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3 ideas
| 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! |
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| Full Idea: Logic (like geometry and arithmetic) applies only to fictitious entities that we have created. | |
| From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §516) | |
| A reaction: This finds Nietzsche on the relativist wing of logical empiricism. The thing is, fictitious entities can have a close relationship with truth, as in a great novel. I believe in necessary logical truth, but there are many ways of slicing it. |