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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation

[matching items together for counting]

8 ideas
Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine]
Counting rests on one-one correspondence, of numerals to objects [Frege]
Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
We can define one-to-one without mentioning unity [Russell]
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]