Jon,list, As always, thanks for your responses and hints. I worked into the following paragraphs a bit and searched for some cycles and conjugacy classes to make sense of "I + J + K = 1 + L + M." It seems that "I + J + K" is the class of interchanges or conversions. " L + M" are a class of 2-cycle decompositions. The number "1" returns it to b. In fact "b" is the 3rd conjugacy class; ie. the identity element. I had hunted for ways to partition and count within a group of 5. I am trying to make sense of the idea of "2 + 2 +1" since I came up earlier with "2+1+1+1." I will leave it be for now. I may have taken: b= f(I (J (K))) and counted the composition (recursive) as "1+1+1" and then counted L + M as "2." Mistake. As far as "reduction" goes, I have been looking for "things that you can and cannot do" (and why) for n< or = 3. That may be an odd principle of method. Nevertheless...........Quine! Jim W
> Date: Mon, 9 Mar 2015 09:45:44 -0400 > From: jawb...@att.net > To: jimwillgo...@msn.com; peirce-l@list.iupui.edu > Subject: 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 > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15789 > JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15790 > > On 3/7/2015 12:31 PM, Jim Willgoose wrote: > > > I am somewhat curious about how setting k=3 or k=4 > > might effect the so-called "reduction thesis." > > I don't believe the number of converses has any bearing on reducibility. > Whether relations of a given adicity are reducible under composition or > projections or not is either an immediate consequence of the definition > of relational composition or dependent on the existence of a universal > construction for uniquely determining a relation from a collection of > relations of lower adicity. Just off hand, I don't see the number of > converses entering into that. > > > 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. > > I think it's fairly standard that monadic predicate calculus > and propositional calculus amount to the same thing. There > are a couple of articles by Quine that nail that down quite > nicely and develop further extensions of the underlying idea. > > Peirce's 1870 Logic of Relatives sets out a radical approach to > the role of indices and quantifiers in logic, a perspective whose > potential has yet to be fully explored even today. I discuss this > at some length in my commentary on that paper: > > http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives > > Regards, > > Jon > > -- > > 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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