[Inquiry] Re: Kaina Stoicheia

[Jon Awbrey]

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KS.  Note 19

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| I begin, then, by showing that a law is
| not a mere common character of events.
|
| Suppose that a man throwing a pair of dice, which were
| all that honest dice are supposed to be, were to throw
| sixes a hundred times running.  Every mathematician will
| admit that that would be no ground for expecting the next
| throw to turn up sixes.  It is true that in any actual case
| in which we should see sixes thrown a hundred times running we
| should very rightly be confident that the next throw would turn up
| sixes likewise.  But why should we do so?  Can anybody sincerely deny
| that it would be because we should think the throwing of a hundred
| successive sixes was an almost infallible indication of there
| being some real connection between those throws, so that the
| series not merely a uniformity in the common character of
| turning up sixes, but something more, a result of a real
| circumstance about the dice connecting the throws?
|
| This example illustrates the logical principle that mere community of
| character between the members of a collection is no argument, however
| slender, tending to show that the same character belongs to another
| object not a member of that collection and not (as far as we have
| any reason to think) having any real connection with it, unless
| perchance it be in having the character in question.  For the
| usual supposition that we make about honest dice is that there
| will be no real connection (or none of the least significance)
| between their different throws.  I know that writer has copied
| writer in the feeble analysis of chance as consisting in our
| ignorance.  But the calculus of probabilities is pure nonsense
| unless it affords assurance in the long run.  Now what assurance
| could there be concerning a long run of throws of a pair of dice,
| if, instead of knowing they were honest dice, we merely did not
| know whether they were or not, or if, instead of knowing that
| there would be no important connection between the throws,
| we merely did not know that there would be.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 250-251
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.

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