34 ideas
| 17070 | Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart] |
| 17072 | We need comprehensiveness, as well as self-coherence [Smart] |
| 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] |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| 17073 | I simply reject evidence, if it is totally contrary to my web of belief [Smart] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17077 | The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart] |
| 17078 | Universe expansion explains the red shift, but not vice versa [Smart] |
| 17061 | Explanation of a fact is fitting it into a system of beliefs [Smart] |
| 17074 | Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart] |
| 17076 | Deducing from laws is one possible way to achieve a coherent explanation [Smart] |
| 17071 | An explanation is better if it also explains phenomena from a different field [Smart] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17062 | If scientific explanation is causal, that rules out mathematical explanation [Smart] |
| 17075 | Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart] |
| 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] |
| 17063 | Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart] |