Combining Texts

All the ideas for 'fragments/reports', 'Letter to Shumacher' and 'The Metaphysics of Space-Time Substantivalism'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
10855 Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss]
     Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound.
     From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7
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 / C. Space / 4. Substantival Space
19035 General Relativity allows substantivalism about space-time - that it has independent properties [Hoefer]
     Full Idea: General Relativity describes space-time in a way that allows it to exist with determinate properties not reducible to the properties and relations of its material contents. Hence nearly all physicists and philosophers writing on GR are substantivalists.
     From: Carl Hoefer (The Metaphysics of Space-Time Substantivalism [1996], p.5), quoted by Barbara Vetter - Potentiality 7.3
     A reaction: I'm encouraged by this, as I instinctly favour substantivalism. Imagine removing all the objects from space-time, one by one. What happens as you approach the end of the task? Once they are removed, can they be replaced?
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.