4 ideas
| 16886 | The truth of an axiom must be independently recognisable [Frege] |
| Full Idea: It is part of the concept of an axiom that it can be recognised as true independently of other truths. | |
| From: Gottlob Frege (On Euclidean Geometry [1900], 183/168), quoted by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: Frege thinks the axioms of arithmetic all reside in logic. |
| 8249 | Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra] |
| Full Idea: Lesniewski distinguished the part-whole relationship from class membership. Membership is not transitive: if s is an element of t, and t of u, then s is not an element of u, whereas a part of a part is a part of the whole. | |
| From: report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7 | |
| A reaction: If I am a member of a sports club, and my club is a member of the league, I am not thereby a member of the league (so clubs are classes, not wholes). This distinction is clearly fairly crucial in ontology. |
| 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. |