6 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 22442 | If lies were ever acceptable, with would undermine all duties based on contract [Kant] |
| Full Idea: Truthfulness is a duty that must be regarded as the basis of all duties to be grounded on a contract, the law of which is made uncertain and useless if even the least exception to it is admitted. | |
| From: Immanuel Kant (On a supposed right to lie [1797], p.30) | |
| A reaction: Should we keep contracts which are made by means of deception and coercion? Where could such absolute authority for contracts come from? Do contracts and treaties tend to lapse after a long period of time? |
| 22441 | The law will protect you if you tell a truth which results in murder [Kant] |
| Full Idea: If you have by a lie prevented someone bent on murder from committing the deed, then you are legally accountable for all the consequences that might arise from it. But if you keep strictly to the truth, then public justice can hold nothing against you. | |
| From: Immanuel Kant (On a supposed right to lie [1797], p.29) | |
| A reaction: Shocking, from a supposedly great thinker. Cowardly hiding behind a perverse law. What would Kant do if the law were changed, to condemn someone who told a truth which would probably lead to a murder? Would he accept a jail sentence? |