32 ideas
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] |
16235 | Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley] |
14753 | The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider] |
16072 | 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman] |
14751 | Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider] |
16071 | Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman] |
16234 | Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley] |
13278 | Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki] |
14750 | Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider] |
21227 | The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol] |
21215 | The representation may not be a likeness [Velarde-Mayol] |
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] |
21219 | Find the essence by varying an object, to see what remains invariable [Velarde-Mayol] |