donkey sentences

donkey sentences sentences exemplified by ‘Every man who owns a donkey beats it’, ‘If a man owns a donkey, he beats it’, and similar forms, which have posed logical puzzles since medieval times but were noted more recently by Geach. At issue is the logical form of such sentences – specifically, the correct construal of the pronoun ‘it’ and the indefinite noun phrase ‘a donkey’. Translations into predicate logic by the usual strategy of rendering the indefinite as existential quantification and the pronoun as a bound variable (cf. ‘John owns a donkey and beats it’ P (Dx) (x is a donkey & John owns x & John beats x)) are either ill-formed or have the wrong truth conditions. With a universal quantifier, the logical form carries the controversial implication that every donkey-owning man beats every donkey he owns. Efforts to resolve these issues have spawned much significant research in logic and linguistic semantics. See also LOGICAL FORM. R.E.W.

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