ONT Re: Inquiry Driven Systems
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Note 14
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CP 2.652. Three Logical Sentiments
| But there remains an important point to be cleared up.
| According to what has been said, the idea of probability
| essentially belongs to a kind of inference which is repeated
| indefinitely. An individual inference must be either true or
| false, and can show no effect of probability; and, therefore,
| in reference to a single case considered in itself, probability
| can have no meaning. Yet if a man had to choose between drawing
| a card from a pack containing twenty-five red cards and a black one,
| or from a pack containing twenty-five black cards and a red one, and
| if the drawing of a red card were destined to transport him to eternal
| felicity, and that of a black one to consign him to everlasting woe, it
| would be folly to deny that he ought to prefer the pack containing the
| larger proportion of red cards, although, from the nature of the risk,
| it could not be repeated. It is not easy to reconcile this with our
| analysis of the conception of chance. But suppose he should choose
| the red pack, and should draw the wrong card, what consolation would
| he have? He might say that he had acted in accordance with reason,
| but that would only show that his reason was absolutely worthless.
| And if he should choose the right card, how could he regard it
| as anything but a happy accident? He could not say that if
| he had drawn from the other pack, he might have drawn the
| wrong one, because an hypothetical proposition such as,
| "if A, then B", means nothing with reference to a single
| case. Truth consists in the existence of a real fact
| corresponding to the true proposition. Corresponding
| to the proposition, "if A, then B", there may be the
| fact that 'whenever' such an event as A happens such
| an event as B happens. But in the case supposed, which
| has no parallel as far as this man is concerned, there
| would be no real fact whose existence could give any
| truth to the statement that, if he had drawn from the
| other pack, he might have drawn a black card. Indeed,
| since the validity of an inference consists in the truth
| of the hypothetical proposition that 'if' the premisses be
| true the conclusion will also be true, and since the only real
| fact which can correspond to such a proposition is that whenever
| the antecedent is true the antecedent is so also, it follows that
| there can be no sense in reasoning in an isolated case, at all.
|
| C.S. Peirce, 'Collected Papers', CP 2.652
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