5 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. |
| 22040 | Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel] |
| Full Idea: Actual freedom is not something immediately existent in mindedness, but is something to be produced by the mind's own activity. It is thus as the producer of its freedom that we have to consider mindedness in philosophy. | |
| From: Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817], §382, Zusatz), quoted by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Pinkard glosses this as an agent being free by being the centre of a group of social responsibilities. Hence I presume small children have no freedom. Presumably we could deprive citizens of all responsibility, and hence of metaphysical freedom. |
| 22039 | Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard] |
| Full Idea: Hegel argued that it was the impossibility of a naturalistic account of normativity that distinguished Geist from nature, not Geist's being any kind of metaphysical substance. | |
| From: report of Georg W.F.Hegel (Philosophy of Mind (Encylopedia III) [1817]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Hegel always seems to want to have his cake and eat it. Without a mental substance, how can Geist not be part of nature? What is Geist made of? Is his view functionalist? But that is usually naturalistic. Is normativity magic? |