However, the _Dictum_ makes a further statement of a synthetic or real character, namely, that _when these conditions are fulfilled an inference is justified_; that then the major and minor terms are brought into comparison through the middle, and that the major term may be predicated affirmatively or negatively of all or part of the minor.

It is this real assertion that justifies us in calling the _Dictum_ an Axiom.
Sec.4.Whether the Laws of Thought may not fully explain the Syllogism without the need of any synthetic principle has, however, been made a question.

Take such a syllogism as the following: All domestic animals are useful; All pugs are domestic animals: .'.

All pugs are useful.
Here (an ingenious man might urge), having once identified pugs with domestic animals, that they are useful follows from the Law of Identity.
If we attend to the meaning, and remember that what is true in one form of words is true in any other form, then, all domestic animals being useful, of course pugs are.

It is merely a case of subalternation: we may put it in this way: All domestic animals are useful: .'.