Combining Texts

All the ideas for 'Beyond internal Foundations to external Virtues', 'Giordano Bruno and Hermetic Tradition' and 'Cardinality, Counting and Equinumerosity'

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23 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought
9288 The magic of Asclepius enters Renaissance thought mixed into Ficino's neo-platonism [Yates]
9291 The dating, in 1614, of the Hermetic writings as post-Christian is the end of the Renaissance [Yates]
2. Reason / A. Nature of Reason / 6. Coherence
8877 We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa]
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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
8884 The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa]
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
8878 It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8880 In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8881 Most of our knowledge has insufficient sensory support [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8882 Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa]
8883 Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
8885 Some features of a thought are known directly, but others must be inferred [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
8876 Much propositional knowledge cannot be formulated, as in recognising a face [Sosa]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8879 Fully comprehensive beliefs may not be knowledge [Sosa]