Combining Texts

All the ideas for 'teaching', 'Inquiry Concerning Virtue or Merit' and 'Knowledge and the Philosophy of Number'

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26 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
5896 Speak the truth, for this alone deifies man [Pythagoras, by Porphyry]
1. Philosophy / B. History of Ideas / 2. Ancient Thought
3051 Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
7485 For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6237 Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
6234 If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury]
22. Metaethics / B. Value / 2. Values / d. Health
3053 Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6233 A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
6236 People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury]
23. Ethics / A. Egoism / 1. Ethical Egoism
6235 Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
6232 Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
5244 For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
375 When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato]
638 Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle]
553 Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle]
554 Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle]
644 For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
5642 For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7467 The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson]