Line 5,962: |
Line 5,962: |
| ====Note 11==== | | ====Note 11==== |
| | | |
− | <pre>
| + | 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. |
− | | Consider what effects that might 'conceivably'
| + | |
− | | have practical bearings you 'conceive' the
| + | Returning to the example of an abstract group that we had before: |
− | | objects of your 'conception' to have. Then,
| |
− | | your 'conception' of those effects is the
| |
− | | 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,
| + | <br> |
− | 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:
| + | {| 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> |
| + | |} |
| | | |
− | Table 1. Klein Four-Group V_4
| + | <br> |
− | 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 |
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− | | % | | | |
| |
− | o---------o---------o---------o---------o---------o
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− | | % | | | |
| |
− | | f % f | e | h | g |
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− | | % | | | |
| |
− | o---------o---------o---------o---------o---------o
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− | | % | | | |
| |
− | | g % g | h | e | f |
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− | | % | | | |
| |
− | o---------o---------o---------o---------o---------o
| |
− | | % | | | |
| |
− | | h % h | g | f | e |
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− | | % | | | |
| |
− | 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: |