8 ideas
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| Full Idea: Metaphysics is the most general attempt to make sense of things. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
| A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
| 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. |
| 13163 | Circles must be bounded, so cannot be infinite [Leibniz] |
| Full Idea: An infinite circle is impossible, since any circle is bounded by its circumference. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114) | |
| A reaction: This is interesting if one is asking what the essence of a circle must be. If is tempting to say merely that the radii must be equal, but can they have the length of some vast transfinite number? The circumference must be 2π bigger. |
| 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. |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
| 13162 | Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz] |
| Full Idea: The ancient Sloth's Syllogism says that if something is foreseen and infallible, it will happen without my effort, and if it is not foreseen, it will not happen, even though I am able to do it. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.113) | |
| A reaction: Presumable the foreseeing is to be done by the oracle, and not by the slothful person. |
| 19339 | Evil is a negation of good, which arises from non-being [Leibniz] |
| Full Idea: The cause of good is positive, but evil is a defect, that is, a privation or negation, and consequently, it arises from nothingness or nonbeing. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114) | |
| A reaction: He goes on to illustrate his idea from mathematics. He is modifying Augustine's view that evil is an absence of good, by adding nonbeing as the driving force behind it. Doesn't sound very persuasive to me. |
| 13164 | God only made sin possible because a much greater good can be derived from it [Leibniz] |
| Full Idea: We must believe that God would not have allowed sin nor would he have created things he knows will sin, if he could not derive from them a good incomparably greater than the resulting evil. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.115) | |
| A reaction: Why 'must' we believe this? Do we have to imagine all the genocides shrinking to insignificance once we grasp the wonderful goods that can be derived from them? The end justifies the means. Genocide is actually a good thing. Hm. |