28 ideas
| 14519 | It is a great good to show reverence for a wise man [Epicurus] |
| 14518 | In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 14524 | Bodies are combinations of shape, size, resistance and weight [Epicurus] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
| 14522 | What happens to me if I obtain all my desires, and what if I fail? [Epicurus] |
| 3563 | Pleasure and virtue entail one another [Epicurus] |
| 3560 | Justice is merely a contract about not harming or being harmed [Epicurus] |
| 14517 | We value our own character, whatever it is, and we should respect the characters of others [Epicurus] |
| 14513 | Justice is a pledge of mutual protection [Epicurus] |
| 14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
| 23812 | Force is what turns man into a thing, and ultimately into a corpse [Weil] |
| 23813 | Only people who understand force, and don't respect it, are capable of justice [Weil] |
| 14520 | It is small-minded to find many good reasons for suicide [Epicurus] |