Combining Texts

All the ideas for 'teaching', 'Matter and Memory' and 'Mathematical logic and theory of types'

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22 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 / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407 The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
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 / C. Sources of Mathematics / 6. Logicism / b. Type theory
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
23478 Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18126 A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
21846 Bergson was a rallying point, because he emphasised becomings and multiplicities [Bergson, by Deleuze]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
21854 Bergson showed that memory is not after the event, but coexists with it [Bergson, by Deleuze]
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]
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]
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]