Combining Philosophers

All the ideas for Paul Thagard, Moritz Schlick and John von Neumann

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

24 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
13737 The empiricist says that metaphysics is meaningless, rather than false [Schlick]
2. Reason / A. Nature of Reason / 6. Coherence
17596 Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard]
17597 Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard]
17598 Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard]
3. Truth / A. Truth Problems / 6. Verisimilitude
17602 Verisimilitude comes from including more phenomena, and revealing what underlies [Thagard]
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]
14. Science / B. Scientific Theories / 1. Scientific Theory
17601 Neither a priori rationalism nor sense data empiricism account for scientific knowledge [Thagard]
14. Science / C. Induction / 6. Bayes's Theorem
17600 Bayesian inference is forced to rely on approximations [Thagard]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
17064 1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart]
17065 2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart]
17066 3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart]
17067 4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart]
17068 5: Contradictory propositions incohere [Thagard, by Smart]
17069 6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
17599 The best theory has the highest subjective (Bayesian) probability? [Thagard]