His daughter Tamsin Geach has reported that Peter Geach has passed away Saturday. He was 91 years old. In his long and fruitful career Geach had made a number of important contributions to the philosophies of logic, language, and mind, and to the interpretation of Frege, Wittgenstein and Aquinas.
Geach is now probably best known for providing the canonical statement of the embedding problem: for theories that deny that certain classes of statements are factual (capable of being true or false), like expressivism says about moral claims, it is a problem that these statements can be embedded within logical inferences. The expressivist understands 'don't torture the cat' as something like 'boo to torturing the cat!'. But you can make an argument like 'if it is wrong to torture the cat, it is wrong to get someone else to torture the cat; since it's wrong to torture the cat, it's wrong to get someone else to torture the cat'. This looks for all the world like a straightforward inference, the but expressivist can't say this, because you need truth-apt statements to make an argument, and they deny that claims like 'it is wrong to torture the cat' could be true or false. So, the expressivist can't explain a large amount of things that we normally say without any problem.
Geach was married to the late Elizabeth Anscombe, and together the two of them did as much as anybody else to improve our understanding of propositions and propositional attitudes, and to flesh out our understanding of intelligent actions. They both were converts to Catholicism and tirelessly worked within its intellectual tradition, trying to bring the work of especially Thomas Aquinas to modern attention and prominence. Geach was honoured by the Pope for his work.
I'd like to suggest to you a characteristically short and incisive paper of his, 'Good and Evil', wherein Geach introduced a distinction which still continues to bear fruit in meta-ethics and value theory. Geach asks us to distinguish *attributive* from *predicative* adjectives, with predicative adjectives like 'yellow' and 'round' being ones where 'something is an x y' means it is an x and it is a y (a yellow apple is both an apple and yellow), whereas this is not true for attributive predicates like 'large' and 'tall'--a large flea is not large. Geach suggests that 'good' and similar evaluative adjectives are attributive and not predicative. This would mean that analyses like those of GE Moore miss their target ('yellow' was the adjective Moore compared 'good' to), and that to make an evaluation of something means that you are comparing it with some appropriate class of things (a large flea is large compared to other fleas, but not as compared to chairs, tables, dogs, humans, boats, houses, and so on).
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