Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Intention'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18086 Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
     Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
     From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18092 Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
     Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
     From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
     A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
20041 Intentional actions are those which are explained by giving the reason for so acting [Anscombe]
     Full Idea: Intentional actions are those to which a certain sense of the question 'Why?' is given application; the sense is of course that in which the answer, if positive, gives a reason for acting.
     From: G.E.M. Anscombe (Intention [1957], p.9), quoted by Rowland Stout - Action 2 'Two kinds'
     A reaction: This works better for grand large-scale actions than for small ones, like taking the knife out of the drawer before the fork. Kahnemann nowadays tells us that the reasons we articulate might not be the ones that are operative.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
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
27. Natural Reality / G. Biology / 3. Evolution
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.