59 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] |
21382 | Things get smaller without end [Anaxagoras] |
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] |
481 | Nothing is created or destroyed; there is only mixing and separation [Anaxagoras] |
21822 | Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus] |
17995 | Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras] |
20802 | Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero] |
13257 | The senses are too feeble to determine the truth [Anaxagoras] |
22761 | We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus] |
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] |
13256 | Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras] |
13784 | Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
22858 | There is collective action, where a trend is manifest, but is not attributable to individuals [Lukes] |
18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
22854 | Power is a capacity, which may never need to be exercised [Lukes] |
22850 | Hidden powers are the most effective [Lukes] |
22852 | The pluralist view says that power is restrained by group rivalry [Lukes] |
22855 | One-dimensionsal power is behaviour in observable conflicts of interests [Lukes] |
22856 | Political organisation brings some conflicts to the fore, and suppresses others [Lukes] |
22857 | The two-dimensional view of power recognises the importance of controlling the agenda [Lukes] |
22859 | Power can be exercised to determine a person's desires [Lukes] |
22863 | Power is the capacity of a social class to realise its interests [Lukes] |
22860 | The evidence for the exertion of power need not involve a grievance of the powerless [Lukes] |
22861 | Power is affecting a person in a way contrary to their interests [Lukes] |
21133 | Supreme power is getting people to have thoughts and desires chosen by you [Lukes] |
22851 | In the 1950s they said ideology is finished, and expertise takes over [Lukes] |
22862 | Liberals take people as they are, and take their preferences to be their interests [Lukes] |
22853 | Anyone who thinks capitalism can improve their lives is endorsing capitalism [Lukes] |
631 | For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle] |
22727 | Mind creates the world from a mixture of pure substances [Anaxagoras, by ] |
550 | Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle] |
21383 | The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos] |
13208 | Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle] |
367 | Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato] |
21381 | Germs contain microscopic organs, which become visible as they grow [Anaxagoras] |
22726 | When things were unified, Mind set them in order [Anaxagoras] |
2629 | Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero] |
480 | Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras] |
7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |
5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |