Combining Texts

All the ideas for 'fragments/reports', 'Law and Authority' and 'Universal Arithmetick'

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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.
25. Social Practice / B. Equalities / 1. Grounds of equality
20486 Only liberty, equality and sympathy can stand up to anti-social people [Kropotkin]
     Full Idea: Liberty, equality and practical human sympathy are the only effective barriers we can oppose to the anti-social instincts of certain among us.
     From: Peter (Pyotr) Kropotkin (Law and Authority [1886], 1 'Anarchism'), quoted by Jonathan Wolff - An Introduction to Political Philosophy (Rev)
     A reaction: One might state it more succinctly as 'only the social can oppose the anti-social'. The dominance in society of essentially anti-social people seems to have become a major political fact in 2017, in the UK and the USA.
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.