6 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 15538 | Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis] |
| Full Idea: Semantic indecision will suffice to explain the phenomenon of vagueness. [note] Provided that there exist the many precisifications for us to be undecided between. If you deny this, you will indeed have need of vague objects. | |
| From: David Lewis (Many, but almost one [1993], 'Two solutions') | |
| A reaction: [He mentions Van Inwagen 1990:213-83] There seem to be three solutions to vague objects: that they really are vague, that they are precise but we can't know precisely, or Lewis's view. I like Lewis's view. Do animals have any problem with vagueness? |
| 15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
| Full Idea: Boethius argued that universals can be successfully isolated by abstraction, even if they do not exist as separate entities in the world. | |
| From: report of Boethius (Second Commentary on 'Isagoge' [c.517]) by Claude Panaccio - Medieval Problem of Universals 'Sources' | |
| A reaction: Personally I rather like this unfashionable view. I can't think of any other plausible explanation, unless it is a less conscious psychological process of labelling. Boethius's idea led to medieval 'immanent realism'. |
| 15537 | If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis] |
| Full Idea: To deny that there are many cats on the mat (because removal of a few hairs seems to produce a new one), we must either deny that the many are cats, or else deny that the cats are many. ...I think both alternatives lead to successful solutions. | |
| From: David Lewis (Many, but almost one [1993], 'The paradox') | |
| A reaction: He credits the problem to Geach (and Tibbles), and says it is the same as Unger's 'problem of the many' (Idea 15536). |
| 15536 | We have one cloud, but many possible boundaries and aggregates for it [Lewis] |
| Full Idea: Many surfaces are equally good candidates to be boundaries of a cloud; therefore many aggregates of droplets are equally good candidates to be the cloud. How is it that we have just one cloud? And yet we do. This is Unger's (1980) 'problem of the many'. | |
| From: David Lewis (Many, but almost one [1993], 'The problem') | |
| A reaction: This is the problem of vague objects, as opposed to the problem of vague predicates, or the problem of vague truths, or the problem of vague prepositions (like 'towards'). |
| 15539 | Basic to pragmatics is taking a message in a way that makes sense of it [Lewis] |
| Full Idea: The cardinal principle of pragmatics is that the right way to take what is said, if at all possible, is the way that makes sense of the message. | |
| From: David Lewis (Many, but almost one [1993], 'A better solution') | |
| A reaction: Thus when someone misuses a word, suggesting nonsense, we gloss over it, often without even mentioning it, because the underlying sense is obvious. A good argument for the existence of propositions. Lewis doesn't mention truth. |