26 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] |
5998 | From the necessity of the past we can infer the impossibility of what never happens [Diod.Cronus, by White,MJ] |
20832 | The Master Argument seems to prove that only what will happen is possible [Diod.Cronus, by Epictetus] |
14304 | Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19544 | Closure says if you know P, and also know P implies Q, then you must know Q [Dretske] |
19545 | We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske] |
19547 | Reasons for believing P may not transmit to its implication, Q [Dretske] |
19546 | Knowing by visual perception is not the same as knowing by implication [Dretske] |
19548 | The only way to preserve our homely truths is to abandon closure [Dretske] |
19549 | P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske] |
19550 | We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske] |
6024 | Thought is unambiguous, and you should stick to what the speaker thinks they are saying [Diod.Cronus, by Gellius] |