Hi Mary, I'm 2 or 3 replies behind and moving kinda slow of late, and there are messages now coming to me, as yours and previously Markku's did, with the correct List address, I think, but not going to the List, which is getting me confused. Ben wrote a note about checking to see if people have multiple send addresses, so maybe that is the problem, I don't know. Or maybe it has to do with the number of addresses in the cc lists being truncated. I will try trimming those.
By way of the briefest reply until I get more time ... My topic here is not self-reference but logical consistency. In themselves those are independent issues, only incidentally and inessentially entangled in the syntactic confidence games of the so-called liar paradox. Regards, Jon On 8/5/2015 11:44 AM, Libertin, Mary wrote:
Hi Jon, I am hesitant to accept your conclusions about self-reference if they are meant to be universally true. I take your comments to mean that self-reference is not acceptable, in part, because self-reference is not mathematical. Could you respond to the theses of Louis H. Kauffman in writings on self-reference and recursive forms, and to the thesis of Francisco Valera in “A Calculus for Self Reference” in the International Journal of General Systems 2, 1975, 5-24. I find them convincing, but I am not an expert and look forward to your response. Valera extends the calculus of indications of G. Spencer Brown to encompass all self referential situations in “A Calculus for Self Reference” in the International Journal of General Systems, 2, 1975, 5-25. Louis H. Kauffman, who teaches mathematics, Statistics and Computer Science at University of Illinois at Chicago, asks, in an essay “Self Reference and Recursive Forms,” in The Journal of Social Biological Structure, 1987, 10, 53-72, “Is self reference in language a form of reentry?” His response is yes. An expert on knots and physics, he includes references to mathematical recursions, fractals, set theory, logic, and quantum mechanics. In “Formal Systems: EigenForm” he discusses Foerster’s model for eigenforms and recursions and finds that “iterating an object upon itself is seen to be a key to understanding the nature of objects and the relationship of an observer and the apparent world of the observer.” Kybernetes, 34,1/2 2005. His works on “Kauffman2013” at wordpress.com are further discussions of this. Jorge Soto-Andrade et.al, in “Ouroboros avatars: A mathematics exploration of self-reference and metabolic Closure” (Advances in Artificial Life, ECAL 2011, proceedings of the eleventh European conference on the syntheses and simulation of living systems, Cambridge, MIT Press, 2011) shows how self-reference operates in metabolic systems. My interest in self reference goes way back to Douglas Hofstadter’s An Eternal Golden Braid, which analyzes self-reference in Godel, Escher, and Bach. In my own work I try to apply self-reference to James Joyce’s writings. My framework for understanding Joyce is Peircean, thus my involvement with the Peirce-l and biosemiotics. I am ready to learn of the limitations in my understanding of self-reference. For example, I was amazed to realize that G Spencer Brown’s Laws of Form does not include self-reference. I had until recently assumed the opposite. I would love to have Kauffman engage in a discussion with Jon. Best, Mary Libertin
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