20 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] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
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] |
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] |
7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |