Rabbi Ishmael’s Rules
Nos. 8-9-10, which are some of the Talmud’s harmonization rules, are
all concerned with the following logical problem, formulated with reference to
the following diagram: knowing the lateral relations between four items (the
terms or theses, S1, P1, S2, P2, in the four premises a, b, c, d), what are the
diagonal relations between them (i.e. the conclusions, e)?


Such arguments appear much
simpler, if viewed as successions of Aristotelian syllogisms (which involved
three items, in two premises and one conclusion). They may then be graphically
represented, using Euler diagrams. Their formally valid conclusions are then
manifest for all to see; and the invalidity of some Rabbinic conclusions is then