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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 In counting, numerals are used, not mentioned (as objects that have to correlated)
3 p.196 We can understand cardinality without the idea of one-one correspondence
4 p.198 Understanding 'just as many' needn't involve grasping one-one correspondence
4 p.199 We can know 'just as many' without the concepts of equinumerosity or numbers
5 p.200 Ordinals can define cardinals, as the smallest ordinal that maps the set
5 p.200 The meaning of a number isn't just the numerals leading up to it
5 p.201 Children can use numbers, without a concept of them as countable objects
5 p.202 Counting is the assignment of successively larger cardinal numbers to collections
5 p.202 Is counting basically mindless, and independent of the cardinality involved?
6 p.202 A basic grasp of cardinal numbers needs an understanding of equinumerosity
6 p.203 Equinumerosity is not the same concept as one-one correspondence
6 p.204 Frege's Theorem explains why the numbers satisfy the Peano axioms