The inference, such as it is, depends on the Law of Excluded Middle. Either a term P, or its contradictory, not-P, must be true of any given subject, S: hence to affirm P of all or some S, is equivalent to denying not-P of the same: and, similarly, to deny P, is to affirm not-P. Hence the rule of Obversion;--Substitute for the predicate term its Contrapositive,[5] and change the Quality of the proposition. All S is P = No S is not-P. No S is P = All S is not-P. Some S is P = Some S is not not-P. Some S is not P = Some S is not-P. CONVERSION. The process takes its name from the interchange of the terms. The Predicate-term becomes the Subject-term, and the Subject-term the Predicate-term. When propositions are analysed into relations of inclusion or exclusion between terms, the assertion of any such relation between one term and another, implies a Converse relation between the second term and the first. The statement of this implied assertion is technically known as the CONVERSE of the original proposition, which may be called the _Convertend_. Three 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.