24 ideas
23531 | Philosophers should interpret the world, by expressing its possibilities [Berardi] |
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] |
23538 | Nothingness only exists in consciousness [Berardi] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
14470 | Explanatory exclusion: there cannot be two separate complete explanations of a single event [Kim] |
23532 | The delusion of free will brings a sense of guilt [Berardi] |
23537 | American white men trusted the philosophy of winning, and then discovered losing [Berardi] |
23536 | Community is now a nostalgic memory, which no longer exists [Berardi] |
23534 | Communism failed to unite western workers with the oppressed of the south [Berardi] |
23533 | The economy has replaced medieval theocracy at the centre of our society [Berardi] |
23535 | Western workers turn to nationalism, to avert the effects of globalisation [Berardi] |