here the matter is the same in both, but the form is different—in the first, predication is made concerning every male lion; in the second of only some male lions; the first is universal, the second is particular. Or, again, if we take Some tigers are man-eaters and Some tigers are not man-eaters, here too the matter is the same, but the form is different; for the first proposition is affirmative, whilst the second is negative.
§ 6. Now, according to Hamilton and Whately, pure Logic has to do only with the Form of propositions and arguments. As to their Matter, whether they are really true in fact, that is a question, they said, not for Logic, but for experience, or for the special sciences. But Mill desired so to extend logical method as to test the material truth of propositions: he thought that he could expound a method by which experience itself and the conclusions of the special sciences may be examined.