33 ideas
3870 | The real problem of science is how to choose between possible explanations [Newton-Smith] |
3853 | For science to be rational, we must explain scientific change rationally [Newton-Smith] |
3859 | We do not wish merely to predict, we also want to explain [Newton-Smith] |
3854 | Positivists hold that theoretical terms change, but observation terms don't [Newton-Smith] |
3855 | Critics attack positivist division between theory and observation [Newton-Smith] |
3861 | Theories generate infinite truths and falsehoods, so they cannot be used to assess probability [Newton-Smith] |
3869 | More truthful theories have greater predictive power [Newton-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] |
3867 | De re necessity arises from the way the world is [Newton-Smith] |
3872 | We must assess the truth of beliefs in identifying them [Newton-Smith] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
3857 | Defeat relativism by emphasising truth and reference, not meaning [Newton-Smith] |
3858 | A full understanding of 'yellow' involves some theory [Newton-Smith] |
3863 | The anomaly of Uranus didn't destroy Newton's mechanics - it led to Neptune's discovery [Newton-Smith] |
3864 | Anomalies are judged against rival theories, and support for the current theory [Newton-Smith] |
3862 | All theories contain anomalies, and so are falsified! [Newton-Smith] |
3865 | Why should it matter whether or not a theory is scientific? [Newton-Smith] |
3866 | If theories are really incommensurable, we could believe them all [Newton-Smith] |
3871 | Explaining an action is showing that it is rational [Newton-Smith] |
17366 | Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha] |