32 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
14650 | Maybe proper names involve essentialism [Plantinga] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
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] |
14647 | Surely self-identity is essential to Socrates? [Plantinga] |
14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
14651 | What Socrates could have been, and could have become, are different? [Plantinga] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23262 | Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling] |
23263 | Politics is driven by power cliques [Grayling] |
23254 | Democracies should require a supermajority for major questions [Grayling] |
23255 | It is essential for democracy that voting is free and well informed [Grayling] |
23260 | A cap on time of service would restrict party control and career ambitions [Grayling] |
23253 | Majority decisions are only acceptable if the minority interests are not vital [Grayling] |
23256 | Liberty and equality cannot be reconciled [Grayling] |
23258 | The very concept of democracy entails a need for justice [Grayling] |
23259 | There should be separate legislative, executive and judicial institutions [Grayling] |