By far the most important point in connexion with the dogma of internal relations seems to me to be simply to see clearly the difference between these two propositions (1) and (2), and that (2) does _not_ follow from (1). If this is not understood, nothing in connexion with the dogma, can, I think, be understood. And perhaps the difference may seem so clear, that no more need be said about it. But I cannot help thinking it is not clear to everybody, and that it does involve the rejection of certain views, which are sometimes held as to the meaning of "follows." So I will try to put the point again in a perfectly strict form.
Let P be a relational property, and A a term to which it does in fact belong. I propose to define what is meant by saying that P is internal to A (in the sense we are now concerned with) as meaning that from the proposition that a thing has not got P, it "follows" that it is _other_ than A.
That is to say, this proposition asserts that between the two properties "not having P" and "other than A," there holds that relation which holds between the property "being a right angle" and the property "being an angle," or between the property "red" and the property "coloured," and which we express by saying that, in the case of any thing whatever, from the proposition that that thing is a right angle it follows, or is deducible, that it is an angle.
Let us now adopt certain conventions for expressing this proposition.
We require, first of all, some term to express the _converse_ of that relation which we assert to hold between a particular proposition _q_ and a particular proposition _p_, when we assert that _q follows from_ or _is deducible from p._ Let us use the term "entails" to express the converse of this relation. We shall then be able to say truly that "_p_ entails _q_," when and only when we are able to say truly that "_q_ follows from _p_" or "is deducible from _p_," in the sense in which the conclusion of a syllogism in Barbara follows from the two premisses, taken as one conjunctive proposition; or in which the proposition "This is coloured" follows from "This is red." "_p_ entails _q_" will be related to "_q_ follows from, _p_" in the same way in which "A is greater than B" is related to "B is less than A."