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Single Idea 10022

[from 'Logicism and Ontological Commits. of Arithmetic' by Harold Hodes, in 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism ]

Full Idea

The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero.

Clarification

'Level zero' is for objects, and 'level-one' is for quantifying over objects

Gist of Idea

Numerical terms can't really stand for quantifiers, because that would make them first-level

Source

Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142)

Book Reference

-: 'Journal of Philosophy' [-], p.142


A Reaction

Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers?