51 ideas
| 7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
| 1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 449 | Being is not divisible, since it is all alike [Parmenides] |
| 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] |
| 445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
| 1503 | There is no such thing as nothing [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] |
| 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] |
| 7906 | When the Buddha reached the highest level of insight, he could detect no self in the world [Ashvaghosha] |
| 555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
| 226 | The one is without any kind of motion [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] |
| 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] |
| 7904 | The first stage of trance is calm amidst applied and discursive thinking [Ashvaghosha] |
| 7905 | The Buddha sought ultimate reality and the final goal of existence in his meditations [Ashvaghosha] |
| 7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
| 7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |