49 ideas
1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
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] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
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] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
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] |
19673 | Galileo mathematised movement, and revealed its invariable component - acceleration [Galileo, by Meillassoux] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |
1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |