In the philosophy of mathematics, he is best known for his book "Frege's Conception of Numbers as Objects" (1983), where he argues that Frege's logicist project could be revived by removing the axiom schema of unrestricted comprehension (sometimes referred to as Basic Law V) from the formal system. Arithmetic is then derivable in second-order logic from Hume's principle. He gives informal arguments that (i) Hume's principle plus second-order logic is consistent, and (ii) from it one can produce the Dedekind–Peano axioms. Both results were proven informally by Gottlob Frege (Frege's Theorem), and would later be more rigorously proven by George Boolos and Richard Heck. Wright is one of the major proponents of neo-logicism, alongside his frequent collaborator Bob Hale. He has also written "Wittgenstein and the Foundations of Mathematics" (1980).