21 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] |
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] |
8122 | True works of art transmit completely new feelings [Tolstoy] |
8121 | Art is when one man uses external signs to hand on his feelings to another man [Tolstoy] |
8124 | The highest feelings of mankind can only be transmitted by art [Tolstoy] |
8123 | The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy] |
22710 | People estimate art according to their moral values [Tolstoy] |
8125 | The upper classes put beauty first, and thus freed themselves from morality [Tolstoy] |
8064 | We separate the concept of beauty from goodness, unlike the ancients [Tolstoy] |
7346 | Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P] |
22920 | Do I not fill heaven and earth? saith the Lord [Jeremiah] |
22089 | Am I a God afar off, and not a God close at hand? [Jeremiah] |