Handbook of the History of Logic: - Fordham University Faculty

328 Henrik Lagerlund
III.
Every B is A
Some C is B
Some C is A
IV.
No B is A
Some C is B
Some C is not A
The five syllogisms with indirect conclusions are in various ways reduced to the
first four by using the conversion rules stated above. The five syllogism are:
V.
Every B is A
Every C is B
Some A is C
VI.
No B is A
Every C is B
No A is C
VII.
Every B is A
Some C is B
Some A is C
VIII.
Every B is A
No C is B
Some A is not C
IX.
Some B is A
No C is B
Some A is not C
(V) is reduced to (I) by simple conversion of the conclusion, since by the square
of opposition the universal conclusion in (I) implies a particular. (VI) is reduced
to (II) by simple conversion of the conclusion, and (VII) is reduced to (III) is the
same way. (VIII) is reduced to (IV) by accidental conversion of the major premise,
simple conversion of the minor premise, transposing the premises and renaming
the terms. (IX) is reduced to (IV) in the same way.
The second figure is governed by three rules added to the ones above, namely: