more from William W. Tait

Single Idea 9986

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set]

Full Idea

The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets).

Gist of Idea

The null set was doubted, because numbering seemed to require 'units'


William W. Tait (Frege versus Cantor and Dedekind [1996], IX)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.55

A Reaction

This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely!