Combining Texts

All the ideas for 'fragments/reports', 'Must We Believe in Set Theory?' and 'Apology for Raymond Sebond'

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17 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Why can't a wise man doubt everything? [Montaigne]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne]
3. Truth / A. Truth Problems / 3. Value of Truth
Virtue is the distinctive mark of truth, and its greatest product [Montaigne]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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
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
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
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
Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
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
Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
7. Existence / D. Theories of Reality / 3. Reality
We lack some sense or other, and hence objects may have hidden features [Montaigne]
8. Modes of Existence / D. Universals / 1. Universals
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
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
We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne]
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
15. Nature of Minds / A. Nature of Mind / 1. Mind / d. Location of mind
The soul is in the brain, as shown by head injuries [Montaigne]