22 ideas
10911 | Part-whole is the key relation among truth-makers [Mulligan/Simons/Smith] |
10909 | Truth-makers cannot be the designata of the sentences they make true [Mulligan/Simons/Smith] |
10906 | Moments (objects which cannot exist alone) may serve as truth-makers [Mulligan/Simons/Smith] |
10907 | The truth-maker for a sentence may not be unique, or may be a combination, or several separate items [Mulligan/Simons/Smith] |
10912 | Despite negative propositions, truthmakers are not logical complexes, but ordinary experiences [Mulligan/Simons/Smith] |
10908 | Correspondence has to invoke facts or states of affairs, just to serve as truth-makers [Mulligan/Simons/Smith] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
5880 | Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero] |