38 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] |
15845 | It seems absurd that seeing a person's limbs, the one is many, and yet the many are one [Plato] |
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] |
9867 | It is absurd to define a circle, but not be able to recognise a real one [Plato] |
9865 | Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato] |
15857 | Any mixture which lacks measure and proportion doesn't even count as a mixture at all [Plato] |
14503 | If a mixture does not contain measure and proportion, it is corrupted and destroyed [Plato] |
4447 | If the good is one, is it unchanged when it is in particulars, and is it then separated from itself? [Plato] |
15856 | A thing can become one or many, depending on how we talk about it [Plato] |
374 | If one object is divided into its parts, someone can then say that one are many and many is one [Plato] |
389 | How can you be certain about aspects of the world if they aren't constant? [Plato] |
390 | If goodness involves moderation and proportion, then it seems to be found in beauty [Plato] |
391 | The good involves beauty, proportion and truth [Plato] |
392 | Neither intellect nor pleasure are the good, because they are not perfect and self-sufficient [Plato] |
393 | Good first, then beauty, then reason, then knowledge, then pleasure [Plato, by PG] |
385 | Some of the pleasures and pains we feel are false [Plato] |
387 | A small pure pleasure is much finer than a large one contaminated with pain [Plato] |
373 | Pleasure is certainly very pleasant, but it doesn't follow that all pleasures are good [Plato] |
379 | The good must be sufficient and perfect, and neither intellect nor pleasure are that [Plato] |
371 | Reason, memory, truth and wisdom are far better than pleasure, for those who can attain them [Plato] |
376 | Would you prefer a life of pleasure without reason, or one of reason without pleasure? [Plato] |
382 | It is unlikely that the gods feel either pleasure or pain [Plato] |
381 | We feel pleasure when we approach our natural state of harmony [Plato] |
386 | Intense pleasure and pain are not felt in a good body, but in a worthless one [Plato] |
388 | Hedonists must say that someone in pain is bad, even if they are virtuous [Plato] |
377 | If you lived a life of maximum pleasure, would you still be lacking anything? [Plato] |
378 | A life of pure pleasure with no intellect is the life of a jellyfish [Plato] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |