Combining Texts

All the ideas for 'fragments/reports', 'A Version of Internalist Foundationalism' and 'Cardinality, Counting and Equinumerosity'

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24 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8893 For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour]
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 / 1. Knowledge
8888 The concept of knowledge is so confused that it is best avoided [Bonjour]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
8887 It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
8897 The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
8896 Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8891 My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour]
8892 Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour]
8894 Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
8889 Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
8890 If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
8895 If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour]
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]