Combining Texts

All the ideas for 'Metaphysics: a very short introduction', 'Aspects of Scientific Explanation' and 'Cardinality, Counting and Equinumerosity'

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19 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 / 2. Substance / a. Substance
18617 Substances, unlike aggregates, can survive a change of parts [Mumford]
10. Modality / B. Possibility / 3. Combinatorial possibility
18618 Maybe possibilities are recombinations of the existing elements of reality [Mumford]
18619 Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
18620 Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]
14. Science / A. Basis of Science / 4. Prediction
22179 Explanatory facts also predict, and predictive facts also explain [Hempel, by Okasha]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
6755 For Hempel, explanations are deductive-nomological or probabilistic-statistical [Hempel, by Bird]
17083 The covering-law model is for scientific explanation; historical explanation is quite different [Hempel]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
13052 Hempel rejects causation as part of explanation [Hempel, by Salmon]