6 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. |
| 4867 | Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza] |
| Full Idea: I do not attribute to nature either beauty or deformity, order or confusion. Only in relation to our imagination can things be called beautiful or deformed, ordered or confused. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1665?) | |
| A reaction: This is clearly a statement of Hume's famous later opinion that there are no values ('ought') in nature ('is'). It is a rejection of Aristotelian and Greek teleology. It is hard to argue with, but I have strong sales resistance, rooted in virtue theory. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 4866 | God is a being with infinite attributes, each of them infinite or perfect [Spinoza] |
| Full Idea: I define God as a being consisting in infinite attributes, whereof each is infinite or supremely perfect. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1661) | |
| A reaction: This seems to me the glorious culmination of the hyperbolic conception of God that expands steadily from wood spirits through Zeus, to eventually mop up everything in nature, and then everything that can be imagined beyond nature. All very silly. |
| 4868 | Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza] |
| Full Idea: Those who endeavour to establish God's existence and the truth of religion by means of miracles seek to prove the obscure by what is more obscure. | |
| From: Baruch de Spinoza (Letters to Oldenburg [1665], 1675?) | |
| A reaction: Nicely put. On the whole this has to be right, but one must leave open a possibility. If there is a God, and He seeks to prove Himself by a deed, are we saying this is impossible? Divine intervention might be the best explanation of something. |