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7491
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The phases of human thought are theological, then metaphysical, then positivist [Comte, by Watson]
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Full Idea:
The first phase of humanity was theological, attributing phenomena to a deity, the second metaphysical stage attributed them to abstract forms, the third positive stage abandons ultimate causes and just searches for regularities.
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From:
report of Auguste Comte (Course of Positive Philosophy [1846]) by Peter Watson - Ideas Ch.32
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A reaction:
This is obviously a highly empirical programme, which reasserts Hume's view of the laws of nature. Effectively, positivism just is the rejection of metaphysics.
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5897
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0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
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Full Idea:
1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number.
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From:
report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano'
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A reaction:
Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'.
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