Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Must We Believe in Set Theory?' and 'Human Knowledge: its scope and limits'

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16 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
21757 Philosophy is the conceptual essence of the shape of history [Hegel]
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]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
16489 Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
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]
10. Modality / A. Necessity / 6. Logical Necessity
16490 Some facts about experience feel like logical necessities [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
16488 It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
19. Language / F. Communication / 3. Denial
16491 If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
4786 Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]