Combining Texts

All the ideas for 'Metaphysical Foundations of Natural Science', 'The Apology' and 'Logicism, Some Considerations (PhD)'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13412 Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
13413 We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13411 If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
13415 An adequate account of a number must relate it to its series [Benacerraf]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
15308 Science is the reduction of diverse forces and powers to a smaller number that explain them [Kant]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
1655 If goodness needs true opinion but not knowledge, you can skip the 'examined life' [Vlastos on Plato]