Changes

My plan will be nothing less plodding than to work through all of the principal statements that Peirce has made about the "number of" function up to our present stopping place in the paper, namely, those collected in [[Directory:Jon_Awbrey/Papers/Peirce%27s_1870_Logic_Of_Relatives#Commentary_Note_11.2|Section 11.2]].

My plan will be nothing less plodding than to work through all of the principal statements that Peirce has made about the "number of" function up to our present stopping place in the paper, namely, those collected in [[Directory:Jon_Awbrey/Papers/Peirce%27s_1870_Logic_Of_Relatives#Commentary_Note_11.2|Section 11.2]].

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

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

That is, in a universe of perfect human dentition, the number of the relative term <math>\text{tooth of}\,\underline{~~~~}</math> is equal to the number of teeth of humans divided by the number of humans, that is, <math>32.\!</math>

That is, in a universe of perfect human dentition, the number of the relative term <math>\text{tooth of}\,\underline{~~~~}</math> is equal to the number of teeth of humans divided by the number of humans, that is, <math>32.\!</math>

The 2-adic relative term ''t'' determines a 2-adic relation ''T''&nbsp;&sube;&nbsp;''U''&nbsp;&times;&nbsp;''V'', where ''U'' and ''V'' are two universes of discourse, possibly the same one, that hold among other things all of the teeth and all of the people that happen to be under discussion, respectively.

The 2-adic relative term <math>\mathit{t}\!</math> determines a 2-adic relation <math>T \subseteq U \times V,</math> where <math>U\!</math> and <math>V\!</math> are two universes of discourse, possibly the same one, that contains among other things all the teeth and all the people that happen to be under discussion, respectively.

A rough indication of the bigraph for ''T'' might be drawn as follows, where I have tried to sketch in just the toothy part of ''U'' and the peoply part of ''V''.

A rough indication of the bigraph for <math>T\!</math> might be drawn as follows, where I have tried to sketch in just the toothy part of <math>U\!</math> and the peoply part of <math>V.\!</math>

<pre>

<pre>

t_1    t_32  t_33    t_64  t_65    t_96  ...    ...

t_1    t_32  t_33    t_64  t_65    t_96  ...    ...

     m_1          m_2          m_3          ...

     m_1          m_2          m_3          ...

</pre>

</pre>

Notice that the "number of" function ''v''&nbsp;:&nbsp;''S''&nbsp;&rarr;&nbsp;'''R''' needs the data that is represented by this entire bigraph for ''T'' in order to compute the value [''t''].

Notice that the "number of" function ''v''&nbsp;:&nbsp;''S''&nbsp;&rarr;&nbsp;'''R''' needs the data that is represented by this entire bigraph for ''T'' in order to compute the value [''t''].