5 ideas
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 12694 | Essence is the distinct thinkability of anything [Leibniz] |
| Full Idea: (Essence) is the distinct thinkability (cogitabilitas) of anything. | |
| From: Gottfried Leibniz (Notes on John Wilkins [1672], A6.2.487-8), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1 | |
| A reaction: A very original remark from the young Leibniz. It is neutral as to whether this is a real feature of objects, or a feature of human mental capacities. Presumably accidental features are thinkable, so 'distinct' is the key word. |
| 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. |