Combining Philosophers

All the ideas for Philolaus, Richard G. Heck and Richard T.W. Arthur

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21 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 / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
472 No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus]
10. Modality / B. Possibility / 1. Possibility
19378 Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
19380 Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
1518 Everything must involve numbers, or it couldn't be thought about or known [Philolaus]
1519 Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus]
473 There is no falsehood in harmony and number, only in irrational things [Philolaus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
469 Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
476 Self-created numbers make the universe stable [Philolaus]
27. Natural Reality / E. Cosmology / 1. Cosmology
1787 Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius]