33 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
23853 | Truth is not a object we love - it is the radiant manifestation of reality [Weil] |
18469 | God might necessitate that something happen, but He is not the truth-maker for it [Smith,B] |
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] |
23855 | Creation produced a network or web of determinations [Weil] |
23848 | The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil] |
23854 | Beauty is the proof of what is good [Weil] |
23837 | Respect is our only obligation, which can only be expressed through deeds, not words [Weil] |
23844 | The most important human need is to have multiple roots [Weil] |
23838 | The need for order stands above all others, and is understood via the other needs [Weil] |
23836 | Obligations only bind individuals, not collectives [Weil] |
23840 | A citizen should be able to understand the whole of society [Weil] |
23843 | Even the poorest should feel collective ownership, and participation in grand display [Weil] |
23846 | Culture is an instrument for creating an ongoing succession of teachers [Weil] |
23839 | A lifelong head of society should only be a symbol, not a ruler [Weil] |
23842 | Party politics in a democracy can't avoid an anti-democratic party [Weil] |
23847 | Socialism tends to make a proletariat of the whole population [Weil] |
23845 | The capitalists neglect the people and the nation, and even their own interests [Weil] |
23841 | By making money the sole human measure, inequality has become universal [Weil] |
23835 | People have duties, and only have rights because of the obligations of others to them [Weil] |
23852 | To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil] |
23850 | The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil] |
23851 | Education is essentially motivation [Weil] |
23849 | Religion should quietly suffuse all human life with its light [Weil] |