27 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
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] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
6456 | Sense-data are neutral uninterpreted experiences, separated from objects and judgements [Angeles] |
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] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |