39 ideas
7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
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] |
7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
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] |
10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
10771 | Compactness is important for major theories which have infinitely many axioms [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] |
7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
7692 | Being is maximal consistency [Jacquette] |
7687 | Existence is completeness and consistency [Jacquette] |
7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |