Combining Philosophers

All the ideas for Agathon, Richard G. Heck and Alan McMichael

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17 ideas

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
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]
9. Objects / D. Essence of Objects / 3. Individual Essences
14637 Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael]
9. Objects / D. Essence of Objects / 9. Essence and Properties
14636 Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael]
14640 Maybe essential properties have to be intrinsic, as well as necessary? [McMichael]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14638 Essentialism is false, because it implies the existence of necessary singular propositions [McMichael]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
74 Even God could not undo what has been done [Agathon]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
14639 Individuals enter into laws only through their general qualities and relations [McMichael]