Combining Texts

All the ideas for 'fragments/reports', 'Must We Believe in Set Theory?' and 'Abstract Objects'

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20 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 / 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]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
8915 How we refer to abstractions is much less clear than how we refer to other things [Rosen]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
18. Thought / E. Abstraction / 2. Abstracta by Selection
8917 The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]
18. Thought / E. Abstraction / 5. Abstracta by Negation
8912 Nowadays abstractions are defined as non-spatial, causally inert things [Rosen]
8913 Chess may be abstract, but it has existed in specific space and time [Rosen]
8914 Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen]
18. Thought / E. Abstraction / 6. Abstracta by Conflation
8916 Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8918 Functional terms can pick out abstractions by asserting an equivalence relation [Rosen]
8919 Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen]