8 ideas
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| Full Idea: Metaphysics is the most general attempt to make sense of things. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
| A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 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? |
| 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'). |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
| 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. |