23 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] |
16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
8329 | Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley] |
8324 | The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley] |
8328 | Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley] |
8327 | If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley] |
8330 | Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley] |
8325 | The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley] |