<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 5.50.4611.1300" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2></FONT><BR> </DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"><FONT face=arial,helvetica><FONT size=2>Why is tautology metaphorized as a circle? Self-reference as the <BR>'gravitational architectonic' of logical 'space', perhaps? Finite and <BR>unbounding? It would seem post-identity logics are struggling with <BR>self-affine and self-similar dynamics and a suitable rhetoric. <BR><BR></FONT><FONT lang=0 face=Arial color=#000000 size=3 FAMILY="SANSSERIF"> <BLOCKQUOTE></BLOCKQUOTE> <DIV><BR><BR>English translation please. <BR><BR>Leo Casey <BR>United Federation of Teachers <BR>260 Park Avenue South <BR>New York, New York 10010-7272 (212-598-6869) <BR><BR><FONT size=2>====================</FONT></DIV> <DIV><FONT size=2>Well, in the last couple of decades there has been a growing movement in philosophy [especially those interested in epistemology and it's links to AI research] to develop computer programs that spatialize/visualize systems of  formal logic. It largely gets it's aesthetic inspiration from the works of MSC Escher and, to a lesser extent Rene Magritte. All the old Hercaclitus/Plato issues of constructability/representatibility, sameness/difference/differentiation/otherness, simplicity/complexity get mapped onto the elaborations of Church, Tarski, Turing, Godel, Julia, Mandelbrot, Chaitin and many others. In information theoretic terms, a tautology is redundancy [a rose is a rose is a rose]. If that doesn't display the complexities of self reference within the context of simplicity, nothing does. Whitehead puts the issue thus, "if we cannot speak of the same thing twice, knowledge vanishes taking philosophy with it." So how do we go about visualizing the problems in epistemology and philosophical semantics; for example, the causal theory of reference, or the predicate calculus? Does dynamical systems theory help at all in understanding semantic chaos? You bet.</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>What are we to make of the distinctions between virtuous and viscous circles in arguments? What happens when we map these arguments so we can SEE them as geometrical forms? Where does redundancy leave off and novelty begin? It would be easy to write it all off as philosophical fun and games but self-reference, self-similarity, and self-identity through time are fundamental problems for biological life forms at all space-time scales. Hence, deep problems of formal logic are intimately bound up with our ability to understand living systems [something we're failing at rather badly, as we all know].</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>I could go on, but for those interested in this stuff try:</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>< <A href="http://www.sunysb.edu/philosophy/faculty/pgrim/pgrim.htm">http://www.sunysb.edu/philosophy/faculty/pgrim/pgrim.htm</A> ></FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>< <A href="http://www.lucs.lu.se/People/Peter.Gardenfors/">http://www.lucs.lu.se/People/Peter.Gardenfors/</A> ></FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>Or any of Douglas Hofstader's books. If you can find them, Francisco Varela's "The Principles of Biological Autonomy" and Robert Rosen's "Life Itself" are well worth the work.</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2>Ian</FONT></DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2></FONT> </DIV> <DIV><FONT size=2></FONT></FONT> </DIV></BLOCKQUOTE></FONT></BODY></HTML>