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All the ideas for 'fragments/reports', 'Consciousness, Philosophy and Mathematics' and 'De arcanus motus'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

8728	Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
	Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
	From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
	A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!

8. Modes of Existence / C. Powers and Dispositions / 1. Powers

12733	Because of the definitions of cause, effect and power, cause and effect have the same power [Leibniz]
	Full Idea: The primary mechanical axiom is that the whole cause and the entire effect have the same power [potentia]. ..This depends on the definition of cause, effect and power.
	From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6
	A reaction: This is a useful reminder that if one is going to build a metaphysics on powers (which I intend to do), then the conservation laws in physics are highly relevant.

10. Modality / A. Necessity / 2. Nature of Necessity

12734	Every necessary proposition is demonstrable to someone who understands [Leibniz]
	Full Idea: Every necessary proposition is demonstrable, at least by someone who understands it.
	From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6
	A reaction: This kind of optimism leads to the crisis of the Hilbert Programme in the 1930s. Gödel seems to have conclusively proved that Leibniz was wrong. What would Leibniz have made of Gödel?

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.