17 ideas
5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
8964 | Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz] |
15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
8962 | 'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz] |
8961 | Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz] |
8963 | Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz] |
3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
5244 | For Pythagoreans, justice is simply treating all people the same [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] |
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] |
644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |