www.TheLogician.net © Avi Sion - all rights reserved
© Avi Sion
All rights reserved
© Avi Sion, 2005. All rights reserved.
Note that the first two premises leave open the possibility that subject and predicate may be co-extensive, so that the circles labeled S1 and P1 might be equal in size, and likewise the circles labeled S2 and P2 might be one. On the other hand, the relation between S2 and S1 can only be as above depicted, with S2 smaller than S1.
As for the remaining (predicatal) premise and the conclusion(s), we shall consider each case each in turn.
But first, let us consider what general conclusions can be drawn from the common premises of all such arguments.
Given the major and subjectal premises, we can at the outset, without resort to the other premises, make the following syllogistic inferences and graphic presentation:
Note: I did not mention the above 3/OAO syllogism in my original treatment (Judaic Logic, p. 147).
however, be pointed out that in the case of Rule 10, since the major premise is
particularized in an effort to restore consistency, these initial inferences
Similarly, given the minor and subjectal premises, we can at the outset, without resort to the other premises, make the following syllogistic inference and graphic presentation:
This conclusion is an indefinite particular, note – i.e. in some cases, we may find “All S1 are P2”; and in others, “Only some S1 are P2”.
 Quite incidentally, I notice while writing this that in Future Logic (p. 37), I state that the mood 3/AAI is a derivative of 3/AII; but it could equally be derived from 3/IAI. Similarly, 3/EAO could be derived from either 3/EIO (as stated) or 3/OAO.