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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
13 ideas
from 'Nominalism and Substitutional Quantifiers'
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10785
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Maybe a substitutional semantics for quantification lends itself to nominalism
[Marcus (Barcan)]
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10786
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Anything which refers tends to be called a 'name', even if it isn't a noun
[Marcus (Barcan)]
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10788
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Nominalists see proper names as a main vehicle of reference
[Marcus (Barcan)]
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10787
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Is being just referent of the verb 'to be'?
[Marcus (Barcan)]
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10789
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Nominalists say predication is relations between individuals, or deny that it refers
[Marcus (Barcan)]
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10790
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Quantifiers are needed to refer to infinitely many objects
[Marcus (Barcan)]
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10791
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Substitutional semantics has no domain of objects, but place-markers for substitutions
[Marcus (Barcan)]
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10794
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The nominalist is tied by standard semantics to first-order, denying higher-order abstracta
[Marcus (Barcan)]
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10795
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Substitutional language has no ontology, and is just a way of speaking
[Marcus (Barcan)]
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10796
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If objects are thoughts, aren't we back to psychologism?
[Marcus (Barcan)]
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10797
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Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all
[Marcus (Barcan)]
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10798
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A true universal sentence might be substitutionally refuted, by an unnamed denumerable object
[Marcus (Barcan)]
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10799
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Nominalists should quantify existentially at first-order, and substitutionally when higher
[Marcus (Barcan)]
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