5 ideas
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
| From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
| A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
| 19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
| Full Idea: From the conflict of all the possibles demanding existence, this at once follows, that there exists that series of things by which as many of them as possible exist. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.91) | |
| A reaction: I'm in tune with a lot of Leibniz, but my head swims with this one. He seems to be a Lewisian about possible worlds - that they are concrete existing entities (with appetites!). Could Lewis include Leibniz's idea in his system? |
| 19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
| Full Idea: The sufficient reason for God's choice can be found only in the fitness (convenance) or in the degree of perfection that the several worlds possess. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: The 'fitness' of a world and its 'perfection' seem very different things. A piece of a jigsaw can have wonderful fitness, without perfection. Occasionally you get that sinking feeling with metaphysicians that they just make it up. |
| 4577 | There is no necessity higher than natural necessity, and that is just regularity [Quine] |
| Full Idea: In principle I see no higher or more austere necessity than natural necessity; and in natural necessity, or our attribution of it, I see only Hume's regularities | |
| From: Willard Quine (Necessary Truth [1963], p.76) | |
| A reaction: Presumably this allows logical necessity as a 'lower' necessity, but denies 'metaphysical' necessity, in line with Hume and other tough empiricists. Personally I adore metaphysical necessities, but they are a bit hard to establish conclusively. |
| 19402 | The actual universe is the richest composite of what is possible [Leibniz] |
| Full Idea: The actual universe is the collection of the possibles which forms the richest composite. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: 'Richest' for Leibniz means a maximum combination of existence, order and variety. It's rather like picking the best starting team from a squad of footballers. |