Having thus shown under what conditions the conclusion can be
employed for the demonstration of the premisses, Aristotle proceeds
to state by what transformation it can be employed for the refutation
of them. This he calls _converting_ the syllogism; a most
inconvenient use of the term _convert_ ([Greek: a)ntistre/phein]),
since he had already assigned to that same term more than one other
meaning, distinct and different, in logical procedure.[10] What it
here means is _reversing_ the conclusion, so as to exchange it either
for its contrary, or for its contradictory; then employing this
reversed proposition as a new premiss, along with one of the previous
premisses, so as to disprove the other of the previous
premisses--_i.e._ to prove its contrary or contradictory. The result
will here be different, according to the manner in which the
conclusion is reversed; according as you exchange it for its contrary
or its contradictory. Suppose that the syllogism demonstrated is: A
belongs to all B, B belongs to all C; _Ergo_, A belongs to all C
(_Barbara_). Now, if we reverse this conclusion by taking its
_contrary_, A belongs to no C, and if we combine this as a new premiss
with the major of the former syllogism, A belongs to all B, we shall
obtain as a conclusion B belongs to no C; which is the _contrary_ of
the minor, in the form _Camestres_. If, on the other hand, we reverse
the conclusion by taking its _contradictory_, A does not belong to all
C, and combine this with the same major, we shall have as conclusion,
B does not belong to all C; which is the _contradictory_ of the minor,
and in the form _Baroco_: though in the one case as in the other the
minor is disproved. The major is _contradictorily_ disproved, whether
it be the contrary or the contradictory of the conclusion that is
taken along with the minor to form the new syllogism; but still the
form varies from _Felapton_ to _Bocardo_. Aristotle shows farther how
the same process applies to the other modes of the First, and to the
modes of the Second and Third figures.[11] The new syllogism,
obtained by this process of reversal, is always in a different figure
from the syllogism reversed. Thus syllogisms in the First figure are
reversed by the Second and Third; those in the second, by the First
and Third; those in the Third, by the First and Second.[12]
[Footnote 10: Schol. (ad Analyt. Prior. p. 59, b. 1), p. 190, b. 20,
Brandis. Compare the notes of M. Barthélemy St. Hilaire, pp. 55,
242.]
[Footnote 11: Analyt. Prior. II. viii.-x. p. 59, b. 1-p. 61, a. 4.]
[Footnote 12: Ibid. x. p. 61, a. 7-15.]
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