display all the ideas for this combination of philosophers
5 ideas
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 15524 | Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis] |
| Full Idea: What sets Zermelo's modelling of arithmetic apart from von Neumann's and all the rest is that he identifies the primitive of arithmetic with an appropriately primitive notion of set theory. | |
| From: David Lewis (Parts of Classes [1991], 4.6) | |
| A reaction: Zermelo's model is just endlessly nested empty sets, which is a very simple structure. I gather that connoisseurs seem to prefer von Neumann's model (where each number contains its predecessor number). |
| 15517 | Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis] |
| Full Idea: Renouncing classes means rejecting mathematics. That will not do. Mathematics is an established, going concern. Philosophy is as shaky as can be. | |
| From: David Lewis (Parts of Classes [1991], 2.8) | |
| A reaction: This culminates in his famous 'Who's going to tell the mathematicians? Not me!'. He has just given four examples of mathematics that seems to entirely depend on classes. This idea sounds like G.E. Moore's common sense against scepticism. |
| 15515 | To be a structuralist, you quantify over relations [Lewis] |
| Full Idea: To be a structuralist, you quantify over relations. | |
| From: David Lewis (Parts of Classes [1991], 2.6) |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |