46 ideas
354 | Wisdom makes virtue and true goodness possible [Plato] |
370 | Philosophy is a purification of the soul ready for the afterlife [Plato] |
350 | In investigation the body leads us astray, but the soul gets a clear view of the facts [Plato] |
24226 | The soul on its own enters a pure, unchanging and eternal realm, and experiences wisdom [Plato] |
362 | The greatest misfortune for a person is to develop a dislike for argument [Plato] |
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
21347 | If Simmias is taller than Socrates, that isn't a feature that is just in Simmias [Plato] |
360 | We must have a prior knowledge of equality, if we see 'equal' things and realise they fall short of it [Plato] |
24230 | The Forms arise whenever we talk of something 'in itself'. [Plato] |
24225 | Things like the Equal and the Beautiful, which are real, must be unchanging [Plato] |
24227 | One and one can only become two by sharing in Twoness [Plato] |
368 | Other things are named after the Forms because they participate in them [Plato] |
1 | There is only one source for all beauty [Plato] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
16516 | The ship which Theseus took to Crete is now sent to Delos crowned with flowers [Plato] |
490 | Everything happens by reason and necessity [Leucippus] |
357 | People are obviously recollecting when they react to a geometrical diagram [Plato] |
359 | If we feel the inadequacy of a resemblance, we must recollect the original [Plato] |
9343 | To achieve pure knowledge, we must get rid of the body and contemplate things with the soul [Plato] |
15859 | To investigate the causes of things, study what is best for them [Plato] |
13154 | Do we think and experience with blood, air or fire, or could it be our brain? [Plato] |
364 | One soul can't be more or less of a soul than another [Plato] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
361 | It is a mistake to think that the most violent pleasure or pain is therefore the truest reality [Plato] |
351 | War aims at the acquisition of wealth, because we are enslaved to the body [Plato] |
13156 | Fancy being unable to distinguish a cause from its necessary background conditions! [Plato] |
369 | If the Earth is spherical and in the centre, it is kept in place by universal symmetry, not by force [Plato] |
363 | Whether the soul pre-exists our body depends on whether it contains the ultimate standard of reality [Plato] |