### Ideas from 'Cardinality, Counting and Equinumerosity' by Richard G. Heck [2000], by Theme Structure

#### [found in 'Notre Dame Journal of Formal Logic' (ed/tr -) [- ,]].

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###### 6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
 17453 The meaning of a number isn't just the numerals leading up to it
###### 6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
 17452 Ordinals can define cardinals, as the smallest ordinal that maps the set
###### 6. Mathematics / A. Nature of Mathematics / 3. Numbers / f. Cardinal numbers
 17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity
###### 6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
 17448 In counting, numerals are used, not mentioned (as objects that have to correlated)
 17450 Understanding 'just as many' needn't involve grasping one-one correspondence
 17451 We can know 'just as many' without the concepts of equinumerosity or numbers
 17455 Is counting basically mindless, and independent of the cardinality involved?
 17456 Counting is the assignment of successively larger cardinal numbers to collections
###### 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / d. Peano arithmetic
 17459 Frege's Theorem explains why the numbers satisfy the Peano axioms
###### 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
 17454 Children can use numbers, without a concept of them as countable objects
###### 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
 17449 We can understand cardinality without the idea of one-one correspondence
 17458 Equinumerosity is not the same concept as one-one correspondence