27 ideas
| 291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
| 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] |
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| 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] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [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] |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| 293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |