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.’

Sec. 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.