4 ideas
18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
Full Idea: The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems, | |
From: Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
A reaction: The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted? |
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 |
4800 | Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos] |
Full Idea: Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction. | |
From: report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1 | |
A reaction: The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms. |
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. |