32 ideas
| 14052 | Begin philosophy when you are young, and keep going when you are old [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] |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 14062 | Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus] |
| 1837 | We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus] |
| 1836 | Prudence is more valuable than philosophy, because it avoids confusions of the soul [Epicurus] |
| 14061 | Our own choices are autonomous, and the basis for praise and blame [Epicurus] |
| 14054 | Fearing death is absurd, because we are not present when it occurs [Epicurus] |
| 14053 | It is absurd to fear the pain of death when you are not even facing it [Epicurus] |
| 14055 | The wisdom that produces a good life also produces a good death [Epicurus] |
| 14057 | All pleasures are good, but it is not always right to choose them [Epicurus] |
| 14058 | Pleasure is the goal, but as lack of pain and calm mind, not as depraved or greedy pleasure [Epicurus] |
| 1833 | Pleasure is the first good in life [Epicurus] |
| 14063 | Sooner a good decision going wrong, than a bad one turning out for the good [Epicurus] |
| 14059 | The best life is not sensuality, but rational choice and healthy opinion [Epicurus] |
| 1835 | True pleasure is not debauchery, but freedom from physical and mental pain [Epicurus] |
| 14056 | We only need pleasure when we have the pain of desire [Epicurus] |
| 14060 | Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus] |