52 ideas
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| 448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
| 447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| 1503 | There is no such thing as nothing [Parmenides] |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| 21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
| 452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
| 15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
| 15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
| 15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
| 15436 | Universals are meant to give an account of resemblance [Lewis] |
| 15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
| 15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
| 15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
| 15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
| 15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
| 15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
| 15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
| 15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
| 15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| 1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
| 444 | The first way of enquiry involves necessary existence [Parmenides] |
| 450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
| 451 | Thinking implies existence, because thinking depends on it [Parmenides] |
| 1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
| 3058 | Only reason can prove the truth of facts [Parmenides] |
| 15450 | Maybe abstraction is just mereological subtraction [Lewis] |
| 15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| 5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
| 1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
| 20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
| 226 | The one is without any kind of motion [Parmenides] |
| 1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
| 453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
| 1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
| 5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
| 13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
| 22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
| 1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |
| 1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |