(3) Some A is not either B or bcDEf or bcdEF. The obverse is Some A is b and (B or C or d or e or F) and (B or C or D or e or f); and by the application of the rules summarised in section [433] this will be found to be equivalent to Some A is bC or bDF or bdf or be.
455. The Conversion of Complex Propositions.—Generalising, we may say that we have a process of conversion whenever from a given proposition we infer a new one in which any term that appeared in the predicate of the original proposition now appears in the subject, or vice versâ.
Thus the inference from No A is BC to No B is AC is of the nature of conversion. The process may be simply analysed as follows:—
No A is both B and C,
therefore, Nothing is at the same time A, B, and C,
therefore, No B is both A and C.
The reasoning may also be resolved into a series of ordinary conversions:—
No A is BC,
therefore (by conversion), No BC is A,
that is, within the sphere of C, no B is A,
therefore (by conversion), within the sphere of C, no A is B,
that is, No AC is B,
therefore (by conversion), No B is AC.
Or, it may be treated thus,
No A is BC,
therefore, by section [445], rule (1), No AC is BC,
therefore, also by section [445], rule (1), No AC is B,
therefore (by conversion), No B is AC.
Similarly it may be shewn that from Some A is BC we may infer Some B is AC.
Hence we obtain the following rule: In a universal negative or a particular affirmative proposition any determinant of the subject may be transferred to the predicate or vice versâ without affecting the force of the assertion.