Logic, truth and number: The elementary genesis of arithmetic -- Second-order logic -- A representation of relation algebras using Routley-Meyer frames -- Church’s set theory with a universal set -- Axioms of infinity in Church’s type theory -- Logical objects -- The lambda calculus and adjoint functors -- Atomic Boolean algebras and classical propositional logic -- Improved decision procedures for pure relevant logic -- The “triumph” of first-order languages -- Equivalence relations and groups -- Discriminating coded lambda terms -- ?-calculus as a foundation for mathematics -- Peano’s lambda calculus: The functional abstraction implicit in arithmetic -- The undecidability of ?-definability -- A construction of the provable wellorderings of the theory of species -- Semantics for first and higher order realizability -- Language and equality theory in logic programming -- Alternative (1*): A criterion of identity for intensional entities -- Nominalist paraphrase and ontological commitment -- Peace, justice and computation: Leibniz’ program and the moral and political significance of Church’s theorem -- Tarski’s theorem and NFU -- Church’s theorem and randomness -- Russellian type theory and semantical paradoxes -- The logic of sense and denotation: Extensions and applications -- Analysis, synonymy and sense -- The very possibility of language.