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. This chapter argues that intuitions about the validity and invalidity of such argument forms— especially as revealed in contemplating typical expressions of them in English— could over-rule a result established by the algebraic methods. It offers a theory for the semantics for certain argument forms, those syllogistic-like forms with complexly fractionated quantifiers in addition to Aristotelian and intermediate quantifiers. The theory is motivated by data that are certain intuitions about clear cases— both clear cases of validity and clear cases of invalidity. The chapter provides a moderately highly evaluated semantic theory in that the counter-intuitive results are quite small.
