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All the ideas for 'fragments/reports', 'works' and 'Paraconsistent Logic'

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5 ideas

4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
15382 Paraconsistent reasoning can just mean responding sensibly to inconsistencies [Jago]
     Full Idea: A practical application of paraconsistent reasoning is in large databases. It does not mean that contradictions could be true, but only that we sometimes need to draw sensible conclusions from inconsistent data. 'Dialethists' believe some contradictions.
     From: Mark Jago (Paraconsistent Logic [2010])
     A reaction: Interesting as a more cautious and sensible attitude to the scandal of paraconsistency.
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.
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.