12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Tuesday May 07, 2024
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 04:18, 2 June 2009
, 04:18, 2 June 2009→Note 9: markup
====Note 9====
====Note 9====
{| align="center" cellpadding="0" cellspacing="0" width="90%"
| Consider what effects that might conceivably have
|
|
| Charles Sanders Peirce, "The Maxim of Pragmatism, CP 5.438.
<p>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.</p>
|-
| align="right" | — Charles Sanders Peirce, "Issues of Pragmaticism", [CP 5.438]
|}
One other subject that it would be opportune to mention at this point,
One other subject that it would be opportune to mention at this point, while we have an object example of a mathematical group fresh in mind, is the relationship between the pragmatic maxim and what are commonly known in mathematics as ''representation principles''. As it turns out, with regard to its formal characteristics, the pragmatic maxim unites the aspects of a representation principle with the attributes of what would ordinarily be known as a ''closure principle''. We will consider the form of closure that is invoked by the pragmatic maxim on another occasion, focusing here and now on the topic of group representations.
while we have an object example of a mathematical group fresh in mind,
is the relationship between the pragmatic maxim and what are commonly
known in mathematics as "representation principles". As it turns out,
with regard to its formal characteristics, the pragmatic maxim unites
the aspects of a representation principle with the attributes of what
would ordinarily be known as a "closure principle". We will consider
the form of closure that is invoked by the pragmatic maxim on another
occasion, focusing here and now on the topic of group representations.
Let us return to the example of the so-called "four-group" V_4.
Let us return to the example of the ''four-group'' <math>V_4.\!</math> We encountered this group in one of its concrete representations, namely, as a ''transformation group'' that acts on a set of objects, in this case a set of sixteen functions or propositions. Forgetting about the set of objects that the group transforms among themselves, we may take the abstract view of the group's operational structure, for example, in the form of the group operation table copied here:
We encountered this group in one of its concrete representations,
namely, as a "transformation group" that acts on a set of objects,
in this particular case a set of sixteen functions or propositions.
Forgetting about the set of objects that the group transforms among
themselves, we may take the abstract view of the group's operational
structure, say, in the form of the group operation table copied here:
<br>
<br>
