23 ideas
17949 | Inquiry is the cause of philosophy [Aristotle] |
14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
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] |
14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |