Combining Texts

All the ideas for 'works', 'Homeostasis, Species and Higher Taxa' and 'Necessary Truth'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
10. Modality / A. Necessity / 11. Denial of Necessity
4577 There is no necessity higher than natural necessity, and that is just regularity [Quine]
     Full Idea: In principle I see no higher or more austere necessity than natural necessity; and in natural necessity, or our attribution of it, I see only Hume's regularities
     From: Willard Quine (Necessary Truth [1963], p.76)
     A reaction: Presumably this allows logical necessity as a 'lower' necessity, but denies 'metaphysical' necessity, in line with Hume and other tough empiricists. Personally I adore metaphysical necessities, but they are a bit hard to establish conclusively.
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15150 The properties of an electron can't be explained just as 'clustering' [Chakravartty on Boyd]
     Full Idea: Boyd's homeostatic mechanisms are not responsible for the co-instantiation of the mass, charge and spin of an electron.
     From: comment on Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3
     A reaction: I would have thought that no one has the foggiest idea (unless I have missed something?) about why electrons have those three properties. What is it about electrons that makes them do that? Explanations always run out somewhere. Substratum!
15149 Properties cluster together, either because of intrinsic relations, or because of an underlying process [Boyd, by Chakravartty]
     Full Idea: Boyd analyses 'sociability' between properties in terms of 'homeostasis', as causal relations between properties that favour clustering, or underlying processes that favour coinstantiation, or both.
     From: report of Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3
     A reaction: Chakravarty criticises this claim, but Boyd is clearly onto something. If, like me, you think natural kinds are overrated, you have to like his view.