His early work includes the classic texts Mental Acts and Reference and Generality, the latter defending an essentially modern conception of reference against medieval theories of supposition. His Catholic perspective was integral to his philosophy. He was perhaps the founder of Analytical Thomism (though the current of thought running through his and Elizabeth Anscombe's work to the present day was only ostensibly so named forty years later by John Haldane), the aim of which is to synthesise Thomistic and Analytic approaches. Geach was a student and an early follower of Ludwig Wittgenstein whilst at Cambridge University.
Geach defends the Thomistic position that human beings are essentially rational animals, each one miraculously created. He dismissed Darwinistic attempts to regard reason as inessential to humanity, as "mere sophistry, laughable, or pitiable." He repudiated any capacity for language in animals as mere "association of manual signs with things or performances."
Geach dismissed 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, according to Geach, is truth. While they lived, he saw W.V. Quine and Arthur Prior as his allies, in that they held three truths: that there are no non-existent beings; that a proposition can occur in discourse without being there asserted; and that the sense of a term does not depend on the truth of the proposition in which it occurs. He invented the famous ethical example of the stuck potholer, when arguing against the idea that it might be right to kill a child to save its mother. Jenny Teichman, fellow of New Hall, Cambridge, has characterised Geach's philosophical style as "deliberately outrageous".
His wife and occasional collaborator was the philosopher and Wittgenstein scholar Elizabeth Anscombe. Both converts to Roman Catholicism, they married in 1941 and had seven children. They co-authored the 1961 book Three Philosophers, with Anscombe contributing a section on Aristotle and Geach one each on Aquinas and Gottlob Frege. For a quarter century they were leading figures in the Philosophical Enquiry Group, an annual confluence of Catholic philosophers held at Spode House in Staffordshire that was established by Father Columba Ryan in 1954.