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. |
| 22297 | Dummett saw realism as acceptance of bivalence, rather than of mind-independent entities [Dummett, by Potter] |
| Full Idea: Dummett aimed to characterise realism in terms not of the mind-independence of the entities but of the validity of bivalence for sentences referring to them. | |
| From: report of Michael Dummett (Realism [1982]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 21 'Lang' | |
| A reaction: Hence he called himself a 'philosopher of language', rather than a 'philosopher of thought'. Philosophers of language are more likely to end up as anti-realists, I suspect. |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |