-----------/\---------> All M is S:
/ \
contradictory/ \
.'. Some S is P. ----------- -------- .'. No M is P}
} simply converted
.'. No P is M}

The conclusion of Celarent, simply converted, contradicts the original
major premise of Dimaris, and is therefore false. Therefore the major
premise of Celarent is false, and the conclusion of Dimaris is true. We
might, of course, construct mnemonic names for the Indirect Reduction of
all the Moods: the name of Dimaris would then be Cicari.

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 fo