Combining Texts

All the ideas for 'Cardinality, Counting and Equinumerosity', 'Frege on Apriority (with ps)' and 'Presidential Address of Am. Math. Soc'

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15 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
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 [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]