8 ideas
15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects. | |
From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite |
23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
Full Idea: It is by the natural light that the axioms of mathematics are recognised. If we take away the same quantity from two equal things, …a thing we can easily predict without having experienced it. | |
From: Gottfried Leibniz (Letters to Queen Charlotte [1702], p.189) | |
A reaction: He also says two equal weights will keep a balance level. Plato thinks his slave boy understands halving an area by the natural light, but that is just as likely to be experience. It is too easy to attribut thoughts to a 'natural light'. |
13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
Full Idea: That which is necessary for something does not constitute its essence. Air is necessary for our life, but our life is something other than air. | |
From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
A reaction: Bravo. Why can't modern philosophers hang on to this distinction? They seem to think that because they don't believe in traditional essences they can purloin the word for something else. Same with the word 'abstraction'. |
19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
Full Idea: Intelligible truth is independent of the truth or of the existence outside us of sensible and material things. ....It is generally true that we only know necessary truths by the natural light [of reason] | |
From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
A reaction: A nice quotation summarising a view for which Leibniz is famous - that there is a tight correlation between necessary truths and our a priori knowledge of them. The obvious challenge comes from Kripke's claim that scientists can discover necessities. |
19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
Full Idea: We use the external senses ...to make us know their particular objects ...but they do not make us know what those sensible qualities are ...whether red is small revolving globules causing light, heat a whirling of dust, or sound is waves in air. | |
From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
A reaction: These seems to be exactly the concept of secondary qualities which Locke was promoting. They are unreliable information about the objects we perceive. Primary qualities are reliable information. I like that distinction. |
19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
Full Idea: It can be said that there is nothing in the understanding which does not come from the senses, except the understanding itself, or that which understands. | |
From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
A reaction: Given that Leibniz is labelled as a 'rationalist', this is awfully close to empiricism. Not Locke's 'tabula rasa' perhaps, but Hume's experiences plus associations. Leibniz has a much loftier notion of understanding and reason than Hume does. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |