21 ideas
4424 | A warlike philosopher challenges problems to single combat [Nietzsche] |
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] |
12427 | All of mathematics is properties of the whole numbers [Kronecker] |
10091 | God made the integers, all the rest is the work of man [Kronecker] |
2886 | The distinction between egoistic and non-egoistic acts is absurd [Nietzsche] |
4426 | A bad result distorts one's judgement about the virtue of what one has done [Nietzsche] |
4425 | The overcoming of pity I count among the noble virtues [Nietzsche] |
20132 | To become what you are you must have no self-awareness [Nietzsche] |
20144 | Eternal recurrence is the highest attainable affirmation [Nietzsche] |
2889 | One repays a teacher badly if one remains only a pupil [Nietzsche] |
2887 | I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche] |