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] |
12699 | A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz] |
12700 | Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz] |
12736 | If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber] |
19718 | Indefeasibility does not imply infallibility [Grundmann] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19717 | Can a defeater itself be defeated? [Grundmann] |
19716 | Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann] |
19715 | You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann] |
19713 | Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann] |
19714 | Knowledge requires that there are no facts which would defeat its justification [Grundmann] |
19719 | 'Moderate' foundationalism has basic justification which is defeasible [Grundmann] |
12698 | Every body contains a kind of sense and appetite, or a soul [Leibniz] |