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<p>Let us now take the two statements, ''S'' is ''P'', &Sigma; is ''P'';  let us suppose that &Sigma; is much more distinct than ''S'' and that it is also more extensive.  But we ''know'' that ''S'' is ''P''.  Now if &Sigma; were not more extensive than ''S'', &Sigma; 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?  &Sigma; by being more extensive becomes less intensive;  it is the intension which introduces truth and the extension which introduces falsehood.  If therefore &Sigma; increases the intension of ''S'' more than its extension, &Sigma; 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''&nbsp;is&nbsp;''P'', &Sigma;&nbsp;is&nbsp;''P'';  let us suppose that &Sigma; is much more distinct than ''S'' and that it is also more extensive.  But we ''know'' that ''S''&nbsp;is&nbsp;''P''.  Now if &Sigma; were not more extensive than ''S'', &Sigma;&nbsp;is&nbsp;''P'' would contain more truth than ''S''&nbsp;is&nbsp;P;  being more extensive it ''may'' contain more truth and it may also introduce a falsehood.  Which of these probabilities is the greatest?  &Sigma; by being more extensive becomes less intensive;  it is the intension which introduces truth and the extension which introduces falsehood.  If therefore &Sigma; increases the intension of ''S'' more than its extension, &Sigma; 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 &Pi;, let &Pi; 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 &Pi; is more increased than than its intension, then ''S'' is &Pi; 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''&nbsp;is&nbsp;''P'', ''S''&nbsp;is&nbsp;&Pi;, let &Pi; be at once more ''formal'' and more ''intensive'' than ''P'';  and suppose we only ''know'' that ''S''&nbsp;is&nbsp;''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 &Pi; is more increased than than its intension, then ''S''&nbsp;is&nbsp;&Pi; is likely to contain more truth than ''S''&nbsp;is&nbsp;''P'' and ''vice versa''.  This is the case of ''à&nbsp;posteriori'' reasoning.  We have for instance to choose between

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