Changes

</blockquote>

</blockquote>

====Note 4.====

====Note 4. Peirce (188&ndash;189)====

<pre>

<blockquote>

| Let us now take the two statements, S is P, T is P;

<p>Let us now take the two statements, <math>S\ \operatorname{is}\ P,</math> <math>\Sigma\ \operatorname{is}\ P;</math>  let us suppose that <math>\Sigma\!</math> is much more distinct than <math>S\!</math> and that it is also more extensive.  But we ''know'' that <math>S\ \operatorname{is}\ P.</math>  Now if <math>\Sigma\!</math> were not more extensive than S, <math>\Sigma\ \operatorname{is}\ P</math> would contain more truth than <math>S\ \operatorname{is}\ P;</math> being more extensive it ''may'' contain more truth and it may also introduce a falsehood.  Which of these probabilities is the greatest?  <math>\Sigma\!</math> by being more extensive becomes less intensive;  it is the intension which introduces truth and the extension which introduces falsehood.  If therefore <math>\Sigma\!</math> increases the intension of <math>S\!</math> more than its extension, <math>\Sigma\!</math> is to be preferred to <math>S;\!</math> 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>

| let us suppose that T is much more distinct than S and

 

| that it is also more extensive.  But we 'know' that S is P.

<p>In the two statements, <math>S\ \operatorname{is}\ P,</math> <math>S\ \operatorname{is}\ \Pi,</math> let <math>\Pi\!</math> be at once more ''formal'' and more ''intensive'' than <math>P;\!</math> and suppose we only ''know'' that <math>S\ \operatorname{is}\ P.</math> 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 <math>\Pi\!</math> is more increased than than its intension, then <math>S\ \operatorname{is}\ \Pi</math> is likely to contain more truth than <math>S\ \operatorname{is}\ P</math> and ''vice versa''.  This is the case of ''à posteriori'' reasoning.  We have for instance to choose between

| Now if T were not more extensive than S, T is P would contain

 

| more truth than S is P;  being more extensive it 'may' contain

:{| cellpadding="4"

| more truth and it may also introduce a falsehood.  Which of these

| &nbsp; || Light gives fringes of such and such a description

| probabilities is the greatest?  T by being more extensive becomes

|-

| less intensive;  it is the intension which introduces truth and the

| and   || Light is ether-waves.

| extension which introduces falsehood.  If therefore T increases the

|}

| intension of S more than its extension, T is to be preferred to S;

 

| otherwise not.  Now this is the case of induction.  Which contains

<p>C.S. Peirce, ''Chronological Edition'', CE 1, 188&ndash;189</p>

| most truth, 'neat' and 'deer' are herbivora, or cloven-footed

 

| animals are herbivora?

<p>Charles Sanders Peirce, "Harvard Lectures ''On the Logic of Science''" (1865), ''Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857&nbsp;1866'', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.</p>

</blockquote>

| In the two statements, S is P, S is Q, let Q 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 Q is more

| increased than than its intension, then S is Q 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

|

|   Light gives fringes of such and such a description

|

| and

|

|   Light is ether-waves.

|

| C.S. Peirce, 'Chronological Edition', CE 1, pp. 188-189.

| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),

|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',

| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

</pre>

====Note 5.====

====Note 5.====