7 ideas
| 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. |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |
| 15677 | Moral right is linked to validity and truth, so morality is a matter of knowledge, not an expression of values [Habermas, by Finlayson] |
| Full Idea: According to discourse ethics moral rightness is internally linked to validity and is analogous to truth: ..thus Habermas takes himself to have shown that morality is a matter of knowledge, rather than the expression of contingently held values. | |
| From: report of Jürgen Habermas (Moral Consciousness and Communicative Action [1990]) by James Gordon Finlayson - Habermas Ch.7:102 | |
| A reaction: I can immediately hear Nietzsche asking why you place such a high value on knowledge. Personally I don't assume that values must be 'contingent'. The Aristotelian tradition sees necessary values in facts about human nature. |
| 15671 | Move from individual willing of a general law, to willing norms agreed with other people [Habermas] |
| Full Idea: The emphasis shifts from what each can will without contradiction to be a general law, to what all can will in agreement to be a universal norm. | |
| From: Jürgen Habermas (Moral Consciousness and Communicative Action [1990], p.67), quoted by James Gordon Finlayson - Habermas Ch.5:69 | |
| A reaction: This strikes me as being very close to Scanlon's contractualism. As expressed here, it sounds more vulnerable than Kant's full universality to the problem of Nazis agreeing odious universal norms. Habermas calls it 'discourse ethics'. |