39 ideas
| 6855 | Interesting philosophers hardly every give you explicitly valid arguments [Martin,M] |
| 6856 | Valid arguments can be rejected by challenging the premises or presuppositions [Martin,M] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 6857 | An error theory of perception says our experience is not as it seems to be [Martin,M] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 12157 | Kant gave form and status to aesthetics, and Hegel gave it content [Kant, by Scruton] |
| 20346 | The aesthetic attitude is a matter of disinterestedness [Kant, by Wollheim] |
| 18547 | Only rational beings can experience beauty [Kant, by Scruton] |
| 24172 | It is hard to see why we would have developed Kant's 'disinterested' aesthetic attitude [Cochrane on Kant] |
| 20408 | With respect to the senses, taste is an entirely personal matter [Kant] |
| 20409 | When we judge beauty, it isn't just personal; we judge on behalf of everybody [Kant] |
| 20411 | Saying everyone has their own taste destroys the very idea of taste [Kant] |
| 24170 | Kant thinks beauty ignores its objects, because it is only 'form' engaging with mind [Cochrane on Kant] |
| 22711 | The beautiful is not conceptualised as moral, but it symbolises or resembles goodness [Kant, by Murdoch] |
| 4025 | Kant saw beauty as a sort of disinterested pleasure, which has become separate from the good [Kant, by Taylor,C] |
| 20412 | Beauty is only judged in pure contemplation, and not with something else at stake [Kant] |
| 22046 | The mathematical sublime is immeasurable greatness; the dynamical sublime is overpowering [Kant, by Pinkard] |
| 21458 | The sublime is a moral experience [Kant, by Gardner] |
| 5643 | Aesthetic values are not objectively valid, but we must treat them as if they are [Kant, by Scruton] |
| 20410 | The judgement of beauty is not cognitive, but relates, via imagination, to pleasurable feelings [Kant] |