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