3 ideas
| 14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
| Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities. | |
| From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
| A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world. |
| 10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |
| Full Idea: Mathematics has got rid of possibility by simply assuming that, up to isomorphism anyway, all possibilities are simultaneous actual - actual, that is, in the universe of 'sets'. | |
| From: Hilary Putnam (What is Mathematical Truth? [1975], p.70), quoted by Stewart Shapiro - Philosophy of Mathematics 7.5 |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |
| Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does. | |
| From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1 | |
| A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox. |