40 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
| 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] |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| 11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| 17508 | Science aims at truth, not at 'simplicity' [Putnam] |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| 17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
| 173 | Beauty and goodness are the same [Plato] |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| 172 | Love of ugliness is impossible [Plato] |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| 177 | If a person is good they will automatically become happy [Plato] |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| 17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
| 11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |