, owing to the indefiniteness of the syllogistic symbol for
particular quality, Some. And in truth all such transmutations
of expression are as much entitled to the dignity of being called
Immediate Inferences as most of the processes so entitled.

Dr. Bain uses the word with an approach to this width of application
in discussing all that is now most commonly called Immediate Inference
under the title of Equivalent Forms. The chief objection to this usage
is that the Converse _per accidens_ is not strictly equivalent. A
debater may want for his argument less than the strict equivalent, and
content himself with educing this much from his opponent's admission.
(Whether Dr. Bain is right in treating the Minor and Conclusion of
a Hypothetical Syllogism as being equivalent to the Major, is not so
much a question of naming.)

But in the history of the subject, the traditional usage has been
to confine AEquipollence to cases of equivalence between positive and
negative forms of expression. "Not all are," is equivalent to "Some
are not": "Not none is," to "Some are". In Pre-Aldrichian text-books,
AEquipollence corresponds mainly to what it is now customary to call
(_e.g._, Fowler, pt. iii. c. ii., Keynes, pt. ii. c. vii.) Immediate
Inference based on Opposition. The denial of any proposition involves
the admission of its contradictory. Thus, if the negative particle
"Not" is placed before the sign of Quantity, All or Some, in
a proposition, the resulting proposition is equivalent to the
Contradictory of the original. Not all S is P = Some S is not P.
Not any S is P = No S is P. The mediaeval logicians tabulated these
equivalents, and also the forms resulting from placing the negative
particle after, or both before and after, the sign of Quantity. Under
the title of AEquipollence, in fact, they considered the interpretation
of the negative particle generally. If the negative is placed after
the universal sign, it results in the Contrary: if both before and
after, in the Subaltern. The statement of these equivalents is a
puzzling exercise which no doubt accounts for the prominence given it
by Aristotle and the Schoolmen. The latter helped the student with the
following Mnemonic line: _Prae Contradic., post Contrar., prae postque
Subaltern._[3]

To AEquipollence belonged also the manipulation of the forms known
after the _Summulae_ as _Exponibiles_, notably _Exclusive_ and
_Exceptive propositions_, such as None but barristers a