Combining Philosophers

All the ideas for Jonathan Bennett, Daniel Garber and John von Neumann

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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]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
8439 Maybe each event has only one possible causal history [Bennett]
8440 Maybe an event's time of occurrence is essential to it [Bennett]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
8978 Events are made of other things, and are not fundamental to ontology [Bennett]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
12695 Epicurean atomists say body is sensible, to distinguish it from space. [Garber]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
12705 Epicurean atoms are distinguished by their extreme hardness [Garber]
26. Natural Theory / C. Causation / 1. Causation
8441 Delaying a fire doesn't cause it, but hastening it might [Bennett]
8436 Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett]
26. Natural Theory / C. Causation / 2. Types of cause
8435 Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
10364 Facts are about the world, not in it, so they can't cause anything [Bennett]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
8437 The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett]
8438 A counterfactual about an event implies something about the event's essence [Bennett]
27. Natural Reality / C. Space / 4. Substantival Space
8592 Empty space is measurable in ways in which empty time necessarily is not [Bennett, by Shoemaker]