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Single Idea 10799

[filed under theme 5. Theory of Logic / G. Quantification / 1. Quantification ]

Full Idea

For the nominalist, at level zero, where substituends are referring names, the quantifiers may be read existentially. Beyond level zero, the variables and quantifiers are read sustitutionally (though it is unclear whether this program is feasible).

Gist of Idea

Nominalists should quantify existentially at first-order, and substitutionally when higher

Source

Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167)

Book Ref

'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.167

The 22 ideas from Ruth Barcan Marcus

11180 Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)]
11181 Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)]
11183 The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)]
11182 If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)]
11186 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)]
11185 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)]
11184 Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)]
11187 In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)]
11189 Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)]
10785 Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
10786 Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)]
10788 Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
10787 Is being just referent of the verb 'to be'? [Marcus (Barcan)]
10789 Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)]
10790 Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
10791 Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
10794 The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)]
10795 Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
10796 If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)]
10797 Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]
10798 A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
10799 Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]