Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'Are there propositions?' and 'works'

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35 ideas

3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
13985 A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
13984 Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle]
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 / 1. Overview of Logic
13979 Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
7334 Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
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 / 4. Anti-realism
3303 For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
13988 Many sentences do not state facts, but there are no facts which could not be stated [Ryle]
12. Knowledge Sources / B. Perception / 3. Representation
13983 Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
13980 If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle]
19. Language / A. Nature of Meaning / 1. Meaning
13978 Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
13977 When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle]
19. Language / D. Propositions / 1. Propositions
13976 'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle]
19. Language / D. Propositions / 4. Mental Propositions
13981 Several people can believe one thing, or make the same mistake, or share one delusion [Ryle]
13987 We may think in French, but we don't know or believe in French [Ryle]
19. Language / D. Propositions / 6. Propositions Critique
13989 There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle]
13982 If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle]