35 ideas
| 12772 | Philosophy is a value- and attitude-driven enterprise [Fraassen] |
| 12771 | Is it likely that a successful, coherent, explanatory ontological hypothesis is true? [Fraassen] |
| 12773 | Analytic philosophy has an exceptional arsenal of critical tools [Fraassen] |
| 12770 | We may end up with a huge theory of carefully constructed falsehoods [Fraassen] |
| 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] |
| 13230 | Particular essence is often captured by generality [Steiner,M] |
| 14919 | Empiricists deny what is unobservable, and reject objective modality [Fraassen] |
| 6783 | To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird] |
| 14917 | To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 13229 | Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M] |
| 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] |
| 13231 | Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M] |
| 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] |
| 6784 | Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird] |
| 12769 | Inference to best explanation contains all sorts of hidden values [Fraassen] |
| 13066 | An explanation is just descriptive information answering a particular question [Fraassen, by Salmon] |
| 12768 | We accept many scientific theories without endorsing them as true [Fraassen] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |