46 ideas
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
15891 | Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
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] |
15874 | Scientific properties are not observed qualities, but the dispositions which create them [Harré] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
15884 | Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré] |
15880 | In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré] |
15869 | Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré] |
15881 | We can save laws from counter-instances by treating the latter as analytic definitions [Harré] |
15882 | Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré] |
15887 | 'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré] |
15888 | The grue problem shows that natural kinds are central to science [Harré] |
15889 | It is because ravens are birds that their species and their colour might be connected [Harré] |
15890 | Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré] |
15885 | The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré] |
15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
15886 | Science rests on the principle that nature is a hierarchy of natural kinds [Harré] |
15864 | Classification is just as important as laws in natural science [Harré] |
15865 | Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré] |
15862 | Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré] |
15870 | Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré] |
15871 | Are laws about what has or might happen, or do they also cover all the possibilities? [Harré] |
15876 | Maybe laws of nature are just relations between properties? [Harré] |
15860 | We take it that only necessary happenings could be laws [Harré] |
15872 | Must laws of nature be universal, or could they be local? [Harré] |
15867 | Laws describe abstract idealisations, not the actual mess of nature [Harré] |
15892 | Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré] |
15875 | In counterfactuals we keep substances constant, and imagine new situations for them [Harré] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |