28 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
11064 | Classes can be reduced to propositional functions [Russell, by Hanna] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
6407 | The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling] |
10418 | Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell] |
10047 | Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave] |
23478 | Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell] |
21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
18126 | A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock] |
18128 | Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock] |
18124 | Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock] |
5953 | For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch] |
3023 | Even the foolish may have some virtues [Aristippus young, by Diog. Laertius] |
3026 | Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius] |
3024 | Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius] |
3025 | For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius] |
3019 | No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius] |
3021 | The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius] |
3027 | Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius] |