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.
His Catholic perspective is integral to his philosophy. He is credited with founding the school of Analytical Thomism, whose aim is to present the thought of St Thomas Aquinas in the style of modern philosophy by clearing away the trappings and obscurities of traditional Thomism. He defends the Thomistic position that human beings are essentially rational animals, each one miraculously created. He dismisses Darwinisticistic attempts to regard reason as inessential to our humanity, as "mere sophistry, laughable, or pitiable." He repudiates any capacity for language in animals as mere "association of manual signs with things or performances."
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.
He was recently awarded the order Pro Ecclesia et Pontifice by the Holy See for his philosophical work.
His wife Elizabeth Anscombe is also a philosopher of great reputation. Like Geach, she is a convert to Roman Catholicism.