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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 39 ideas from 'Sameness and Substance Renewed'

14746 What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins]
11900 We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins]
11896 A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P]
15835 Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P]
10679 'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack]
14363 Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P]
14364 A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P]
14749 Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider]
14744 Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider]
14362 Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P]
11831 The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
11832 We learn a concept's relations by using it, without reducing it to anything [Wiggins]
11836 We can use 'concept' for the reference, and 'conception' for sense [Wiggins]
11838 Relativity of Identity makes identity entirely depend on a category [Wiggins]
11839 Do both 'same f as' and '=' support Leibniz's Law? [Wiggins]
11848 Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins]
11847 To identify two items, we must have a common sort for them [Wiggins]
11843 Identity over a time and at a time aren't different concepts [Wiggins]
11841 The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins]
11850 Not every story corresponds to a possible world [Wiggins]
11844 If I destroy an item, I do not destroy each part of it [Wiggins]
11851 Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins]
11852 Is the Pope's crown one crown, if it is made of many crowns? [Wiggins]
11845 Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins]
11858 The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins]
11859 The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins]
11860 Lawlike propensities are enough to individuate natural kinds [Wiggins]
11869 Possible worlds rest on the objects about which we have suppositions [Wiggins]
11870 Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins]
11863 (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins]
11861 We can forget about individual or particularized essences [Wiggins]
11864 Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins]
11865 The possibility of a property needs an essential sortal concept to conceive it [Wiggins]
11866 The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins]
11871 Essences are not explanations, but individuations [Wiggins]
11875 Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins]
11876 It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins]
11879 Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P]
11835 The nominal essence is the idea behind a name used for sorting [Wiggins]