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. |
23218 | The brain has no responsibility for sensations, which occur in the heart [Aristotle] |
Full Idea: And of course, the brain is not responsible for any of the sensations at all. The correct view is that the seat and source of sensation is the region of the heart. | |
From: Aristotle (The Parts of Animals [c.345 BCE]), quoted by Matthew Cobb - The Idea of the Brain 1 | |
A reaction: [Need a reference] Hippocrates's assertion a century earlier made no impression on the great man. I wish he had been a little more circumspect with his own view. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |