6 ideas
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 19555 | People begin to doubt whether they 'know' when the answer becomes more significant [Conee] |
| Full Idea: Fluent speakers typically become increasingly hesitant about 'knowledge' attributions as the practical significance of the right answer increases. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Epistemic') | |
| A reaction: The standard examples of this phenomenon are in criminal investigations, and in philosophical discussions of scepticism. Simple observations I take to have maximum unshakable confidence, except in extreme global scepticism contexts. |
| 19557 | Maybe low knowledge standards are loose talk; people will deny that it is 'really and truly' knowledge [Conee] |
| Full Idea: Maybe variable knowledge ascriptions are just loose talk. This is shown when we ask whether weakly supported knowledge is 'really' or 'truly' or 'really and truly' known. Fluent speakers have a strong inclination to doubt or deny that it is. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Loose') | |
| A reaction: [bit compressed] Conee is suggesting the people are tacitly invariantist about knowledge (they have a fixed standard). But it may be that someone who asks 'do you really and truly know?' is raising the contextual standard. E.g. a barrister. |
| 19556 | Maybe knowledge has fixed standards (high, but attainable), although people apply contextual standards [Conee] |
| Full Idea: It may be that all 'knowledge' attributions have the same truth conditions, but people apply contextually varying standards. The most plausible standard for truth is very high, but not unreachably high. | |
| From: Earl Conee (Contextualism Contested (and reply) [2005], 'Loose') | |
| A reaction: This is the 'invariantist' alternative to contextualism about knowledge. Is it a standard 'for truth'? Either it is or it isn't true, so there isn't a standard. I take the standard to concern the justification. |
| 20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |
| Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God. | |
| From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality' | |
| A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist? |