Combining Texts

All the ideas for 'The Source of Necessity', 'Cardinality, Counting and Equinumerosity' and 'Lectures on Jurisprudence'

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17 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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
12432 Explanation of necessity must rest on something necessary or something contingent [Hale]
12434 Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
12435 The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
12433 If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
12436 Concept-identities explain how we know necessities, not why they are necessary [Hale]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
20930 The existence of law is one thing, its merits and demerits another [Austin,J]