Combining Philosophers

All the ideas for Protagoras, Thoralf Skolem and Lord Kelvin (Wm Thomson)

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24 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17879 Axiomatising set theory makes it all relative [Skolem]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
13536 Skolem did not believe in the existence of uncountable sets [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17878 If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
1553 No perceptible object is truly straight or curved [Protagoras]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17880 Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17881 Mathematician want performable operations, not propositions about objects [Skolem]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
1549 Everything that exists consists in being perceived [Protagoras]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
1545 Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1547 Man is the measure of all things - of things that are, and of things that are not [Protagoras]
3305 There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
3317 You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras]
3313 If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
247 God is "the measure of all things", more than any man [Plato on Protagoras]
606 Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras]
612 Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras]
14. Science / B. Scientific Theories / 1. Scientific Theory
22363 You have only begun to do real science when you can express it in numbers [Kelvin]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6016 Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD]
23. Ethics / B. Contract Ethics / 1. Contractarianism
1580 For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
205 Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
1659 Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
532 Successful education must go deep into the soul [Protagoras]
25. Social Practice / E. Policies / 5. Education / b. Education principles
1552 He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
20644 Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]
28. God / C. Attitudes to God / 5. Atheism
1551 He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras]