3 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. |
| 19393 | What is not active is nothing [Leibniz] |
| Full Idea: We can now show from the inner truths of metaphysics that what is not active is nothing. | |
| From: Gottfried Leibniz (True Method in Philosophy and Theology [1686], p.64) | |
| A reaction: This is Leibniz's rebellion against the Cartesian idea that all that matters for natural existence is spatial extension. I agree (tentatively) with Leibniz's vision of nature here. Modern physics reveals a seething turmoil beneath the placid exterior. |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| Full Idea: Primary matter is nothing if considered at rest. | |
| From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90) | |
| A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings. |