Sec. 9.  The need or use of any Figure but the First has been much discussed by Logicians.  Since, in actual debate, arguments are rarely stated in syllogistic form, and, therefore, if reduced to that form for closer scrutiny, generally have to be treated with some freedom; why not always throw them at once into the First Figure?  That Figure has manifest advantages:  it agrees directly with the Dictum; it gives conclusions in all four propositional forms, and therefore serves every purpose of full affirmation or denial, of showing agreement or difference (total or partial), of establishing the contradictories of universal statements; and it is the only Figure in which the subject and predicate of the conclusion occupy the same positions in the premises, so that the course of argument has in its mere expression an easy and natural flow.

Still, the Second Figure also has a very natural air in some kinds of negative arguments.  The parallelism of the two premises, with the middle term as predicate in both, brings out very forcibly the necessary difference between the major and minor terms that is involved in their opposite relations to the middle term. P is not, whilst S is, M, says Cesare:  that drives home the conviction that S is not P.  Similarly in Camestres:  Deer do, oxen do not, shed their horns.  What is the conclusion?

The Third Figure, again, furnishes in Darapti and Felapton, the most natural forms of stating arguments in which the middle term is singular: 

      Socrates was truthful;
      Socrates was a Greek: 
    .’.  Some Greek was truthful.

Reducing this to Fig I., we should get for the minor premise, Some Greek was Socrates:  which is certainly inelegant.  Still, it might be urged that, in relation to proof, elegance is an extraneous consideration.  And as for the other advantage claimed for Fig.  III.—­that, as it yields only particular conclusions, it is useful in establishing contradictories against universals—­for that purpose none of its Moods can be better than Darii or Ferio.

As for Fig.  IV., no particular advantage has been claimed for it.  It is of comparatively late recognition (sometimes called the ‘Galenian,’ after Galen, its supposed discoverer); and its scientific claim to exist at all is disputed.  It is said to be a mere inversion of Fig.  I.; which is not true in any sense in which Figs.  II. and III. may not be condemned as partial inversions of Fig.  I., and as having therefore still less claim to recognition.  It is also said to invert the order of thought; as if thought had only one order, or as if the order of thought had anything to do with Formal Logic.  Surely, if distinction of Figure be recognised at all, the Fourth Figure is scientifically necessary, because it is inevitably generated by an analysis of the possible positions of the middle term.