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] |
14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
14595 | Can properties exemplify other properties? [Swoyer] |
14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19271 | No rule can be fully explained [Kripke] |
19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |