Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'An Analysis of Knowledge and Valuation' and 'Interview with Baggini and Stangroom'

expand these ideas     |    start again     |     specify just one area for these texts

31 ideas

1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
6859 Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
6862 Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
6858 Formal logic struck me as exactly the language I wanted to think in [Williamson]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
6863 Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
6861 What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
12. Knowledge Sources / B. Perception / 1. Perception
6860 How can one discriminate yellow from red, but not the colours in between? [Williamson]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
21500 We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI]
21501 If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
6556 If anything is to be probable, then something must be certain [Lewis,CI]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21498 Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI]
18. Thought / C. Content / 8. Intension
5828 Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI]