36 ideas
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 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] |
| 13064 | The three basic conceptions of scientific explanation are modal, epistemic, and ontic [Salmon] |
| 13050 | The 'inferential' conception is that all scientific explanations are arguments [Salmon] |
| 13059 | Ontic explanations can be facts, or reports of facts [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] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |