34 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] |
| 8508 | A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC] |
| 8509 | A world is completely constituted by its tropes and their connections [Williams,DC] |
| 8510 | 'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC] |
| 12184 | Logical necessity overrules all other necessities [McFetridge] |
| 15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
| 15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
| 12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
| 12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
| 12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
| 12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
| 12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
| 12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
| 12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
| 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] |