Generalized Quantifier Analysis
Stephen Neale, among others, has defended Russell's theory, and incorporated it into the theory of generalized quantifiers. On this view, 'the' is a quantificational determiner like 'some', 'every', 'most' etc. The definite description 'the' has the following denotation (using lambda notation):
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- λf.λg..
(That is, the definite article 'the' denotes a function which takes a pair of properties f and g to truth just in case there exists something that has the property f, only one thing has the property f, and that thing also has the property g.) Given the denotation of the predicates 'present King of France' (again PKoF for short) and 'bald (B for short)'
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- λx.
- λx.
we then get the Russellian truth conditions via two steps of function application: 'The present King of France is bald' is true just in case ∃x & B(x)]. On this view, definite descriptions like 'the present King of France' do have a denotation (specifically, definite descriptions denote a function from properties to truth values—they are in that sense not syncategorematic, or "incomplete symbols"); but the view retains the essentials of the Russellian analysis, yielding exactly the truth conditions Russell argued for.
Read more about this topic: Definite Description
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