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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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8416
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Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley]
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Full Idea:
Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws.
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From:
Michael Tooley (Causality: Reductionism versus Realism [1990], 2)
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A reaction:
I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns.
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