more from Charles Parsons

Single Idea 17447

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure]

Full Idea

In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.

Gist of Idea

Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal


report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3

Book Reference

-: 'Notre Dame Journal of Formal Logic' [-], p.194

A Reaction

This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.

Related Idea

Idea 17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]