40 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] |
| 20339 | Classes rarely share properties with their members - unlike universals and types [Wollheim] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 20338 | We often treat a type as if it were a sort of token [Wollheim] |
| 20342 | Interpretation is performance for some arts, and critical for all arts [Wollheim] |
| 20343 | A love of nature must precede a love of art [Wollheim] |
| 20348 | A criterion of identity for works of art would be easier than a definition [Wollheim] |
| 20347 | If beauty needs organisation, then totally simple things can't be beautiful [Wollheim] |
| 20331 | It is claimed that the expressive properties of artworks are non-physical [Wollheim] |
| 20345 | Some say art must have verbalisable expression, and others say the opposite! [Wollheim] |
| 20336 | Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim] |
| 20337 | The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim] |
| 20333 | If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim] |
| 20334 | The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim] |
| 20335 | The ideal theory of art neglects both the audience and the medium employed [Wollheim] |
| 20340 | A musical performance has virtually the same features as the piece of music [Wollheim] |
| 20341 | An interpretation adds further properties to the generic piece of music [Wollheim] |
| 20332 | A drawing only represents Napoleon if the artist intended it to [Wollheim] |
| 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] |