Combining Texts

All the ideas for 'fragments/reports', 'Cardinality, Counting and Equinumerosity' and 'Coherence Theory of Truth and Knowledge'

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22 ideas

3. Truth / D. Coherence Truth / 1. Coherence Truth
19081 Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
8806 The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
8252 Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8255 Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8804 Reasons for beliefs are not the same as evidence [Davidson]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
8802 Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
8801 Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
8805 Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
18703 Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]