display all the ideas for this combination of philosophers
3 ideas
| 16949 | Klein summarised geometry as grouped together by transformations [Quine] |
| Full Idea: Felix Klein's so-called 'Erlangerprogramm' in geometry involved characterizing the various branches of geometry by what transformations were irrelevant to each. | |
| From: Willard Quine (Natural Kinds [1969], p.137) |
| 8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine] |
| Full Idea: Geometry can be brought into line with logicism simply by identifying figures with arithmetical relations with which they are correlated thought analytic geometry. | |
| From: Willard Quine (Truth by Convention [1935], p.87) | |
| A reaction: Geometry was effectively reduced to arithmetic by Descartes and Fermat, so this seems right. You wonder, though, whether something isn't missing if you treat geometry as a set of equations. There is more on the screen than what's in the software. |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| Full Idea: The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition. | |
| From: Willard Quine (Word and Object [1960], §54) | |
| A reaction: [compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant. |