7 ideas
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true. | |
| From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism. |
| 10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
| Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them. | |
| From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry. |
| 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. |