| Phi 346-02 Spring 2014 |
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Peter Geach (1916-2013) was one of a number of British philosophers active after WWII who were influenced by the later work of Ludwig Wittgenstein. (Another was Geach’s wife, Elizabeth Anscombe, 1919-2001, who translated both Wittgenstein’s Philosophical Investigations and the account of it by Paul Feyerabend that we discussed in the first half semester.) Geach was unusual among this group for his interest in, and contribution to, logic.
In this short article, Geach employs an idea, presupposition, which attracted the interest of many of those influenced by Wittgenstein, to argue against the analysis of definite descriptions offered by Bertrand Russell. That point is made under the heading (I), pp. 84–86. You should watch for the content of the presupposition, the cases where it arises, and the difference Geach sees between presupposition and implication.
The remainder of the paper falls under heading (II) and concerns technical issues that are not very important for our purposes, so it’s fine to stop reading after the first paragraph of (II). If you’d like to go further, you can use the following glossary to help with the logical notation, which is what Russell used in the work Principia Mathematica (written in collaboration with Alfred North Whitehead) where he worked out his way of basing mathematics on logic.
Glossary
| Operation | Symbol | English | Meaning in context |
| Conjunction | . | and | “A . B” amounts to “A and B” |
| Biconditional | ≡ | if and only if | “A ≡ B” amounts to “A if and only if B” |
| Universal quantifier | (x) | everything, x, is such that | “(x) …x…” amounts to “everything, x, is such that …x…” |
| Existential quantifier | (Ex) | something, x, is such that | “(Ex) …x…” amounts to “something, x, is such that …x…” |
| Description operator | ℩x | the thing, x, such that | “G(℩x Fx)” amounts to “the predicate G is true of the one and only thing that the predicate F is true of” |
| Existence predicate | E! | exists | “E!…” amounts to “… exists” |
Dots are used not only for conjunction; appearing alone or in groups like ‘:’; they are also used as an alternative to parentheses to mark the scope of application of an operation. For example, in ‘(Ey): Gy. (x). Fx ≡ x = y’ (Russell’s analysis of ‘G(℩x Fx)’), the two dots arranged like a colon show that the existential quantifier ‘(Ey)’ applies to the whole rest of the the sentence while the single dot after ‘(x)’ shows that it applies to the whole biconditional ‘Fx ≡ x = y’. On the other hand, the dot after Gy is used for conjunction, a conjunction of ‘Gy’ with the rest of the sentence. So the whole sentence says that there is something y with a pair of properties: (i) the predicate G is true of y and (ii) it is true of everything x that the predicate F is true of x if and only if x is the same thing as y (which is to say that the predicate F is true of y and only y). In other words, it says that G is true of something that F is true of uniquely.