Jon, I have a little problem adjusting to the sign"( )" as the generating element in your Spencer-Brown notes since it has a meaning in Peirce Graphs that is a little bit different for me. The sign is also used, as you know, for graphs, cycles and such. In Peirce graphs, I take the Sheet of Assertion (SA) =True-----> assert (ABC etc,) The problem is not that "( )" doesn't amount to essentially the same thing when talking about a blank sheet or its backside or the universe or any identity function. The problem is that the concrete symbol shape is used in the object language in a way that is less familiar except in the rhetorical cases where Peirce introduces the graphs by saying "something or another is either not the case or...." I guess I would just say "SA," But this got me thinking about the 1880 paper. What to do with "b." Do you add it into the collection of transpositions and thus change the cycle shape? (and maybe rethink n!-1 as a count.) In any case, I am bummed out having discovered that for most 😐 finite groups below about 5, there is no really cool stuff like "orbits" and "stabilizers." Jim W > Date: Mon, 9 Mar 2015 09:45:44 -0400 > From: [email protected] > To: [email protected]; [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 > 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
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
