Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Five Milestones of Empiricism' and 'Cardinality, Counting and Equinumerosity'

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17 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
21757 Philosophy is the conceptual essence of the shape of history [Hegel]
2. Reason / D. Definition / 7. Contextual Definition
19048 Contextual definition shifted the emphasis from words to whole sentences [Quine]
19047 Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
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]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
19049 In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine]
19046 Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
19050 Holism in language blurs empirical synthetic and empty analytic sentences [Quine]