3 ideas
| 13190 | I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz] |
| Full Idea: Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions. | |
| From: Gottfried Leibniz (Letters to Samuel Masson [1716], 1716) | |
| A reaction: With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible. |
| 6215 | 'Contingent' means that the cause is unperceived, not that there is no cause [Hobbes] |
| Full Idea: For contingent, men do not mean that which hath no cause, but that which hath not for cause any thing that we perceive, as when a traveller meets a shower, they both had sufficient causes, but they didn't cause one another, so we say it was contingent. | |
| From: Thomas Hobbes (Of Liberty and Necessity [1654], §95) | |
| A reaction: Contingent nowadays means 'might not have happened', or 'does not happen in all possible worlds'. Personally I share Hobbes' doubts about the concept of contingency, and this is quite a good account of the misunderstanding. |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
| Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose. | |
| From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2 | |
| A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts. |