31 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] |
| 13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
| 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] |
| 8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
| 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] |
| 17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
| 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] |
| 16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
| 9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
| 16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| 8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
| 8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
| 8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
| 8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
| 3115 | Are meaning and expressed concept the same thing? [Burge, by Segal] |
| 14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |