Combining Philosophers

All the ideas for Herodotus, John von Neumann and Karl Popper

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

27 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
22358 Scientific objectivity lies in inter-subjective testing [Popper]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
11946 Propensities are part of a situation, not part of the objects [Popper]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
12177 Human artefacts may have essences, in their purposes [Popper]
9. Objects / D. Essence of Objects / 15. Against Essentialism
5451 Popper felt that ancient essentialism was a bar to progress [Popper, by Mautner]
14. Science / A. Basis of Science / 6. Falsification
22188 Give Nobel Prizes for really good refutations? [Gorham on Popper]
18284 Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
7780 Falsification is the criterion of demarcation between science and non-science [Popper, by Magee]
16830 We don't only reject hypotheses because we have falsified them [Lipton on Popper]
6794 If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper]
6795 When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper]
14. Science / B. Scientific Theories / 2. Aim of Science
3856 Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith]
14. Science / C. Induction / 3. Limits of Induction
7779 There is no such thing as induction [Popper, by Magee]
14. Science / C. Induction / 4. Reason in Induction
3860 Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
12176 Science does not aim at ultimate explanations [Popper]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12175 Galilean science aimed at true essences, as the ultimate explanations [Popper]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
12179 Essentialist views of science prevent further questions from being raised [Popper]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]