(pp. 153-166)

In this chapter we’ll further abstract the semantics of predicate logic in order to be able to use mathematics to study predicate logic. To do that, we’ll have to consider more carefully what it means to classify a collection as a thing.

Consider again the model discussed in Chapter IV. E:

$L(\neg , \to , \wedge , \vee ,\forall ,\exists ;{P_0},{P_1},...,{c_0},{c_1},...)$

realizations of name and predicate symbols; universe

$L(\neg , \to , \wedge , \vee ,\forall ,\exists ;$is a dog, is a cat, eats grass, is a wombat, is the father of; Ralph, Dusty, Howie, Juney)

universe: all animals, living or toy

assignment of references; valuations of atomic wffs; evaluation of$\neg , \to , \wedge , \vee ,\forall ,\exists $

Recall the classical abstraction of...