6 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. |
| 16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
| Full Idea: Ockham is the scholastic paradigm of anti-realism with respect to the categories. | |
| From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 05.3 | |
| A reaction: These are the ten categories mentioned in Aristotle's book 'Categories'. |
| 16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
| Full Idea: Ockham regards Quantity as an entirely superfluous ontological category, …because matter is intrinsically extended. | |
| From: report of William of Ockham (Summula philosophiae naturalis [1320]) by Robert Pasnau - Metaphysical Themes 1274-1671 04.4 |
| 16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
| Full Idea: Matter is made to have a greater or lesser quantity not through its receiving any absolute accident, but through condensation and rarefaction alone. Parts come more or less close together, which can happen with local motion. | |
| From: William of Ockham (Summula philosophiae naturalis [1320], I.13), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.1 | |
| A reaction: This is Ockham at his most modern, rejecting the odd idea of Quantity in favour of a modern corpuscular view of the mere motions of matter. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |