ABSTRACT
Many assumptions and provisos are in effect in understanding and using these squares and formulae. Two assumptions are very important—the “liberal” interpretation of each quantifier, and the presupposition of a constant reference class. Here is an algebraic proof of a 6-quantity syllogistic form, viz., AFK-1 (taken from Appendix II of Peterson 1985a, where also see the analogous proof of ESO-4). The proof is by reductio ad absurdum. Thompson reasoned this way, and his account (1986) of syllogistic-like arguments containing simple and complex percentages did not work. Since Thompson’s validity rules for what he calls “statistical syllogisms” were flawed, new rules were needed to replace them. The simplest form of percentage quantifiers that Thompson used were unmodified percentages.
