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Single Idea 11863

[filed under theme 5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction ]

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'.

The 5 ideas with the same theme [device for referring to an expressed property]:

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]