He was educated at Balliol College, Oxford. He taught philosophy at Birmingham University (1951-1966), and at the University of Leeds (1966-1981). His early work includes the classic texts Mental Acts, and Reference and Generality, which defends an essentially modern conception of reference against medieval theories of supposition. Geach dismisses both pragmatic and epistemic conceptions of truth, commending a version of the correspondence theory proposed by Aquinas. He argues that there is one reality rooted in God himself, who is the ultimate Truthmaker. God is Truth.