Philosophical Writings of Peirce by Peirce Charles S.; Buchler Justus;

Author:Peirce, Charles S.; Buchler, Justus;
Language: eng
Format: epub
ISBN: 1890048
Publisher: Dover Publications
Published: 2012-10-13T00:00:00+00:00

But this coincides with the formula of Induction.... Thus we see that Induction and Hypothesis are nothing but the apagogical inversions of statistical deductions. Accordingly, when r is taken as 1, so that p is “less than 1,” or when r is taken as o, so that ρ is “more than o,” the induction degenerates into a syllogism of the third figure and the hypothesis into a syllogism of the second figure. In these special cases, there is no very essential difference between the mode of reasoning in the direct and in the apagogical form. But, in general, while the probability of the two forms is precisely the same—in this sense, that for any fixed proportion of P’s among the M’s (or of marks of S’s among the marks of the M’s) the probability of any given error in the concluded value is precisely the same in the indirect as it is in the direct form—yet there is this striking difference, that a multiplication of instances will in the one case confirm, and in the other modify, the concluded value of the ratio.

We are thus led to another form for our rule of validity of ampliative inference; namely, instead of saying that the explanatory syllogism must be a good probable deduction, we may say that the syllogism of which the induction or hypothesis is the apagogical modification (in the traditional language of logic, the reduction) must be valid.

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