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. |
| 13197 | The notion of substance is one of the keys to true philosophy [Leibniz] |
| Full Idea: I consider the notion of substance to be one of the keys to the true philosophy. ....I imagine that philosophers will one day know the notion of substance a bit better than they do now. | |
| From: Gottfried Leibniz (Letters to Thomas Burnett [1703], 1699.01.20/30) | |
| A reaction: This is a controversial remark at this historical moment, when the apparent Aristotelian commitment to substances was becoming discredited. Personally I would eliminate substance, but not just because physicists don't refer to it. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 13198 | Gravity is within matter because of its structure, and it can be explained. [Leibniz] |
| Full Idea: I believe that both gravity and elasticity are in matter only because of the structure of the system and can be explained mechanically or through impulsion. | |
| From: Gottfried Leibniz (Letters to Thomas Burnett [1703], 1699 draft) | |
| A reaction: The significance of this remark is that gravity is held (in full knowledge of Newton's work) to be within matter, and not imposed from the outside. I believe we now postulate a particle as part of the explanation. |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |