38 ideas
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
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] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
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] |
1212 | Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch] |
5958 | The sun is always bright; it doesn't become bright when it emerges [Plutarch] |
5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
5959 | Some philosophers say the soul is light [Plutarch] |
5952 | Rather than being the whole soul, maybe I am its chief part? [Plutarch] |
5951 | If atoms have no qualities, they cannot possibly produce a mind [Plutarch] |
5963 | Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
20796 | Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch] |
1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
5948 | The good life involves social participation, loyalty, temperance and honesty [Plutarch] |
1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |
5950 | If only atoms exist, how do qualities arise when the atoms come together? [Plutarch] |
5974 | People report seeing through rocks, or over the horizon, or impossibly small works [Plutarch] |
5957 | Absurd superstitions make people atheist, not disharmony in nature [Plutarch] |
5955 | No one will ever find a city that lacks religious practices [Plutarch] |