<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content="text/html; charset=iso-8859-1" http-equiv=Content-Type> <META content="MSHTML 5.00.2722.2800" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV> </DIV> <DIV><FONT face=Arial size=2>    In my old-fashioned understanding a tautology is  a proposition or statement that is true by virtue of its form. They are a sub=class of analytically true statements or propositions. For example: :Vancouver is the capital of Canada or it is not. Of course I realise there are complications re time etc. but the idea is clear enough. A proposition and its negation disjoined constitute one type of tautology. How is this related to the information theoretic sense of the term? Anyway I thought the original question was whether you could give a non-circular definition of "utility". What is a circular definition? I recall Bentham as claiming that utility meant pleasure and the utility of x its propensity to produce pleasure. Is that circular? </FONT></DIV> <DIV><FONT face=Arial size=2>THe example you give. "A rose is a rose is a rose" is indeed tautologous because of its form A is A is A   although I am not sure Hegel would accept that it is redundant to repeat the :"is  A" part. So some tautologies namely the type that have the general form  A is A is A...etc are redundant. Howver this is just one type of tautology. How are tautologies instantiating tautological propositional functions of the form :"P or not P" redundant? And how do tautologies of the form "A is A is A.."" convey the complexity of self-reference in the context of simplicity? I havent a clue what that means. It doesnt seem like "What is written on this blackboard is false" which is paradoxical since if true it would seem to be false and if false, true and you get what you would call viscous or sticky circles I guess...lol</FONT></DIV> <DIV><FONT face=Arial size=2>    I thought circularity in defiitions were roughly of this sort: X is defined as Y and when Y is defined it is by X. so that the definition goes in a circle in the sense of ultimately defining what is to be defined by what is to be defined rather than some conceptually distinct predicate or definiens. The metaphorical appropriateness is this: if you trace around a circle you at some point arrive at the point where you began. Is there something amiss or mysterious about this. What?</FONT></DIV> <DIV><FONT face=Arial size=2>    The standard definition of " bachelor" is not circular. "bachelor" is defined as"unmarried male" but "unmarried male" is not defined as "bachelor" even though "bachelor" and "unmarried male" are extensionally equivalent . However if you defined happiness as pleasure and then pleasure as happiness in turn that would be circular I would consider Bentham's definition of utility non-circular.</FONT></DIV> <DIV><FONT face=Arial size=2>    Definitions of the type " A bachelor is an unmarried male" are sometimes also called tautologies but these are not true because they exemplify a specific form. If you mean by a tautology any statement that can be determined as true by analysis of the terms involved then definitions of this type are also tautologies since as Kant put it the concept of the predicate term(s) (definiens) are included in the concept of the subject term (definiendum). However unless you consider simple identity statements of the form A = A as definitions definitions will not involve redundancy. Tautologies such as a bachelor is an unmarried male are not redundant even though extensionally equivalent to a bachelor is a bachelor. It is redundant however to say that Ted is a bachelor and that he is an unmarried male. However, in special circumstances this could be informative and non-redundant--if for example the second clause was added to explain to someone what a bachelor is..Of course there are quibbles too. He is a married bachelor of arts..</FONT></DIV> <DIV> </DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>CHeers, Ken Hanly</FONT></DIV> <DIV> </DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>      </FONT></DIV> <BLOCKQUOTE dir=ltr style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> <A href="mailto:seamus2001@home.com" title=seamus2001@home.com>Ian Murray</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A href="mailto:lbo-talk@lists.panix.com" title=lbo-talk@lists.panix.com>lbo-talk@lists.panix.com</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, July 06, 2001 10:27 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: (no subject)</DIV> <DIV><BR></DIV> <DIV><FONT face=Arial size=2></FONT><BR> </DIV> <BLOCKQUOTE dir=ltr style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px; PADDING-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 color=#000000 face=Arial lang=0 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></BLOCKQUOTE></FONT></BODY></HTML>