Church’s Ontological Development

This chapter examines the evolution of Church’s views on ontology. In his early reviews Church focused on the inferential side of the COC (criterion of ontological commitment). I propose an analogy with game theory to understand an early review of Quine’s work: there is a “one-shot” view of nominalism (Church) and a plural view (Quine; similar to indefinitely repeated games). In his paper “Ontological Commitment”, Church proposes his own version of the COC focused on the inferential role of the existential quantifier. He also uses his COC as a consistence criterion and provides counterexamples to it. The chapter also includes a detailed critical analysis of his 1958 Harvard talk (a principle of tolerance in ontology follows from it). One of his most important contributions for our study of the \(\lambda \) -calculus is the array of conceptual (abstract) entities proposed in his seminal paper “Intensional Semantics”: concepts of individuals, function concepts, class concepts, and truth-value concepts. Another consideration that is directly reflected in the design of the \(\lambda \) -calculus is the minimization of its syncategorematic notions (corresponding to functional abstraction and application). Finally, the functional ontology of the \(\lambda \) -calculus is sketched in this chapter and developed in detail in Chap. 10 .