Single Idea 10798

[catalogued under 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification]

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 Reference

'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.