7 ideas
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 15201 | That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN] |
| Full Idea: The fact that Queen Anne has been dead for some years is not, in the strict sense of 'about', a fact about Queen Anne; it is not a fact about anyone or anything - it is a general fact. | |
| From: Arthur N. Prior (Changes in Events and Changes in Things [1968], p.13), quoted by Robin Le Poidevin - Past, Present and Future of Debate about Tense 1 b | |
| A reaction: He distinguishes 'general facts' (states of affairs, I think) from 'individual facts', involving some specific object. General facts seem to be what are expressed by negative existential truths, such as 'there is no Loch Ness Monster'. Useful. |
| 22899 | 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN] |
| Full Idea: One says 'thank goodness that is over', ..and it says something which it is impossible which any use of any tenseless copula with a date should convey. It certainly doesn't mean the same as 'thank goodness that occured on Friday June 15th 1954'. | |
| From: Arthur N. Prior (Changes in Events and Changes in Things [1968]), quoted by Adrian Bardon - Brief History of the Philosophy of Time 4 'Pervasive' | |
| A reaction: [Ref uncertain] This seems to be appealing to ordinary usage, in which tenses have huge significance. If we take time (with its past, present and future) as primitive, then tenses can have full weight. Did tenses mean anything at all to Einstein? |
| 1466 | Claims about God don't seem to claim or deny anything tangible, so evidence is irrelevant [Flew, by PG] |
| Full Idea: An assertion is logically equivalent to denying its opposite, but claims about a 'gardener', or God, make neither claims nor denials of anything, so no evidence can count against the claim, or for it. | |
| From: report of Antony Flew (Theology and Falsification [1950]) by PG - Db (ideas) |
| 1465 | You can't claim a patch of land is tended by a 'gardener' if there is no evidence, and all counter-evidence is rejected [Flew, by PG] |
| Full Idea: If someone claimed a patch of land was tended by a 'gardener', but there was never a shred of evidence to support this view, the claim would gradually dissolve into meaninglessness, especially if it was suggested that evidence was irrelevant. | |
| From: report of Antony Flew (Theology and Falsification [1950]) by PG - Db (ideas) |
| 1467 | Religious people seem unwilling to accept any evidence that God does not love us, so their claim is unfalsifiable [Flew, by PG] |
| Full Idea: Religious people seem unwilling to accept any evidence which shows that God does not love us, so what would they accept? If nothing counts that way, their claim is unfalsifiable, and hence meaningless. | |
| From: report of Antony Flew (Theology and Falsification [1950]) by PG - Db (ideas) |