Combining Texts

All the ideas for 'Logicism, Some Considerations (PhD)', 'Mathematical Intuition' and 'Lecture on Nominalism'

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8 ideas

2. Reason / F. Fallacies / 1. Fallacy
21697 The Struthionic Fallacy is that of burying one's head in the sand [Quine]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
21698 All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
21696 Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]