The practical difficulties, of course, consist in the reduction of the conclusions and arguments of common speech to definite terms thus simply related. Once they are so reduced, their independence or the opposite is obvious. Therein lies the virtue of the Syllogism.
Before proceeding to show in how many ways two terms may be Syllogised through a third, we must have technical names for the elements.
The third term is called the Middle (M) (τὸ μέσον): the other two the Extremes (ἄκρα).
The Extremes are the Subject (S) and the Predicate (P) of the conclusion.
In an affirmative proposition (the normal form) S is contained in P: hence P is called the Major[1] term (τὸ μεῖζον), and S the Minor (τὸ ἔλαττον), being respectively larger and smaller in extension. All difficulty about the names disappears if we remember that in bestowing them we start from the conclusion. That was the problem (προβλῆμα) or thesis in dialectic, the question in dispute.
The two Premisses, or propositions giving the relations between the two Extremes and the Middle, are named on an equally simple ground.
One of them gives the relation between the Minor Term, S, and the Middle, M. S, All or Some, is or is not in M. This is called the Minor Premiss.
The other gives the relation between the Major Term and the Middle. M, All or Some, is or is not in P. This is called the Major Premiss.[2]
[Footnote 1:] Aristotle calls the Major the First (τὸ πρῶτον) and the Minor the last (τὸ ἔσχατον), probably because that was their order in the conclusion when stated in his most usual form, "P is predicated of S," or "P belongs to S".