ee modes of Conversion are commonly recognised:--(_a_) SIMPLE
CONVERSION; (_b_) CONVERSION _per accidens_ or by limitation; (_c_)
CONVERSION BY CONTRAPOSITION.

(_a_) E and I can be simply converted, only the terms being
interchanged, and Quantity and Quality remaining the same.

If S is wholly excluded from P, P must be wholly excluded from S. If
Some S is contained in P, then Some P must be contained in S.

(_b_) A cannot be simply converted. To know that All S is contained in
P, gives you no information about that portion of P which is outside
S. It only enables you to assert that Some P is S; that portion of P,
namely, which coincides with S.

O cannot be converted either simply or _per accidens_. Some S is not P
does not enable you to make any converse assertion about P. All P
may be S, or No P may be S, or Some P may be not S. All the three
following diagrams are compatible with Some S being excluded from P.

[Illustration:

Concentric circles of S and P - P in centre

S in one circle and P in another circle.

S and P each in a circle, overlapping circle.
]

(_c_) Another mode of Conversion, known by mediaeval logicians
following Boethius as _Conversio per contra positionem terminorum_, is
useful in some syllogistic manipulations. This Converse is obtained
by substituting for the predicate term its Contrapositive or
Contradictory, not-P, making the consequent change of Quality, and
simply converting. Thus All S is P is converted into the equivalent No
not-P is S.[6]

Some have called it "Conversion by Negation," but "negation"
is manifestly too wide and common a word to be thus arbitrarily
restricted to the process of substituting for one term its opposite.

Others (and this has some mediaeval usage in its favour, though not the
most intelligent) would call the form All not-P is not-S (the Obverse
or Permutation of No not-P is S), the Converse by Contraposition. This
is to conform to an imaginary rule that in Conversion the Converse
must be of the same Quality with the Convertend. But the essence of
Conversion is the interchange of Subject and Predicate: the Quality is
not in the definition except by a bungle: it is an accident. No
not-P is S, and Some not-P is S are the forms used in Syllogism,
and therefore specially named. Unless a form had a use, it was left
unnamed, like the Subalternate forms of Syllogism: Nomen habent
nullum: nec, si bene colligis, usum.

TABLE OF CONTRAPOSITIVE CONV