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All the ideas for 'fragments/reports', 'Against Structural Universals' and 'Russell's Mathematical Logic'

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28 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
15435 If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
15451 I assume there could be natural properties that are not instantiated in our world [Lewis]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
15433 Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
15436 Universals are meant to give an account of resemblance [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
15438 We can add a primitive natural/unnatural distinction to class nominalism [Lewis]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15448 The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis]
15449 If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis]
15439 The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis]
15441 The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis]
15445 Butane and Isobutane have the same atoms, but different structures [Lewis]
15434 Structural universals have a necessary connection to the universals forming its parts [Lewis]
15437 We can't get rid of structural universals if there are no simple universals [Lewis]
9. Objects / C. Structure of Objects / 5. Composition of an Object
15446 Composition is not just making new things from old; there are too many counterexamples [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
15440 A whole is distinct from its parts, but is not a further addition in ontology [Lewis]
15444 Different things (a toy house and toy car) can be made of the same parts at different times [Lewis]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
15450 Maybe abstraction is just mereological subtraction [Lewis]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
15443 Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]