In this example P is predicated of M, a term distributed; in which term, M, S is given as included; so that P may be predicated of S.

Many arguments, however, are of a type superficially different from the above:  as—­

      No wise man (P) fears death (M);
      Balbus (S) fears death (M): 
    .’.  Balbus (S) is not a wise man (P).

In this example, instead of P being predicated of M, M is predicated of P, and yet S is given as included not in P, but in M. The divergence of such a syllogism from the Dictum may, however, be easily shown to be superficial by writing, instead of No wise man fears death, the simple, converse, No man who fears death is wise.

Again: 

      Some dogs (M) are friendly to man (P);
      All dogs (M) are carnivores (S): 
    .’.  Some carnivores (S) are friendly to man (P).

Here P is predicated of M undistributed; and instead of S being included in M, M is included in S:  so that the divergence from the type of syllogism to which the Dictum directly applies is still greater than in the former case.  But if we transpose the premises, taking first

    All dogs (M) are carnivores (P),

then P is predicated of M distributed; and, simply converting the other premise, we get—­

    Some things friendly to man (S) are dogs (M): 

whence it follows that—­

    Some things friendly to man (S) are carnivores (P);

and this is the simple converse of the original conclusion.

Once more: 

      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 Sec. 2); and the processes by which they are shown to be unessential differences are called Reduction (see Sec. 6).

Sec. 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.