37 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| 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] |