Combining Texts

All the ideas for 'fragments/reports', 'Philosophical Insignificance of A Priori Knowledge' and 'On boundary numbers and domains of sets'

expand these ideas     |    start again     |     specify just one area for these texts

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9 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism

13407

All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17832

Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

13028

Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]

5. Theory of Logic / L. Paradox / 3. Antinomies

17626

The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

13409

Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau]

12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts

13406

A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau]

12. Knowledge Sources / E. Direct Knowledge / 2. Intuition

13408

Intuition and thought-experiments embody substantial information about the world [Papineau]

19. Language / A. Nature of Meaning / 5. Meaning as Verification

13410

Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]