8 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. |
| 4692 | It is not true that killing and allowing to die (or acts and omissions) are morally indistinguishable [Foot] |
| Full Idea: Many philosophers (e.g. Rachels) have argued that there is no morally relevant distinction between killing and allowing to die (or the related 'acts and omissions'),..as in not sending food, or sending poisoned food. I disagree. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.78) | |
| A reaction: It appears that some omissions are worse than acts. It is more honest to just shoot an injured person, than to walk away and leave them to die. A range of cases. |
| 4694 | Making a runaway tram kill one person instead of five is diverting a fatal sequence, not initiating one [Foot] |
| Full Idea: If a runaway tram is heading towards a track on which five people are standing, and there is someone who can switch the points, diverting it onto a track where there is one person,...this is diverting a fatal sequence, not starting a new one. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.85) | |
| A reaction: Suppose the one person was of immense community value, or someone you personally hated? Clearly she is interested in the agent's virtue, rather than the actual consequences. |
| 4693 | The right of non-interference (with a 'negative duty'), and the right to goods/services ('positive') [Foot] |
| Full Idea: There are rights to non-interference (and their corresponding "negative duties"), and the rights to goods and services (with corresponding "positive duties"). Interference usually needs more justification than withholding goods. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.82) | |
| A reaction: This invites the question of which is the stronger, and whether paternalism can overrule non-interference, or an expectation of self-sufficiency overrule the positive rights. |
| 9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
| Full Idea: God is not wise, but more-than-wise; God is not good, but more-than-good. | |
| From: William of Ockham (Reportatio [1330], III Q viii) | |
| A reaction: [He is quoting 'Damascene'] I quote this for interest, but I very much doubt whether Damascene or William knew what it meant, and I certainly don't. There seems to have been a politically correct desire to invent super-powers for God. |
| 9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
| Full Idea: What we abstract is said to belong to perfection in so far as it can be predicated of God and can stand for Him. For if such a concept could not be abstracted from a creature, then in this life we could not arrive at a cognition of God's wisdom. | |
| From: William of Ockham (Reportatio [1330], III Q viii) | |
| A reaction: This seems to be the germ of an important argument. Without the ability to abstract from what is experienced, we would not be able to apply general concepts to things which are beyond experience. It is a key idea for empiricism. |