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|Main interests||Philosophical Logic, History of philosophy, Philosophy of religion|
|Notable ideas||Analytical Thomism|
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 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. He defends the Thomistic position that human beings are essentially rational animals, each one miraculously created. He dismisses Darwinistic 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.
His wife was the noted philosopher and Wittgenstein scholar Elizabeth Anscombe. Both converts to Roman Catholicism, they had seven children.
- (edited, with Max Black) Translations from the Philosophical Writings of Gottlob Frege, 1952/1960/1966
- "Good and Evil," Analysis (1956)
- Mental Acts: Their Content and Their Objects, 1957/1997
- Three Philosophers: Aristotle; Aquinas; Frege (with G.E.M. Anscombe), 1961
- Reference and Generality: An Examination of Some Medieval and Modern Theories, 1962
- God and the Soul, 1969/2001
- Logic Matters, 1972
- Reason and Argument, 1976
- "Saying and Showing in Frege and Wittgenstein," Acta Philosophica Fennica 28 (1976): 54-70
- Truth, Love, and Immortality: An Introduction to McTaggart’s Philosophy, 1979
- (edited) Wittgenstein’s Lectures on Philosophical Psychology, 1946–47: Notes by P.T. Geach, K.J. Shah, and A.C. Jackson, 1989
- Logic and Ethics (edited by Jacek Holowka), 1990
- Truth and Hope: The Furst Franz Josef und Furstin Gina Lectures Delivered at the International Academy of Philosophy in the Principality of Liechtenstein, 1998 (ISBN 0-268-04215-2)