Combining Texts

All the ideas for 'fragments/reports', 'Proslogion' and 'Cardinality, Counting and Equinumerosity'

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22 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]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [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 / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
21241 Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm]
21243 An existing thing is even greater if its non-existence is inconceivable [Anselm]
21244 Conceiving a greater being than God leads to absurdity [Anselm]
21242 If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm]
1421 A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm]
21245 The word 'God' can be denied, but understanding shows God must exist [Anselm]
21246 Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm]
21247 Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
1420 Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm]