30 ideas
| 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] |
| 16776 | Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus] |
| 7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
| 7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
| 7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
| 7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
| 7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
| 7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
| 7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
| 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] |
| 7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |