56 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
21382 | Things get smaller without end [Anaxagoras] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
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] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
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] |
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] |
5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
22673 | Wherever there is a small community, the association of the people is natural [Tocqueville] |
22676 | The people are just individuals, and only present themselves as united to foreigners [Tocqueville] |
22679 | Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville] |
22680 | People would be much happier and freer in small nations [Tocqueville] |
22675 | In American judges rule according to the Constitution, not the law [Tocqueville] |
22677 | A monarchical family is always deeply concerned with the interests of the state [Tocqueville] |
22683 | Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville] |
22669 | Aristocracy is constituted by inherited landed property [Tocqueville] |
22674 | In Europe it is thought that local government is best handled centrally [Tocqueville] |
22678 | An election, and its lead up time, are always a national crisis [Tocqueville] |
22682 | Universal suffrage is no guarantee of wise choices [Tocqueville] |
22670 | Slavery undermines the morals and energy of a society [Tocqueville] |
22681 | The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville] |
22672 | It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville] |
22671 | Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville] |
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] |
5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |
7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |