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Ideas of Richard G. Heck, by Text
[American, fl. 2000, At Harvard University.]
2000

Cardinality, Counting and Equinumerosity

3

p.194

17448

In counting, numerals are used, not mentioned (as objects that have to correlated)

3

p.196

17449

We can understand cardinality without the idea of oneone correspondence

4

p.198

17450

Understanding 'just as many' needn't involve grasping oneone correspondence

4

p.199

17451

We can know 'just as many' without the concepts of equinumerosity or numbers

5

p.200

17453

The meaning of a number isn't just the numerals leading up to it

5

p.201

17454

Children can use numbers, without a concept of them as countable objects

5

p.202

17456

Counting is the assignment of successively larger cardinal numbers to collections

5

p.202

17455

Is counting basically mindless, and independent of the cardinality involved?

6

p.202

17457

A basic grasp of cardinal numbers needs an understanding of equinumerosity

6

p.203

17458

Equinumerosity is not the same concept as oneone correspondence

6

p.204

17459

Frege's Theorem explains why the numbers satisfy the Peano axioms
