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Single Idea 10591

[filed under theme 8. Modes of Existence / B. Properties / 11. Properties as Sets ]

Full Idea

In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably.

Gist of Idea

Logicians use 'property' and 'set' interchangeably, with little hanging on it

Source

Stewart Shapiro (Higher-Order Logic [2001], 2.2.1)

Book Ref

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.36

A Reaction

Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties.

The 22 ideas with the same theme [properties are just classes of certain objects]:

21575 When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell]
9127 Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
15478 Properties are the respects in which objects resemble, which places them in classes [Martin,CB]
12672 Properties and relations are discovered, so they can't be mere sets of individuals [Ellis]
19173 Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson]
9783 While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R]
15399 The property of being F is identical with the set of objects, in all possible worlds, which are F [Lewis, by Cameron]
15732 Properties don't seem to be sets, because different properties can have the same set [Lewis]
15733 Accidentally coextensive properties come apart when we include their possible instances [Lewis]
15734 If a property is relative, such as being a father or son, then set membership seems relative too [Lewis]
9655 Trilateral and triangular seem to be coextensive sets in all possible worlds [Lewis]
9653 It would be easiest to take a property as the set of its instances [Lewis]
10723 A property is the set of its actual and possible instances [Lewis, by Oliver]
16290 I believe in properties, which are sets of possible individuals [Lewis]
15516 A property is any class of possibilia [Lewis]
4038 Properties are sets of their possible instances (which separates 'renate' from 'cordate') [Lewis, by Mellor/Oliver]
14499 Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki]
7703 If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette]
18511 Properties have causal roles which sets can't possibly have [Heil]
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
21729 Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
10413 The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer]