41 ideas
3123 | Science is in the business of carving nature at the joints [Segal] |
3125 | Psychology studies the way rationality links desires and beliefs to causality [Segal] |
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] |
3105 | Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal] |
3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
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] |
3113 | The success and virtue of an explanation do not guarantee its truth [Segal] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
3112 | Folk psychology is ridiculously dualist in its assumptions [Segal] |
3108 | If 'water' has narrow content, it refers to both H2O and XYZ [Segal] |
3110 | Humans are made of H2O, so 'twins' aren't actually feasible [Segal] |
3124 | Externalists can't assume old words refer to modern natural kinds [Segal] |
3117 | Concepts can survive a big change in extension [Segal] |
3104 | Must we relate to some diamonds to understand them? [Segal] |
3103 | Maybe content involves relations to a language community [Segal] |
3111 | Externalism can't explain concepts that have no reference [Segal] |
3109 | If content is external, so are beliefs and desires [Segal] |
3116 | Maybe experts fix content, not ordinary users [Segal] |
3121 | If content is narrow, my perfect twin shares my concepts [Segal] |
3118 | If thoughts ARE causal, we can't explain how they cause things [Segal] |
3119 | Even 'mass' cannot be defined in causal terms [Segal] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |