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Single Idea 10791
[filed under theme 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
]
Full Idea
On a substitutional semantics of a first-order language, a domain of objects is not specified. Variables do not range over objects. They are place markers for substituends (..and sentences are true-for-all-names, or true-for-at-least-one-name).
Clarification
'Substituends' are things that can inserted for the place markers
Gist of Idea
Substitutional semantics has no domain of objects, but place-markers for substitutions
Source
Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.165)
Book Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.165
The
22 ideas
from Ruth Barcan Marcus
11180
|
Essentialist sentences are not theorems of modal logic, and can even be false
[Marcus (Barcan)]
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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
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'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
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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)]
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