Combining Texts

All the ideas for 'Cardinality, Counting and Equinumerosity', 'Metaphysics' and 'Three-Dimensionalism v Four-Dimensionalism'

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16 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]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
16771 A composite is a true unity if all of its parts fall under one essence [Scheibler]
9. Objects / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
14590 If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
14591 Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne]
10. Modality / A. Necessity / 11. Denial of Necessity
14589 A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne]
27. Natural Reality / C. Space / 6. Space-Time
14588 Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne]