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Full Idea
Critics say if there are nondenumerably many objects, then on the substitutional view there might be true universal sentences falsified by an unnamed object, and there must always be some such, for names are denumerable.
Gist of Idea
A true universal sentence might be substitutionally refuted, by an unnamed denumerable object
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
A Reaction
[See Quine 'Reply to Prof. Marcus' p.183] The problem seems to be that there would be names which are theoretically denumerable, but not nameable, and hence not available for substitution. Marcus rejects this, citing compactness.
| 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)] |
| 10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
| 10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| 10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
| 10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
| 10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |