3 ideas
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
| Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |
| From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |
| A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
| 15664 | Ideology is 'socially necessary illusion' or 'socially necessary false-consciousness' [Adorno, by Finlayson] |
| Full Idea: Adorno defines ideology as 'socially necessary illusion' or 'socially necessary false-consciousness' (and the young Habermas accepted something like this definition). | |
| From: report of Theodor W. Adorno (works [1955]) by James Gordon Finlayson - Habermas Ch.1:11 | |
| A reaction: The marxism seems to reside in the view that such things are always 'false'. If they gradually became 'true', would they cease to be ideology? Is it impossible for widespread beliefs to be 'true'? |