R. Ishmael’s Rule No. 8(a) – “lelamed oto hadavar” – the generalizing version of “lelamed”, may be depicted as follows, since its fourth premise is:
All P2 are P1, but not all P1 are P2 (predicatal premise).
The four premises formally yield the conclusion “Some S1 are P2” (etc.), which is compatible with the two outcomes shown in our diagram.
Rabbi Ishmael concludes (more generally and more specifically) that “All S1 are P2”, which means that he at the outset generalizes the formal conclusion, and precludes the other formal alternative (some S1 are not P2). No reason is given for this hasty action. Thus, note well, although the Rabbinical conclusion is in this case compatible with the formal one, it is not identical with it. Strictly speaking, it is a non-sequitur. The best we can say for it is that it is a legitimate inductive preference to select the more general alternative; however, the Rabbis should remain open to occasional particularization of their conclusion, if it is found to lead to some contradiction elsewhere.