Combining Texts

All the ideas for 'fragments/reports', 'On Platonism in Mathematics' and 'Protrepticus (frags)'

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6 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles

17949	Inquiry is the cause of philosophy [Aristotle]
	Full Idea: Inquiry is the cause of philosophy.
	From: Aristotle (Protrepticus (frags) [c.334 BCE]), quoted by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.120
	A reaction: The earlier part of the quote says philosophical thinking is inescapable (even if philosophy is impossible). I suppose we would call it 'curiosity'.

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304	Very few things in set theory remain valid in intuitionist mathematics [Bernays]
	Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
	From: Paul Bernays (On Platonism in Mathematics [1934])

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303	Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
	Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
	A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306	Mathematical abstraction just goes in a different direction from logic [Bernays]
	Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
	From: Paul Bernays (On Platonism in Mathematics [1934], p.268)
	A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.

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.