Combining Texts

All the ideas for 'fragments/reports', 'Against the Physicists (two books)' and 'Infinity: Quest to Think the Unthinkable'

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

43 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
20768 Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
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]
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
10860 An ordinal number is defined by the set that comes before it [Clegg]
10861 Beyond infinity cardinals and ordinals can come apart [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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
22744 Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22748 Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
22746 If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus]
17. Mind and Body / D. Property Dualism / 4. Emergentism
22741 The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
3049 The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
3549 Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
22747 A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
22749 Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
22750 Time is divisible, into past, present and future [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22742 Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus]
22751 If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus]
28. God / A. Divine Nature / 2. Divine Nature
22730 All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus]
22739 God must suffer to understand suffering [Sext.Empiricus]
28. God / A. Divine Nature / 3. Divine Perfections
22738 The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus]
28. God / B. Proving God / 1. Proof of God
22734 God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
22736 God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus]
22740 God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
22735 The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus]
28. God / C. Attitudes to God / 4. God Reflects Humanity
22732 The perfections of God were extrapolations from mankind [Sext.Empiricus]
28. God / C. Attitudes to God / 5. Atheism
22728 Gods were invented as watchers of people's secret actions [Sext.Empiricus]
22737 An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus]
29. Religion / A. Polytheistic Religion / 1. Animism
22731 It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus]