8 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
| Full Idea: Events are not basic items in the universe; they should not be included in any fundamental ontology...all the truths about them are entailed by and explained and made true by truths that do not involve the event concept. | |
| From: Jonathan Bennett (Events and Their Names [1988], p.12), quoted by Peter Simons - Events 3.1 | |
| A reaction: Given the variable time spans of events, their ability to coincide, their ability to contain no motion, their blatantly conventional component, and their recalcitrance to individuation, I say Bennett is right. |
| 8063 | Baumgarten founded aesthetics in 1750 [Baumgarten, by Tolstoy] |
| Full Idea: Baumgarten founded aesthetics in the year 1750. | |
| From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.2 | |
| A reaction: He gave it a label, separated it off from the rest of philosophy, and made taste the main focus. The philosophy of art goes back to at least Plato's 'Republic' and 'Symposium'. |
| 8118 | Beauty is an order between parts, and in relation to the whole [Baumgarten, by Tolstoy] |
| Full Idea: Beauty is defined by Baumgarten as a correspondence, that is, an order of parts in their mutual relations to each other and in their relation to the whole. | |
| From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.3 | |
| A reaction: This may be one aspect of what is beautiful, but rather more than a nice arrangement is probably needed for art. We must distinguish flower arranging from poetic drama. Some masterpieces are rather messily arranged. |
| 8117 | Perfection comes through the senses (Beauty), through reason (Truth), and through moral will (Good) [Baumgarten, by Tolstoy] |
| Full Idea: For Baumgarten, Beauty is the Perfect (the Absolute), recognised through the senses; Truth is the Perfect perceived through reason; Goodness is the Perfect reached by moral will. | |
| From: report of Alexander Baumgarten (Aesthetica [1739]) by Leo Tolstoy - What is Art? Ch.3 | |
| A reaction: At last, after many years of searching, I have found the origin of that great trio of ideals: Beauty, Goodness and Truth. Tolstoy sneers at them, but a person could do a lot worse than spending their lives trying to promote them. |
| 10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
| Full Idea: Facts are not the sort of item that can cause anything. A fact is a true proposition (they say); it is not something in the world but is rather something about the world. | |
| From: Jonathan Bennett (Events and Their Names [1988], p.22), quoted by Jonathan Schaffer - The Metaphysics of Causation 1.1 | |
| A reaction: Compare 10361. Good argument, but maybe 'fact' is ambiguous. See Idea 10365. Events are said to be more concrete, and so can do the job, but their individuation also seems to depend on a description (as Davidson has pointed out). |