51 ideas
192 | Only one thing can be contrary to something [Plato] |
4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
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] |
15754 | Without properties we would be unable to express the laws of nature [Armstrong] |
4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
8531 | In most sets there is no property common to all the members [Armstrong] |
15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
20184 | The only real evil is loss of knowledge [Plato] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
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] |
191 | Everything resembles everything else up to a point [Plato] |
8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
188 | Socrates did not believe that virtue could be taught [Plato] |
8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |
8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |