Combining Texts

All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'Set Theory and the Continuum Hypothesis' and 'fragments/reports'

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28 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
1553 No perceptible object is truly straight or curved [Protagoras]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
14248 We could accept the integers as primitive, then use sets to construct the rest [Cohen]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
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
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]
3317 You can only state the problem of the relative warmth of an object by agreeing on the underlying object [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]
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]
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]