<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> |