4 ideas
| 17992 | The main aim of philosophy is to describe the whole Universe. [Moore,GE] |
| Full Idea: It seems to me that the most important and interesting thing which philosophers have tried to do ...is to give a general description of the whole of the Universe. | |
| From: G.E. Moore (Some Main Problems of Philosophy [1911], Ch. 1) | |
| A reaction: He adds that they aim to show what is in it, and what might be in it, and how the two relate. This sort of big view is the one I favour. I think the hallmark of philosophical thought is a high level of generality. He next proceeds to defend common sense. |
| 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. |
| 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. |