28 ideas
| 21793 | Genuine truth is the resolution of the highest contradiction [Hegel] |
| 21795 | What I hold true must also be part of my feelings and character [Hegel] |
| 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] |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| 14595 | Can properties exemplify other properties? [Swoyer] |
| 14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 18549 | Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton] |
| 22043 | Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard] |
| 22042 | Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard] |
| 20413 | For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge] |
| 20394 | The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S] |
| 21794 | The main purpose of art is to express the unity of human life [Hegel] |
| 20415 | Art forms a bridge between the sensuous world and the world of pure thought [Hegel] |