4 ideas
| 17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
| Full Idea: A deeper justification for believing in [mathematical] propositions [apart from pragmatism] lies in finding their place in a logicist proof structure, by understanding the grounds within this structure that support them. | |
| From: Tyler Burge (Frege on Knowing the Foundations [1998], 3) | |
| A reaction: This generalises to doubting something until you see what grounds it. |
| 19387 | Hypotheses come from induction, which is comparison of experiences [Leibniz] |
| Full Idea: We construct a hypothesis on the basis of an induction, that is on the basis of a comparison of experiences. | |
| From: Gottfried Leibniz (Elements of Law and Justice [1669], p.2) | |
| A reaction: This fits the traditional positivist picture of science (observe-hypothesise-predict-observe). I like the definition of induction as 'comparison of experiences', because it doesn't reduce it to sequences of objects, and points to coherence. |
| 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. |