Combining Texts

All the ideas for 'fragments/reports', 'Mathematical Intuition' and 'Letters to Wolff'

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4 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
     Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve.
     From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics
     A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics.
9. Objects / D. Essence of Objects / 9. Essence and Properties
The properties of a thing flow from its essence [Leibniz]
     Full Idea: It is the same to look for perfection in an essence and in the properties that flow from an essence.
     From: Gottfried Leibniz (Letters to Wolff [1715], 1715.05.18)
     A reaction: It is helpful to have Leibniz spelling out his commitment to the traditional view of essence, as that from which the more evident properties flow.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
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
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.