Jon,list. Thanks for the math references and graphic links. It seems that n! can be further limited by n!/k(k-1) but it is a choice. It seems Peirce might pair correlates or fix the relate in such a way that the number of orders on a 5-element diminishes to 20 or 10 depending on whether you want 2 pair or not. I am somewhat curious about how setting k=3 or k=4 might effect the so=called "reduction thesis." Thanks for the reference to symmetry groups. Honestly, I don't want to hunt around for geometric intuitions, but this one seemed to fit. I would rather have the same information contained in a matrice, which strikes me as the more generalized form anyway. Btw, I am beginning to think that Peirce has no time or need for an individual variable for non-relatives. It' s like...."why bother" They aren't true variables anyway. With that in mind, maybe drop quantifiers too. Jim W > Date: Sat, 7 Mar 2015 10:42:18 -0500 > From: [email protected] > To: [email protected] > Subject: [PEIRCE-L] Re: Peirce's 1880 “Algebra Of Logic” Chapter 3 • > Selection 7 > > Thread: > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15762 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15768 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15769 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15771 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15772 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15773 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15787 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15788 > > Jim, List, > > The set of converses of a k-place relation, > of which there are k! in number, does exhibit > a kind of "geometric" structure when we think > about the operations that transform them among > themselves, and this is given by the so-called > "symmetric group on k letters, commonly notated > as Sym(X), where X is the given set of "letters", > or else Sym(k) or even just S_k, where k is the > cardinality of X. > > (One of my favorite first books on group theory was > ''Groups and Their Graphs'' by Grossman and Magnus, > and I see this is still available for about $15-20.) > > I set out a little excursus on some of the group theory > involved in Peirce's theory of signs and representations > at the following place: > > http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation > > There is a discussion of Sym(3) toward the end of that section. > > Regards, > > Jon > > P.S. Jim, if you're going to be doing much graphics, you might > look into getting LibreOffice ( http://www.libreoffice.org/ ). > It's free, I actually prefer it to MicroSoft Office, and the > Drawing component is very easy to use. —JA > > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache
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