31 ideas
| 5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
| 1922 | Spiritual qualities only become advantageous with the growth of wisdom [Plato] |
| 3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| 11259 | How can you seek knowledge of something if you don't know it? [Plato] |
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| 20219 | True opinions only become really valuable when they are tied down by reasons [Plato] |
| 5985 | Seeking and learning are just recollection [Plato] |
| 5986 | The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato] |
| 1923 | As a guide to action, true opinion is as good as knowledge [Plato] |
| 1919 | You don't need to learn what you know, and how do you seek for what you don't know? [Plato] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| 3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
| 1913 | Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato] |
| 1921 | If virtue is a type of knowledge then it ought to be taught [Plato] |
| 1927 | It seems that virtue is neither natural nor taught, but is a divine gift [Plato] |
| 1918 | How can you know part of virtue without knowing the whole? [Plato] |
| 1916 | Even if virtues are many and various, they must have something in common to make them virtues [Plato] |
| 5244 | For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle] |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| 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] |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| 7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |