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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14534
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Shoemaker moved from properties as powers to properties bestowing powers [Shoemaker, by Mumford/Anjum]
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Full Idea:
Shoemaker ventured the theory in 1980 that properties just are clusters of powers, but he has subsequently abandoned this, and now thinks properties bestow their bearers with causal powers.
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From:
report of Sydney Shoemaker (Self, Body and Coincidence [1999], p.297) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 1.1
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A reaction:
Like Mumford and Anjum, I prefer the earlier theory. I think taking powers as basic is the only story that really makes sense. A power is intrinsic and primitive, whereas properties are complex, messy, partly subjective, and higher level.
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