No pigs (P) are philosophers (M);
Some philosophers (M) are hedonists (S):
∴ Some hedonists (S) are not pigs (P).
In this case, instead of P being predicated of M distributed, M is predicated of P distributed; and instead of S (or part of it) being included in M, we are told that some M is included in S. Still there is no real difficulty. Simply convert both the premises, and we have:
No philosophers (M) are pigs (P);
Some hedonists (S) are philosophers (M).
Whence the same conclusion follows; and the whole syllogism plainly conforms directly to the Dictum.
Such departures as these from the normal syllogistic form are said to constitute differences of Figure (see [§ 2]); and the processes by which they are shown to be unessential differences are called Reduction (see [§ 6]).
§ 2. Figure is determined by the position of the Middle Term in the premises; of which position there are four possible variations. The middle term may be subject of the major premise, and predicate of the minor, as in the first example above; and this position, being directly conformable to the requirements of the Dictum, is called the First Figure. Or the middle term may be predicate of both premises, as in the second of the above examples; and this is called the Second Figure. Or the middle term may be subject of both premises, as in the third of the above examples; and this is called the Third Figure. Or, finally, the middle term may be predicate of the major premise, and subject of the minor, as in the fourth example given above; and this is the Fourth Figure.
It may facilitate the recollection of this most important point if we schematise the figures thus:
The horizontal lines represent the premises, and at the angles formed with them by the slanting or by the perpendicular lines the middle term occurs. The schema of Figure IV. resembles Z, the last letter of the alphabet: this helps one to remember it in contrast with Figure I., which is thereby also remembered. Figures II. and III. seem to stand back to back.
§ 3. The Moods of each Figure are the modifications of it which arise from different combinations of propositions according to quantity and quality. In Figure I., for example, four Moods are recognised: A.A.A., E.A.E., A.I.I., E.I.O.