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174 bytes added ,  04:34, 3 June 2009
→‎Note 11: del redun + markup
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====Note 11====
 
====Note 11====
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<pre>
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Continuing to draw on the manageable materials of group representations, we examine a few of the finer points involved in regarding the pragmatic maxim as a representation principle.
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| Consider what effects that might 'conceivably'
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| have practical bearings you 'conceive' the
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Returning to the example of an abstract group that we had before:
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| objects of your 'conception' to have.  Then,
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| your 'conception' of those effects is the
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| whole of your 'conception' of the object.
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|
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| Charles Sanders Peirce,
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| "Maxim of Pragmaticism", CP 5.438.
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Continuing to draw on the reduced example of group representations,
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<br>
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I would like to draw out a few of the finer points and problems of
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regarding the maxim of pragmatism as a principle of representation.
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Let us revisit the example of an abstract group that we had befour:
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
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|+ <math>\text{Klein Four-Group}~ V_4</math>
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|- style="height:50px"
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| width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot</math>
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| width="22%" style="border-bottom:1px solid black" |
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<math>\operatorname{e}</math>
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| width="22%" style="border-bottom:1px solid black" |
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<math>\operatorname{f}</math>
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| width="22%" style="border-bottom:1px solid black" |
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<math>\operatorname{g}</math>
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| width="22%" style="border-bottom:1px solid black" |
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<math>\operatorname{h}</math>
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|- style="height:50px"
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| style="border-right:1px solid black" | <math>\operatorname{e}</math>
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| <math>\operatorname{e}</math>
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| <math>\operatorname{f}</math>
 +
| <math>\operatorname{g}</math>
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| <math>\operatorname{h}</math>
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|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{f}</math>
 +
| <math>\operatorname{f}</math>
 +
| <math>\operatorname{e}</math>
 +
| <math>\operatorname{h}</math>
 +
| <math>\operatorname{g}</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{g}</math>
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| <math>\operatorname{g}</math>
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| <math>\operatorname{h}</math>
 +
| <math>\operatorname{e}</math>
 +
| <math>\operatorname{f}</math>
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|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{h}</math>
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| <math>\operatorname{h}</math>
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| <math>\operatorname{g}</math>
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| <math>\operatorname{f}</math>
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| <math>\operatorname{e}</math>
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|}
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Table 1.  Klein Four-Group V_4
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<br>
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o---------o---------o---------o---------o---------o
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|        %        |        |        |        |
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|    ·    %    e    |    f    |    g    |    h    |
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|        %        |        |        |        |
  −
o=========o=========o=========o=========o=========o
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|        %        |        |        |        |
  −
|    e    %    e    |    f    |    g    |    h    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    f    %    f    |    e    |    h    |    g    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    g    %    g    |    h    |    e    |    f    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    h    %    h    |    g    |    f    |    e    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
      +
<pre>
 
I presented the regular post-representation
 
I presented the regular post-representation
 
of the four-group V_4 in the following form:
 
of the four-group V_4 in the following form:
Jon Awbrey
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