Combining Philosophers

All the ideas for Vassilis Politis, John von Neumann and Steven Pinker

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24 ideas

2. Reason / D. Definition / 1. Definitions
11257 The Pythagoreans were the first to offer definitions [Politis, by Politis]
3. Truth / A. Truth Problems / 4. Uses of Truth
11235 'True of' is applicable to things, while 'true' is applicable to words [Politis]
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 / A. Nature of Existence / 3. Being / e. Being and nothing
11277 Maybe 'What is being? is confusing because we can't ask what non-being is like [Politis]
7. Existence / C. Structure of Existence / 2. Reduction
7508 Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
11248 Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis]
12. Knowledge Sources / D. Empiricism / 2. Associationism
7510 Connectionists say the mind is a general purpose learning device [Pinker]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
7513 Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker]
16. Persons / F. Free Will / 5. Against Free Will
7509 Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
7511 Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker]
7512 There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
7505 Many think that accepting human nature is to accept innumerable evils [Pinker]
27. Natural Reality / G. Biology / 2. Life
7516 In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker]
27. Natural Reality / G. Biology / 3. Evolution
7515 All the evidence says evolution is cruel and wasteful, not intelligent [Pinker]
7514 Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker]