Combining Texts

All the ideas for 'The Middle Works (15 vols, ed Boydston)', 'Cardinality, Counting and Equinumerosity' and 'Vagaries of Definition'

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20 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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
8203 All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine]
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]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
22868 The value and truth of knowledge are measured by success in activity [Dewey]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
22865 Habits constitute the self [Dewey]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
8202 Meaning is essence divorced from things and wedded to words [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
8201 The distinction between meaning and further information is as vague as the essence/accident distinction [Quine]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22871 The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22876 Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
22875 Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
22874 Individuality is only developed within groups [Dewey]