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JUDAIC LOGIC

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DIAGRAM 7

R. Ishmael’s Rule No. 10 – “shelo kheinyano– is difficult to depict since it concerns a conflict resolution. Its fourth premise is:

No P1 is P2 / No P2 is P1 (predicatal premise).

As the following first diagram shows this premise is in conflict with the others, since if the circles representing P1 and P2 cannot overlap at all, then the circles S1 and S2 cannot satisfy all the given conditions regarding them. The problem can be faced in a number of ways:

(a) That is, if S2 is wholly in S1, and S2 is wholly in P2, then S1 cannot be wholly in P1. We could accept this and propose that S1 is partly in P1 – and partly (to an extent at least enough for S1 to cover S2) in P2.

(b) Alternatively, if S2 is wholly in S1, and S1 is wholly in P1, then S2 cannot be wholly in P2. We could accept this and propose that S2 is partly in P2, and partly in P1; but if we say so, we must also assume S2 is not entirely (but only partly) within S1.

(c) We might also resolve our dilemma by assuming S1 and S2 not to at all overlap, like P1 and P2.

Diagram 7a

R. Ishmael’s preferred option, for resolving the conflict dealt with by Rule No. 10, seems to have been (a). That is, he kept the subjectal and predicatal premises, and even the minor premise, unchanged and chose to tinker only with the major premise, concluding: “Some, but not all, S1 are P1”. Diagrammatically, this Rabbinical resolution of the conflict looks as follows:

Diagram 7b

This is a formally acceptable option, even though not the only conceivable option. That is, though the Rabbinical response is not per se in error, it should be kept in mind by them that other inductive responses are possible if the need arise, i.e. if this response later prove undesirable for some reason.

2016-08-21T13:07:28+00:00