44 ideas
| 15169 | Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle] |
| 15164 | We seem to base necessities on thought experiments and imagination [Sidelle] |
| 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] |
| 15180 | There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle] |
| 15184 | Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle] |
| 15172 | Clearly, essential predications express necessary properties [Sidelle] |
| 15181 | Being a deepest explanatory feature is an actual, not a modal property [Sidelle] |
| 15173 | That the essence of water is its microstructure is a convention, not a discovery [Sidelle] |
| 15185 | We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle] |
| 15175 | Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 15032 | Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider] |
| 15179 | To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle] |
| 15171 | The necessary a posteriori is statements either of identity or of essence [Sidelle] |
| 15167 | Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle] |
| 15177 | Contradictoriness limits what is possible and what is imaginable [Sidelle] |
| 15176 | The individuals and kinds involved in modality are also a matter of convention [Sidelle] |
| 15174 | A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle] |
| 15183 | 'Dthat' operates to make a singular term into a rigid term [Sidelle] |
| 15165 | A priori knowledge is entirely of analytic truths [Sidelle] |
| 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] |
| 15168 | That water is essentially H2O in some way concerns how we use 'water' [Sidelle] |
| 15166 | Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle] |
| 15182 | Because some entities overlap, reference must have analytic individuation principles [Sidelle] |
| 15178 | Can anything in science reveal the necessity of what it discovers? [Sidelle] |