36 ideas
| 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] |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| 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] |
| 4871 | A thing is free if it acts only by the necessity of its own nature [Spinoza] |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |