Combining Texts

All the ideas for 'fragments/reports', 'Lysis' and 'The Architecture of Mathematics'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
     Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures.
     From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79
     A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s.
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
295 The good is beautiful [Plato]
     Full Idea: The good is beautiful.
     From: Plato (Lysis [c.400 BCE], 216d)
     A reaction: also Timaeus 87c
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
294 People say that friendship exists only between good men [Plato]
     Full Idea: People say that friendship exists only between good men.
     From: Plato (Lysis [c.400 BCE], 214d)
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.