Combining Texts

All the ideas for 'works', 'How Things Might Have Been' and 'Cardinality, Counting and Equinumerosity'

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30 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 / A. Existence of Objects / 5. Individuation / a. Individuation
11897 A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P]
11898 Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
11883 A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11889 Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P]
9. Objects / D. Essence of Objects / 3. Individual Essences
11877 An individual essence is the properties the object could not exist without [Mackie,P]
11882 No other object can possibly have the same individual essence as some object [Mackie,P]
11886 There are problems both with individual essences and without them [Mackie,P]
9. Objects / D. Essence of Objects / 5. Essence as Kind
11909 Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P]
11899 Why are any sortals essential, and why are only some of them essential? [Mackie,P]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
11906 The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P]
9. Objects / E. Objects over Time / 12. Origin as Essential
11894 Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11887 Transworld identity without individual essences leads to 'bare identities' [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11890 De re modality without bare identities or individual essence needs counterparts [Mackie,P]
11892 Things may only be counterparts under some particular relation [Mackie,P]
11893 Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
11884 The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11905 Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
11907 Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P]