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====Note 10====
 
====Note 10====
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The genealogy of this conception of pragmatic representation is very intricate.  I'll sketch a few details that I think I remember clearly enough, subject to later correction.  Without checking historical accounts, I won't be able to pin down anything approaching a real chronology, but most of these notions were standard furnishings of the 19th Century mathematical study, and only the last few items date as late as the 1920's.
    
<pre>
 
<pre>
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| Consider what effects that might conceivably have
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| practical bearings you conceive the objects of your
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| conception to have.  Then, your conception of those
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| effects is the whole of your conception of the object.
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|
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| Charles Sanders Peirce, "The Maxim of Pragmatism, CP 5.438.
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The genealogy of this conception of pragmatic representation is very intricate.
  −
I will delineate some details that I presently fancy I remember clearly enough,
  −
subject to later correction.  Without checking historical accounts, I will not
  −
be able to pin down anything like a real chronology, but most of these notions
  −
were standard furnishings of the 19th Century mathematical study, and only the
  −
last few items date as late as the 1920's.
  −
   
The idea about the regular representations of a group is universally known
 
The idea about the regular representations of a group is universally known
 
as "Cayley's Theorem", usually in the form:  "Every group is isomorphic to
 
as "Cayley's Theorem", usually in the form:  "Every group is isomorphic to
Jon Awbrey
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