|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._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Geach’s donkey/Cresswell: indicates a bound individual variable, instead of a description "the donkey, he has" - universal quantifier: simple Category - then: - with Lewis: "unselective quantifier" (simply binds all variables) - problem: more difficult than existantial quantification: has antecedens and consequens (order no longer matters) - then generalized universal quantification: generalized quantors exclude mixed quantors - Variant: if-sentence.
Geach's Donkey/Cresswell: he shows a bound individual variable instead of a description "The donkey he owns" - universal quantifier:
If we leave ∀ in the simple category of <0, <0,1>, <0,1>>, we need two ∀'s:
(22) ‹∀, ‹a donkey›, ‹λx, ‹∀, ‹man, ‹which , ‹λy, ‹y, has, x››› ‹λ, y, ‹y beats, ‹it, x››››››.
Everyday translation: every donkey is an x so that every man who has x beats x.
Problem: more difficult than in the case of existence quantification: here there is antecedence and consequence (order does not matter any longer) - then generalized universal quantifier:
: The generalized ∀ would have to be for (22) in the category ‹0, ‹0,1›, ‹0,1›, ‹0,1 ›› and (21) (Geach's donkeys) would be
(23) ‹∀, ‹‹λxy ‹a man, ‹which, ‹λz ‹has zy››› , x›, ‹λxy ‹a donkey y››, ‹λxy, ‹beats x ‹it y››››››.
Problem: how to deal with it. Universal quantifier: the semantics for ∀ is:
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984