5 ideas
| 14799 | Metaphysics rests on observations, but ones so common we hardly notice them [Peirce] |
| Full Idea: Metaphysics really rests on observations, whether consciously or not. The only reason this is not recognised is that it rests upon kinds of phenomena with which every man's experience is so saturated that he pays no particular attention to them. | |
| From: Charles Sanders Peirce (The Approach to Metaphysics [1898], p.311) | |
| A reaction: I think this is entirely right. I would say that the only thing that distinguishes metaphysical thought is its extreme level of generality, which makes it very hard to substantiate, because it is so remote from its evidential base. |
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
| From: Paul Bernays (On Platonism in Mathematics [1934]) |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
| A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
| From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
| A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
| 7294 | No crime and no punishment without a law [Roman law] |
| Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law. | |
| From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws? |