33 ideas
| 9307 | Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen] |
| 9297 | You can't understand love in terms of 'if and only if...' [Svendsen] |
| 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] |
| 9308 | If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen] |
| 20769 | Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius] |
| 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] |
| 9309 | Emotions have intentional objects, while a mood is objectless [Svendsen] |
| 9304 | Death appears to be more frightening the less one has lived [Svendsen] |
| 9298 | We can be unaware that we are bored [Svendsen] |
| 9301 | Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen] |
| 9302 | We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen] |
| 9310 | The profoundest boredom is boredom with boredom [Svendsen] |
| 9311 | We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen] |
| 9303 | The concept of 'alienation' seems no longer applicable [Svendsen] |