32 ideas
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [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] |
| 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] |
| 21833 | Research suggest that we overrate conscious experience [Flanagan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 23111 | If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick] |
| 21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
| 21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
| 21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
| 21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
| 23059 | Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray] |
| 4129 | It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick] |
| 20588 | Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf] |
| 21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
| 21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |