Changes

<math>\begin{array}{lllr}

<math>\begin{array}{lllr}

\mathrm{m}

\mathrm{m}

& = & \mathrm{J} ~+\!\!,~ \mathrm{K} ~+\!\!,~ \mathrm{L} ~+\!\!,~ \mathrm{M} & = ~ \mathbf{1}

& = &

\mathrm{J} ~+\!\!,~ \mathrm{K} ~+\!\!,~ \mathrm{L} ~+\!\!,~ \mathrm{M} \qquad = &

\mathbf{1}

\\[6pt]

\\[6pt]

\mathrm{f}

\mathrm{f}

Now let's see if we can use this picture to make sense of the following statement:

Now let's see if we can use this picture to make sense of the following statement:

{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

{| align="center" cellspacing="6" width="90%" <!--QUOTE-->

|

|

<p>For instance, if our universe is perfect men, and there are as many teeth to a Frenchman (perfect understood) as there are to any one of the universe, then:</p>

<p>For instance, if our universe is perfect men, and there are as many teeth to a Frenchman (perfect understood) as there are to any one of the universe, then:</p>

: <p>[''t''][''f''] = [''tf'']</p>

<p>(Peirce, CP 3.76).</p>

 

<p>holds arithmetically.  (CP 3.76).</p>

|}

|}

In the lingua franca of statistics, Peirce is saying this:  That if the population of Frenchmen is a "fair sample" of the general population with regard to dentition, then the morphic equation [''tf''] = [''t''][''f''], whose transpose gives [''t''] = [''tf'']/[''f''], is every bite as true as the defining equation in this circumstance, namely, [''t''] = [''tm'']/[''m''].

In the language of statistics, Peirce is saying this:  That if the population of Frenchmen is a ''fair sample'' of the general population with regard to dentition, then the morphic equation <math>[\mathit{t}\mathrm{f}] = [\mathit{t}][\mathrm{f}],\!</math> whose transpose gives <math>[\mathit{t}] = [\mathit{t}\mathrm{f}]/[\mathrm{f}],\!</math> is every bit as true as the defining equation in this circumstance, namely, <math>[\mathit{t}] = [\mathit{t}\mathrm{m}]/[\mathrm{m}].\!</math>

===Commentary Note 11.21===

===Commentary Note 11.21===