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Full Idea
The Lambda Abstraction Operator: We can write (λx)[Man x], which may be read as 'the property that any x has just if x is a man'.
Gist of Idea
(λx)[Man x] means 'the property x has iff x is a man'.
Source
David Wiggins (Sameness and Substance Renewed [2001], 4.2)
Book Ref
Wiggins,David: 'Sameness and Substance Renewed' [CUP 2001], p.113
A Reaction
This technical device seems to be a commonplace in modern metaphysical discussions. I'm assuming it can be used to discuss properties without venturing into second-order logic. Presumably we could call the property here 'humanity'.
11863 | (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins] |
11176 | The property of Property Abstraction says any suitable condition must imply a property [Fine,K] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
13703 | λ can treat 'is cold and hungry' as a single predicate [Sider] |