30 ideas
4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
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] |
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] |
9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
11181 | Aristotelian essentialism involves a 'natural' or 'causal' interpretation of modal operators [Marcus (Barcan)] |
11184 | Aristotelian essentialism is about shared properties, individuating essentialism about distinctive properties [Marcus (Barcan)] |
11180 | Essentialist sentences are not theorems of modal logic, and can even be false [Marcus (Barcan)] |
11186 | 'Essentially' won't replace 'necessarily' for vacuous properties like snub-nosed or self-identical [Marcus (Barcan)] |
11185 | 'Is essentially' has a different meaning from 'is necessarily', as they often cannot be substituted [Marcus (Barcan)] |
11182 | If essences are objects with only essential properties, they are elusive in possible worlds [Marcus (Barcan)] |
4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
11183 | The use of possible worlds is to sort properties (not to individuate objects) [Marcus (Barcan)] |
11187 | In possible worlds, names are just neutral unvarying pegs for truths and predicates [Marcus (Barcan)] |
4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
11189 | Dispositional essences are special, as if an object loses them they cease to exist [Marcus (Barcan)] |