Combining Philosophers

All the ideas for Aeschylus, John von Neumann and Michael Tooley

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

22 ideas

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]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
7810 The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling]
26. Natural Theory / C. Causation / 2. Types of cause
8388 Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley]
8389 Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley]
26. Natural Theory / C. Causation / 4. Naturalised causation
8416 Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley]
26. Natural Theory / C. Causation / 5. Direction of causation
8393 We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
8390 Causation is directly observable in pressure on one's body, and in willed action [Tooley]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
8418 Quantum physics suggests that the basic laws of nature are probabilistic [Tooley]
8392 Probabilist laws are compatible with effects always or never happening [Tooley]
8399 The actual cause may not be the most efficacious one [Tooley]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
8391 In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
8394 Explaining causation in terms of laws can't explain the direction of causation [Tooley]
8398 Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley]