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3 ideas
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled. | |
From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08 | |
A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them. |
457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed. | |
From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f | |
A reaction: also Aristotle 314b08 |