Combining Texts

All the ideas for 'reports', 'reports' and 'Infinity: Quest to Think the Unthinkable'

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

49 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
1798 He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1800 Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, 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
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]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
6595 If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
6593 The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
6592 Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1805 Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius]
1807 Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius]
1810 Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius]
1802 Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius]
1801 Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius]
1804 Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius]
1808 Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius]
1806 Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius]
1809 Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius]
1803 Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7352 Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P]
22. Metaethics / B. Value / 2. Values / g. Love
6289 Love your enemies [Jesus]
6292 Love thy neighbour as thyself [Jesus]
23. Ethics / B. Contract Ethics / 2. Golden Rule
5356 Treat others as you would have them treat you [Jesus]
23. Ethics / B. Contract Ethics / 4. Value of Authority
6286 Blessed are the merciful: for they shall obtain mercy [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
6290 Except ye become as little children, ye shall not enter heaven [Jesus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
6287 If you lust after a woman, you have committed adultery [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
6285 Blessed are the meek; for they shall inherit the earth [Jesus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
6288 Don't resist evil, but turn the other cheek [Jesus]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
6293 It is almost impossible for the rich to go to heaven [Jesus]
26. Natural Theory / C. Causation / 7. Eliminating causation
3062 There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
3063 Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
6291 No one is good except God [Jesus]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
7351 Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P]