36 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] |
| 15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
| 15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
| 15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
| 15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
| 15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
| 15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
| 15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
| 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] |
| 15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
| 15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
| 15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
| 15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
| 15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
| 15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
| 15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
| 15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
| 15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
| 15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
| 15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |