Geach Peter (b.1916), English philosopher and logician whose main work has been in logic and philosophy of language. A great admirer of McTaggart, he has published a sympathetic exposition of the latter’s work (Truth, Love and Immortality, 1979), and has always aimed to emulate what he sees as the clarity and rigor of the Scottish idealist’s thought. Greatly influenced by Frege and Wittgenstein, Geach is particularly noted for his powerful use of what he calls ‘the Frege point,’ better called ‘the Frege-Geach point,’ that the same thought may occur as asserted or unasserted and yet retain the same truth-value. The point has been used by Geach to refute ascriptivist theories of responsibility, and can be employed against noncognitivist theories of ethics, which are said to face the Frege-Geach problem of accounting for the sense of moral ascriptions in contexts like ‘If he did wrong, he will be punished’. He is also noted for helping to bring Frege to the English-speaking world, through co-translations with Max Black (1909– 88). In logic he is known for proving, independently of Quine, a contradiction in Frege’s way out of Russell’s paradox (Mind, 1956), and for his defense of modern Fregean-Russellian logic against traditional Aristotelian-Scholastic logic. He also has a deep admiration for the Polish logicians.
In metaphysics, Geach is known for his defense of relative identity, the thesis that an object a can be the same F (where F is a kind-term) as an object b while not being the same G, even though a and b are both G’s. His spirited defense of the thesis has been met by equally vigorous attacks, and it has not received wide acceptance. An obvious application of the thesis is to the defense of the doctrine of the Trinity (e.g., the Father is the same god as the Son but not the same person), which has caught the attention of some philosophers of religion. Geach’s main works include Mental Acts (1958), which attacks dispositional theories of mind, Reference and Generality (1962), which contains much important work on logic, and the collection Logic Matters (1972). A notable defender of Catholicism (despite his animadversions against Scholastic logic), his religious views find their greatest exposure in God and the Soul (1969), Providence and Evil (1977), and The Virtues (1977). He is married to the philosopher Elizabeth Anscombe. See also ASCRIPTIVISM , FREGE, IDENTITY, MCTAGGART, RUSSELL , WITTGENSTEI. D.S.O.