Philosophy Lexicon of Arguments

Donkey sentences, philosophy: term for logical problems, which preferably, but not essentially refer to donkeys. An early example is Buridan's donkey. A modern donkey sentence is "Geach's donkey" "Anyone who has a donkey beats it." Formal logic is here too rigid to map the possible limiting cases that are not problematic for the everyday language. See also existential quantification, universal quantification, range, scope, quantification, quantifiers, brackets, branched quantifiers.
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Cresswell 172
Geach's Donkey/If-Sentence/Cresswell: E.g.
(25) When a man has a donkey, he beats it.
Problem: (25) has two indeterminate noun phrases.
Kamp: (1983, 279) has an example with only one indeterminate noun phrase. E.g.
(26) When Pedro has a donkey, he beats it.
Undefined: a donkey - defined: Pedro.
Tradition/Problem: the phrase a donkey must be represented by an existence quantifier: (Ex) (donkey(x u ...).
But the obvious interpretation of (26) is
(27) (x)((donkey x u Pedro has x)> Pedro beats x).
Kamp: there are cases where the quantifier can be changed from the existence to the universal quantifier. If it does not bind a variable in the consequence, we have as a logical equivalence:
I 173
(28) (x) (Fx> P) โ‰ก (ExFx> P).
Solution/Kamp: Kamp analyzes undetermined phrases (descriptions) as predicates (see above). And the universal quantification becomes part of the meaning of "if". (P. 288-90).
LewisVsKamp/Cresswell: (Lewis 1975a, S 11) that is fine for most natural meanings of (26), but there is a problem:
(29) Sometimes when Pedro has a donkey, Pedro beats it.
Seems to mean that there is at least one donkey that Pedro has and which is beaten by him.
Solution/Lewis: the role of "if" is merely to restrict the noun. That is, (29) has the meaning that (22) would have if we had โˆƒ instead of โˆ€.

Kamp I
From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory (Studies in Linguistics and Philosophy)

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Ed. Martin Schulz, access date 2017-05-29