Combining Texts

All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'On the spiritual perfection of life' and 'Of the Laws of Ecclesiastical Polity'

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15 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
22102 Arguing with opponents uncovers truths, and restrains falsehoods [Aquinas]
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 / 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]
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]
25. Social Practice / C. Rights / 1. Basis of Rights
19896 It is not a law if not endorsed by the public [Hooker,R]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
19891 Rule of law is superior to autonomy, because citizens can see what is expected [Hooker,R]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
19897 Human laws must accord with the general laws of Nature [Hooker,R]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
17005 Natural things observe certain laws, and things cannot do otherwise if they retain their forms [Hooker,R]