36 ideas
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
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] |
10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
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] |
10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
10416 | Can properties have parts? [Swoyer] |
10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
10406 | One might hope to reduce possible worlds to properties [Swoyer] |
10404 | Extreme empiricists can hardly explain anything [Swoyer] |
10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
10409 | Research suggests that concepts rely on typical examples [Swoyer] |
10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
10411 | Two properties can have one power, and one property can have two powers [Swoyer] |