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<p>In every induction we have given some remarkable fact or piece of information:</p>

<p>In every induction we have given some remarkable fact or piece of information:</p>

 

: <p>S is B,</p>

| align="center" | <math>S ~\operatorname{is}~ B</math>

 

<p>where B is an object of connotation.  We infer that something else:</p>

 

<p>where <math>B\!</math> is an object of connotation.  We infer that something else:</p>

: <p>T is B.</p>

 

| align="center" | <math>\Sigma ~\operatorname{is}~ B</math>

<p>Let us suppose that T contains more ''information'' than S.  Then, if T is no more extensive than S, "T is B" is a better judgment than "S is B" because it contains more information without predicating B of anything doubtful.</p>

<p>Let us suppose that <math>\Sigma\!</math> contains more ''information'' than <math>S.\!</math> Then, if <math>\Sigma\!</math> is no more extensive than <math>S,\!</math> <math>\Sigma ~\operatorname{is}~ B</math> is a better judgment than <math>S ~\operatorname{is}~ B</math> because it contains more information without predicating <math>B\!</math> of anything doubtful.</p>

<p>Thus, it is better to say "All men are mortal" than "all rational animals are mortal" for the former implies the latter and contains no more possibility of error and is more ''distinct''.</p>

<p>Thus, it is better to say "All men are mortal" than "all rational animals are mortal" for the former implies the latter and contains no more possibility of error and is more ''distinct''.</p>

<p>But in every case of induction T is also more extensive than S.  Then in case S is a true symbol and "S is B" is a single true judgment, this judgment or proposition must be the result of induction, as we saw in the last lecture that all propositions are.  The question is, therefore, which is the preferable theory, "S is B" or "T is B".  The greater information of T causes the latter theory to contain more truth but its greater extension renders it liable to more error.  If in T the extension of S is increased more than the information is, the connotation will be diminished and 'vice versa'.  Accordingly the greater the connotation of T relatively to that of S, the better is the theory proposed, "T is B".</p>

<p>But in every case of induction <math>\Sigma\!</math> is also more extensive than <math>S.\!</math> Then in case <math>S\!</math> is a true symbol and <math>S ~\operatorname{is}~ B</math> is a single true judgment, this judgment or proposition must be the result of induction, as we saw in the last lecture that all propositions are.  The question is, therefore, which is the preferable theory, <math>S ~\operatorname{is}~ B</math> or <math>\Sigma ~\operatorname{is}~ B.</math> The greater information of <math>\Sigma\!</math> causes the latter theory to contain more truth but its greater extension renders it liable to more error.  If in <math>\Sigma\!</math> the extension of <math>S\!</math> is increased more than the information is, the connotation will be diminished and ''vice versa''.  Accordingly the greater the connotation of <math>\Sigma\!</math> relatively to that of <math>S,\!</math> the better is the theory proposed, <math>\Sigma ~\operatorname{is}~ B.</math></p>

<p>Which of the two theories to select in any case will depend upon the motives which influence us.  In a desperate practical case, if one's life depends upon taking the right one, he ought to select the one whose subject has the greatest connotation.  In a cool speculation where safety is the essential;  the least extensive should be taken.</p>

<p>Which of the two theories to select in any case will depend upon the motives which influence us.  In a desperate practical case, if one's life depends upon taking the right one, he ought to select the one whose subject has the greatest connotation.  In a cool speculation where safety is the essential;  the least extensive should be taken.</p>

<p>So much for the preference between two theories.  But in proceeding from fact to theory — in such a case as that about ''neat'', ''swine'', ''sheep'', and ''deer'' — S is a mere enumerative term and has no connotation at all.  In this case therefore T increases the connotation of S absolutely and "T is B" ought therefore to be absolutely preferred to "S is B" and be accepted assertorically;  as long as there is no question between this theory and some other and as long as it is not opposed by some other induction. (Peirce 1865, "Harvard Lecture 10.  Grounds of Induction", CE 1, 285).</p>

<p>So much for the preference between two theories.  But in proceeding from fact to theory &mdash; in such a case as that about ''neat'', ''swine'', ''sheep'', and ''deer'' &mdash; <math>S\!</math> is a mere enumerative term and has no connotation at all.  In this case therefore <math>\Sigma\!</math> increases the connotation of <math>S\!</math> absolutely and <math>\Sigma ~\operatorname{is}~ B</math> ought therefore to be absolutely preferred to <math>S ~\operatorname{is}~ B</math> and be accepted assertorically;  as long as there is no question between this theory and some other and as long as it is not opposed by some other induction.</p>

 

<p>(Peirce 1865, Harvard Lecture 10 : Grounds of Induction, CE 1, 285).</p>

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===Selection 34===

===Selection 34===