31 ideas
7278 | Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)] |
7281 | Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)] |
7282 | Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)] |
7284 | If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang 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] |
7289 | Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23403 | You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)] |
7285 | Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)] |
7277 | The perfect man has no self [Zhuangzi (Chuang Tzu)] |
7286 | To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)] |
7279 | If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)] |
23404 | Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)] |
20443 | The aesthetic attitude is nothing more than paying close attention [Dickie, by Giovannelli] |
7283 | Great courage is not violent [Zhuangzi (Chuang Tzu)] |
7280 | As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)] |
7288 | Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)] |
7287 | Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)] |