Combining Texts

All the ideas for 'fragments/reports', 'Cardinality, Counting and Equinumerosity' and 'Towards a Critique of Hegel's Philosophy'

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19 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19441 All philosophies presuppose their historical moment, and arise from it [Feuerbach]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23367 Even pointing a finger should only be done for a reason [Epictetus]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19442 I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach]
2. Reason / C. Styles of Reason / 1. Dialectic
19444 Each proposition has an antithesis, and truth exists as its refutation [Feuerbach]
19445 A dialectician has to be his own opponent [Feuerbach]
3. Truth / A. Truth Problems / 3. Value of Truth
19443 Truth forges an impersonal unity between people [Feuerbach]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
19446 To our consciousness it is language which looks unreal [Feuerbach]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
19447 The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach]