39 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] |
| 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 13047 | It is knowing 'why' that gives scientific understanding, not knowing 'that' [Salmon] |
| 13065 | Understanding is an extremely vague concept [Salmon] |
| 13054 | Correlations can provide predictions, but only causes can give explanations [Salmon] |
| 13067 | For the instrumentalists there are no scientific explanations [Salmon] |
| 13055 | Good induction needs 'total evidence' - the absence at the time of any undermining evidence [Salmon] |
| 13046 | Scientific explanation is not reducing the unfamiliar to the familiar [Salmon] |
| 13058 | Why-questions can seek evidence as well as explanation [Salmon] |
| 13050 | The 'inferential' conception is that all scientific explanations are arguments [Salmon] |
| 13059 | Ontic explanations can be facts, or reports of facts [Salmon] |
| 13064 | The three basic conceptions of scientific explanation are modal, epistemic, and ontic [Salmon] |
| 13049 | We must distinguish true laws because they (unlike accidental generalizations) explain things [Salmon] |
| 13051 | Deductive-nomological explanations will predict, and their predictions will explain [Salmon] |
| 13053 | A law is not enough for explanation - we need information about what makes a difference [Salmon] |
| 13061 | Flagpoles explain shadows, and not vice versa, because of temporal ordering [Salmon] |
| 13045 | Explanation at the quantum level will probably be by entirely new mechanisms [Salmon] |
| 13062 | Does an item have a function the first time it occurs? [Salmon] |
| 13063 | Explanations reveal the mechanisms which produce the facts [Salmon] |
| 13060 | Can events whose probabilities are low be explained? [Salmon] |
| 13056 | Statistical explanation needs relevance, not high probability [Salmon] |
| 13057 | Think of probabilities in terms of propensities rather than frequencies [Salmon] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |