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. |
21227 | The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol] |
Full Idea: All philosophies inspired in the Cogito have the problem of building a bridge from the starting point of consciousness to the external world. The result of this is the isolation and solitude of the very ego. | |
From: Victor Velarde-Mayol (On Husserl [2000], 4.7.2) | |
A reaction: This strikes me as a pretty good reason not to develop a philosophy which is inspired by the Cogito. |
21215 | The representation may not be a likeness [Velarde-Mayol] |
Full Idea: Representationalism is the doctrine that maintains that the object is represented in consciousness by means of an image. ...One should not confuse an image with a likeness. | |
From: Victor Velarde-Mayol (On Husserl [2000], 2.4.3) | |
A reaction: Helpful reminder that sense-data or whatever may not be a likeness. But then how do they represent? Symbolic representation needs massive interpretation. |
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? |
21219 | Find the essence by varying an object, to see what remains invariable [Velarde-Mayol] |
Full Idea: Eidetic Reduction consists of producing variations in the individual object until we see what is invariable in it. What is invariable is its essence or Eidos. | |
From: Victor Velarde-Mayol (On Husserl [2000], 3.2.2) | |
A reaction: This strikes me as an excellent idea. It more or less describes the method of science. Chemical atoms were thought to be unsplittable, until someone tried a new variation for dealing with them. |