Combining Texts

All the ideas for 'Why coherence is not enough', 'Intros to Russell's 'Essays in Analysis'' and 'Realism in Mathematics'

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

8 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
21554 Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
21553 It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8840 There are five possible responses to the problem of infinite regress in justification [Cleve]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
8841 Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]