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. |
| 14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
| Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition. | |
| From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3 | |
| A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers? |
| 22593 | Our sensation of light may not be the same as what produces the sensation [Descartes] |
| Full Idea: There can be a difference between our sensation of light and what is in the objects that produce that sensation in us. | |
| From: René Descartes (The World [1631]), quoted by Ian Dunt - How to be a Liberal 1 | |
| A reaction: Note only that they 'may' differ, and that he does not assert that they are entirely different. Secondary qualities give information, and are not just mental events. |
| 16569 | The Hot, Cold, Wet and Dry of the philosophers need themselves to be explained [Descartes] |
| Full Idea: If you find it strange that in explaining these elements I do not use the qualities called Hot, Cold, Wet and Dry - as the philosophers do - I shall say to you that these qualities themselves seem to me to need explanation. | |
| From: René Descartes (The World [1631], 9:25-6), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 1.3 | |
| A reaction: Nice. I take pushing the boundaries of explanation back (or down) to be the basic driving force of all human thought, in metaphysics as well as in physics. |
| 20964 | Descartes said there was conservation of 'quantity of motion' [Descartes, by Papineau] |
| Full Idea: Descartes incorporated the conservation of what he called 'quantity of motion', by which he meant mass times speed. | |
| From: report of René Descartes (The World [1631]) by David Papineau - Thinking about Consciousness App 2 | |
| A reaction: Mass times velocity is now called 'momentum'. Is this the first ever conservation law? There are now lots of them. |