26 ideas
10365 | We might use 'facta' to refer to the truth-makers for facts [Mellor, by Schaffer,J] |
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] |
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] |
8568 | A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor] |
8564 | There is obviously a possible predicate for every property [Mellor] |
8566 | We need universals for causation and laws of nature; the latter give them their identity [Mellor] |
8565 | If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor] |
5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
5833 | Education is the greatest of human goods [Xenophon] |
4785 | Causal statements relate facts (which are whatever true propositions express) [Mellor, by Psillos] |
8567 | Singular causation requires causes to raise the physical probability of their effects [Mellor] |
8408 | Probabilistic causation says C is a cause of E if it increases the chances of E occurring [Mellor, by Tooley] |