33 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 7306 | If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 7322 | Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A] |
| 7325 | Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A] |
| 7324 | Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A] |
| 7323 | If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A] |
| 7315 | 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A] |
| 7328 | The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A] |
| 7329 | Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A] |
| 7333 | The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A] |
| 23262 | Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling] |
| 23263 | Politics is driven by power cliques [Grayling] |
| 23255 | It is essential for democracy that voting is free and well informed [Grayling] |
| 23254 | Democracies should require a supermajority for major questions [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] |