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, 03:36, 12 November 2008→Note 4. Peirce (CE 1, 188–189)
<p>Let us now take the two statements, ''S'' is ''P'', Σ is ''P''; let us suppose that Σ is much more distinct than ''S'' and that it is also more extensive. But we ''know'' that ''S'' is ''P''. Now if Σ were not more extensive than ''S'', Σ is ''P'' would contain more truth than ''S'' is P; being more extensive it ''may'' contain more truth and it may also introduce a falsehood. Which of these probabilities is the greatest? Σ by being more extensive becomes less intensive; it is the intension which introduces truth and the extension which introduces falsehood. If therefore Σ increases the intension of ''S'' more than its extension, Σ is to be preferred to ''S''; otherwise not. Now this is the case of induction. Which contains most truth, ''neat'' and ''deer'' are herbivora, or cloven-footed animals are herbivora?</p>
<p>Let us now take the two statements, ''S'' is ''P'', Σ is ''P''; let us suppose that Σ is much more distinct than ''S'' and that it is also more extensive. But we ''know'' that ''S'' is ''P''. Now if Σ were not more extensive than ''S'', Σ is ''P'' would contain more truth than ''S'' is P; being more extensive it ''may'' contain more truth and it may also introduce a falsehood. Which of these probabilities is the greatest? Σ by being more extensive becomes less intensive; it is the intension which introduces truth and the extension which introduces falsehood. If therefore Σ increases the intension of ''S'' more than its extension, Σ is to be preferred to ''S''; otherwise not. Now this is the case of induction. Which contains most truth, ''neat'' and ''deer'' are herbivora, or cloven-footed animals are herbivora?</p>
<p>In the two statements, ''S'' is ''P'', ''S'' is Π, let Π be at once more ''formal'' and more ''intensive'' than ''P''; and suppose we only ''know'' that ''S'' is ''P''. In this case the increase of formality gives a chance of additional truth and the increase of intension a chance of error. If the extension of Π is more increased than than its intension, then ''S'' is Π is likely to contain more truth than ''S'' is ''P'' and ''vice versa''. This is the case of ''à posteriori'' reasoning. We have for instance to choose between
<p>In the two statements, ''S'' is ''P'', ''S'' is Π, let Π be at once more ''formal'' and more ''intensive'' than ''P''; and suppose we only ''know'' that ''S'' is ''P''. In this case the increase of formality gives a chance of additional truth and the increase of intension a chance of error. If the extension of Π is more increased than than its intension, then ''S'' is Π is likely to contain more truth than ''S'' is ''P'' and ''vice versa''. This is the case of ''à posteriori'' reasoning. We have for instance to choose between:</p>
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