20 ideas
1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
21546 | We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell] |
13838 | A decent modern definition should always imply a semantics [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] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
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] |
21531 | Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell] |
21545 | I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell] |
3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |