Abstract

This chapter introduces the base logic, a system of _singular logic_. It is markedly different from the classical predicate calculus, for besides accommodating unique (singular) descriptions and functional terms as bona fide singular terms and allowing for empty terms, it is topic neutral: it accommodates the possibility that nothing exists, and also the possibility that so many things exist that no single object can serve as a domain. The first is dealt with by admitting empty variables, and the second by stripping out set-theoretic machinery. The appendix to the chapter proves the metatheorems listed in the text, and demonstrates axiomatizability by proving the soundness and completeness of the axioms presented for singular logic.