36 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| 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] |
| 6685 | 'Subjectivism' is an extension of relativism from the social group to the individual [Graham] |
| 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] |
| 6699 | The chain of consequences may not be the same as the chain of responsibility [Graham] |
| 6698 | Negative consequences are very hard (and possibly impossible) to assess [Graham] |
| 6700 | We can't criticise people because of unforeseeable consequences [Graham] |
| 6704 | Egoism submits to desires, but cannot help form them [Graham] |
| 6701 | Rescue operations need spontaneous benevolence, not careful thought [Graham] |
| 6693 | 'What if everybody did that?' rather misses the point as an objection to cheating [Graham] |
| 6691 | It is more plausible to say people can choose between values, than that they can create them [Graham] |
| 6688 | Life is only absurd if you expected an explanation and none turns up [Graham] |
| 6705 | Existentialism may transcend our nature, unlike eudaimonism [Graham] |
| 6690 | A standard problem for existentialism is the 'sincere Nazi' [Graham] |
| 6689 | The key to existentialism: the way you make choices is more important than what you choose [Graham] |
| 6706 | The great religions are much more concerned with the religious life than with ethics [Graham] |
| 6709 | Western religion saves us from death; Eastern religion saves us from immortality [Graham] |