Combining Texts

All the ideas for 'fragments/reports', 'Universal Arithmetick' and 'Lewis on Perdurance versus Endurance'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17783 A number is not a multitude, but a unified ratio between quantities [Newton]
     Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity.
     From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2
     A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern.
7. Existence / B. Change in Existence / 1. Nature of Change
15541 Maybe particles are unchanging, and intrinsic change in things is their rearrangement [Lowe, by Lewis]
     Full Idea: Lowe's solution the 'temporary intrinsics' problem is that particles have no temporary intrinsic properties; they may be safely supposed to endure, and large things consist of those enduring particles, undergoing rearrangement but no intrinsic change.
     From: report of E.J. Lowe (Lewis on Perdurance versus Endurance [1987]) by David Lewis - Rearrangement of Particles II
     A reaction: A mere rearrangement of particles doesn't sound the same as a change in properties, which must involve causal powers in some way.
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.