36 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] |
| 362 | The greatest misfortune for a person is to develop a dislike for argument [Plato] |
| 13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
| 13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
| 13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
| 13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
| 13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
| 13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
| 13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
| 13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
| 13029 | Set Existence: ∃x (x = x) [Kunen] |
| 13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
| 13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 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] |
| 1 | There is only one source for all beauty [Plato] |
| 368 | Other things are named after the Forms because they participate in them [Plato] |
| 16516 | The ship which Theseus took to Crete is now sent to Delos crowned with flowers [Plato] |
| 359 | If we feel the inadequacy of a resemblance, we must recollect the original [Plato] |
| 357 | People are obviously recollecting when they react to a geometrical diagram [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] |
| 361 | It is a mistake to think that the most violent pleasure or pain is therefore the truest reality [Plato] |
| 6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
| 6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
| 6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
| 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] |
| 5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |