31 ideas
| 6319 | Wise people choose inaction and silence [Laozi (Lao Tzu)] |
| 6325 | One who knows does not speak; one who speaks does not know [Laozi (Lao Tzu)] |
| 6321 | Vulgar people are alert; I alone am muddled [Laozi (Lao Tzu)] |
| 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] |
| 6328 | To know yet to think that one does not know is best [Laozi (Lao Tzu)] |
| 6323 | Pursuit of learning increases activity; the Way decreases it [Laozi (Lao Tzu)] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6331 | Truth is not beautiful; beautiful speech is not truthful [Laozi (Lao Tzu)] |
| 6330 | One with no use for life is wiser than one who values it [Laozi (Lao Tzu)] |
| 6327 | Do good to him who has done you an injury [Laozi (Lao Tzu)] |
| 23402 | The highest virtue is achieved without effort [Laozi (Lao Tzu)] |
| 6324 | To gain in goodness, treat as good those who are good, and those who are not [Laozi (Lao Tzu)] |
| 6322 | There is no crime greater than having too many desires [Laozi (Lao Tzu)] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 6320 | The best rulers are invisible, the next admired, the next feared, and the worst are exploited [Laozi (Lao Tzu)] |
| 6329 | People are hard to govern because authorities love to do things [Laozi (Lao Tzu)] |
| 6326 | The better known the law, the more criminals there are [Laozi (Lao Tzu)] |
| 23401 | A military victory is not a thing of beauty [Laozi (Lao Tzu)] |