25 ideas
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] |
23551 | It is necessary for a belief that it be held for a length of time [Fricker,M] |
12739 | If we are dreaming, it is sufficient that the events are coherent, and obey laws [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23558 | Offering knowledge needs accuracy and sincerity; receiving it needs testimonial justice [Fricker,M] |
23550 | Burge says we are normally a priori entitled to believe testimony [Fricker,M] |
23552 | We assess testimonial probabilities by the speaker, the listener, the facts, and the circumstances [Fricker,M] |
23553 | Testimonial judgement is not logical, but produces reasons and motivations [Fricker,M] |
23555 | Assessing credibility involves the impact of both the speaker's and the listener's social identity [Fricker,M] |
12738 | Successful prediction shows proficiency in nature [Leibniz] |
23554 | Judgements can be unreflective and non-inferential, yet rational, by being sensitive to experience [Fricker,M] |
23557 | To judge agents in remote times and cultures we need a moral resentment weaker than blame [Fricker,M] |