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. |
| 19355 | The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz] |
| Full Idea: The soul does many things without knowing how it does them - when it does them by means of confused perceptions and unconscious inclinations or appetites. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L]) | |
| A reaction: This increasingly strikes me as a wonderful and important insight for its time. He's really paid attention to his own mind, and given up the simplistic view that derives from Descartes. Are birds conscious? Yes or no! Silly. |
| 19350 | We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz] |
| Full Idea: I think we should keep both sides: we should be more Democritean and make all actions of bodies mechanical and independent of souls, and we should also be more than Platonic and hold that all actions of souls are immaterial and independent of mechanism. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [C]) | |
| A reaction: This is about as dualist as it is possible to get. It certainly looks as if many of Leibniz's doctrines are rebellions against Spinoza (in this case his 'dual aspect monism'). I take Leibniz to be utterly but heroically wrong. |
| 19356 | Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz] |
| Full Idea: In music, the soul counts the beats of the vibrating object which makes the sound, and when these beats regularly coincide at short intervals, it finds them pleasing. Thus it counts without knowing it. | |
| From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L]) | |
| A reaction: Only a mathematician would see music this way! He is defending his account of the unconscious mind. The proposal that we unconsciously count sounds highly implausible. He needs to recognise the patterns that ground mathematics. |
| 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 |
| 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. |