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. |
| 15312 | We get the idea of power by abstracting from ropes, magnets and electric shocks [Priestley] |
| Full Idea: A rope sustains weight, a magnet attracts iron, a charged electrical jar gives a shock, and from these and other similar observations, we get the idea of power, universally and abstractly considered. | |
| From: Joseph Priestley (Theological and other works [1790], p.191), quoted by Harré,R./Madden,E.H. - Causal Powers 9.II.B | |
| A reaction: I agree with this, in that we appear to be observing powers directly, and are not observing something which can then be reduced to non-powers. Nature just can't be a set of inert structures, with forces 'imposed' on them. |
| 19727 | Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaña] |
| Full Idea: The best definition of reliabilism seems to be: the agent has evidence, and bases the belief on the evidence, and the actual conditional reliability of the belief on the evidence is high enough. | |
| From: Juan Comesaña (Reliabilism [2011], 4.4) | |
| A reaction: This is Comesaña's own theory, derived from Alston 1998, and based on conditional probabilities. |
| 19725 | In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaña] |
| Full Idea: If the processes of belief-formation are unreliable (perhaps in a sceptical scenario), then reliabilism has the consequence that those victims can never have justified beliefs (which Sosa calls the 'new evil demon problem'). | |
| From: Juan Comesaña (Reliabilism [2011], 4.1) | |
| A reaction: That may be the right outcome. Could you have mathematical knowledge in a sceptical scenario? But that would be different processes. If I might be a brain in a vat, then it's true that I have no perceptual knowledge. |
| 19726 | How do we decide which exact process is the one that needs to be reliable? [Comesaña] |
| Full Idea: The reliabilist has the problem of finding a principled way of selecting, for each token-process of belief formation, the type whose reliability ratio must be high enough for the belief to be justified. | |
| From: Juan Comesaña (Reliabilism [2011], 4.3) | |
| A reaction: The question is which exact process I am employing for some visual knowledge (and how the process should be described). Seeing, staring, squinting, glancing.... This seems to be called the 'generality problem'. |
| 15311 | Attraction or repulsion are not imparted to matter, but actually constitute it [Priestley] |
| Full Idea: Attraction or repulsion appear to me not to be properly what is imparted to matter, but what really makes it what it is, in so much that, without it, it would be nothing at all. | |
| From: Joseph Priestley (Theological and other works [1790], p.237), quoted by Harré,R./Madden,E.H. - Causal Powers 9.II.B | |
| A reaction: This is music to the ears of anyone who thinks that powers are the fundamentals of nature (like me). |