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. |
| 5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
| Full Idea: The soul, when it has partaken of intelligence and reason and concord, is not merely a work but also a part of god and has come to be not by his agency but both from him as source and out of his substance. | |
| From: Plutarch (67: Platonic Questions [c.85], II.1001) | |
| A reaction: A most intriguing shift of view from earlier concepts of the psuché. How did this come about? This man is a pagan. The history is in the evolution of Platonism. See 'The Middle Platonists' by John Dillon. Davidson is also very impressed by reason. |
| 4581 | Virtues and vices are like secondary qualities in perception, found in observers, not objects [Hume] |
| Full Idea: Vice and virtue may be compared to sounds, colours, heat and cold, which, according to modern philosophy, are not qualities in objects but perceptions in the mind. | |
| From: David Hume (Letters [1739], to Hutcheson 1740) | |
| A reaction: Very revealing about the origin of the is/ought idea, but this is an assertion rather than an argument. Most Greeks treat value as a primary quality of things (e.g. life, harmony, beauty, health). |
| 4580 | All virtues benefit either the public, or the individual who possesses them [Hume] |
| Full Idea: I desire you to consider if there be any quality that is virtuous, without having a tendency either to the public good or to the good of the person who possesses it. | |
| From: David Hume (Letters [1739], to Hutcheson 1739) | |
| A reaction: Obviously this is generally true. How, though, does it benefit the individual to secretly preserve their integrity? I go round to visit a friend to repay a debt; I am told they have died; I quietly leave some money on the table and leave. Why? |
| 4579 | The idea of a final cause is very uncertain and unphilosophical [Hume] |
| Full Idea: Your sense of 'natural' is founded on final causes, which is a consideration that appears to me pretty uncertain and unphilosophical. | |
| From: David Hume (Letters [1739], to Hutcheson 1739) | |
| A reaction: This is the rejection of Aristotelian teleology by modern science. I agree that the notion of utterly ultimate final cause is worse than 'uncertain' - it is an impossible concept. Nevertheless, I prefer Aristotle to Hume. Nature can teach us lessons. |
| 20705 | That events could be uncaused is absurd; I only say intuition and demonstration don't show this [Hume] |
| Full Idea: I never asserted so absurd a proposition as that anything might arise without a cause: I only maintained that our certainty of the falsehood of that proposition proceeded neither from intuition nor from demonstration, but from another source. | |
| From: David Hume (Letters [1739], 1754), quoted by Brian Davies - Introduction to the Philosophy of Religion 5 'God' | |
| A reaction: Since the other source is habit, he is being a bit disingenuous. While rational intuition and demonstration give a fairly secure basis for the universality of causation, mere human habits of expectation give very feeble grounds. |