ABSTRACT
This chapter discusses the relation of truistic implication, and setting out an axiom system that characterizes it. It explains the concepts of free and bound occurrences of individual variables, and the concept of a regular substitution. The chapter describes some of the deeper properties of quantificational logic, in particular the strong completeness theorem, compactness, the Lowenheim-Skolem theorem, and undecidability. It explores some of the limits in the expressive capacities of quantificational logic. The undecidability of quantificational logic is closely related to another result of philosophical interest: the essential incompleteness of arithmetic and set theory. There are two ways of approaching the expression of identity in the context of quantificational logic. One is to treat identity as a relation like any other, to be symbolized by a binary relation symbol. The other approach is to treat identity as part of logic itself, by reducingit to indistmguishabffity.
