5 ideas
| 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. |
| 13197 | The notion of substance is one of the keys to true philosophy [Leibniz] |
| Full Idea: I consider the notion of substance to be one of the keys to the true philosophy. ....I imagine that philosophers will one day know the notion of substance a bit better than they do now. | |
| From: Gottfried Leibniz (Letters to Thomas Burnett [1703], 1699.01.20/30) | |
| A reaction: This is a controversial remark at this historical moment, when the apparent Aristotelian commitment to substances was becoming discredited. Personally I would eliminate substance, but not just because physicists don't refer to it. |
| 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 |
| 13198 | Gravity is within matter because of its structure, and it can be explained. [Leibniz] |
| Full Idea: I believe that both gravity and elasticity are in matter only because of the structure of the system and can be explained mechanically or through impulsion. | |
| From: Gottfried Leibniz (Letters to Thomas Burnett [1703], 1699 draft) | |
| A reaction: The significance of this remark is that gravity is held (in full knowledge of Newton's work) to be within matter, and not imposed from the outside. I believe we now postulate a particle as part of the explanation. |
| 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. |