Dear Lotfi, Thank you very much for the references. As you know, I am familiar with at least one of the papers to which you refer. But one of the papers (the one with your lecture in Siena) is completely unknown to me. I will revisit the perception papers and try to do a better job of grasping the argument made there. I will also look at the Siena lecture. Eventually 96 but only quite some time in the future (see note below) 96 I may report back to this list.
On your point about bivalent logic and legal (normative) reasoning: my inclination is to agree that bivalent logic (of the sort found in the standard probability calculus) fails to capture much of what's going on in legal reasoning but that this is so, not so much because of the complexity of legal reasoning, but because the kind of uncertainty found in legal reasoning is not the sort of uncertainty that the standard probability calculus addresses (well). But I can imagine that you and I are saying roughly the same thing. -- Having just said what I have said above I very much hasten to add that I once gave a lecture 96 see P. Tillers, The Value of Evidence in Law, 39 No. Ire. Leg. Q. 167 (1988) -- in which I argued (and I have not changed my view) that legal questions are more like factual questions than most legal scholars & legal professionals suppose. My thesis has found some resonance - -- if not a general chorus of hosannas -- in the community of legal scholars. See, e.g., Ronald J. Allen & Michael S. Pardo, The Myth of the Law-Fact Distinction, 97 Northwestern University Law Review 1769 (2003). It might be argued: To the extent my argument in the Northern Ireland Legal Quarterly flies, to that extent normative legal reasoning is not as unamenable to Bayesian analysis as I now seem to suppose. But a thesis with reverse spin is also possible: to whatever extent my Northern Ireland argument flies, to that extent it follows that reasoning about "factual" hypothesis has features that elude the standard probability calculus. I incline toward the latter hypothesis -- because, as I explained in one of my earlier messages to this list, I think that in legal contexts (and, I suspect, in many other contexts) argument about "factual" issues is suffused (to a substantial extent) with semantic uncertainty. A word of apology: I tend to get loquacious about some issues. I fear I have worn out the patience of the members of the list. I beg for your forgiveness. The only interesting point that I can offer in my defense is that the question of the relative extent to which, e.g., fuzzy logic and the standard probability calculus capture important features of, e.g., normative reasoning in law and reasoning about factual questions in law offers an important window on the possibility and the extent (and, dare I say, the probability) of the rule of law. The old debates among legal scholars about this question were quite interesting in their own time but (in my view) they have grown tired and sterile. (But, I assure you, not every legal scholar -- far from it! -- agrees with my inclination to think that study of fuzzy sets, probability theory, etc. is of much 93practical94 use for attempts to solve legal problems. For example, Ron Allen, who was cited above, believes such 93formalizations94 offer few if any payoffs for law. [I suspect Ron will shortly speak up and either affirm or clarify what I have just said!]) Now, my dear colleagues, I plan to follow, for quite some time (4-8 weeks), Wittgenstein's famous admonition in the TRACTATUS: wovon man nicht reden kann, darFCber muss man schweigen. My very best wishes & thanks, peter t ***** Peter Tillers http://tillers.net Professor of Law Cardozo School of Law, Yeshiva University 55 Fifth Avenue, New York, NY 10003 (212) 790-0334; FAX (212) 790-0205 [EMAIL PROTECTED] - -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Lotfi A. Zadeh Sent: Monday, November 10, 2003 12:54 PM To: [EMAIL PROTECTED] Subject: [UAI] causal_ vs_ functional models? Dear Peter: In your comment (10-27-03), you ask some pertinent questions. My views regarding some of the issues which you raise may be found in the following: 1. L.A. Zadeh, "A New Direction in AI--Toward a Computational Theory of Perceptions," AI Magazine,Vol. 22, No. 1, 73-84, 2001. (Downloadable: http:// www-bisc.cs.berkeley.edu/zadeh) 2. L.A. Zadeh, "Toward a Perception-B, Vol. 105, 233-264, 2002 (Downloadable: http://www-bisc.cs.berkeley.edu/BISCProgram/Projects.htm 3. "Probability Theory and Fuzzy Logic," lecture delivered at the Conference on the Logic of Soft Computing, University of Siena, Italy, November 2, 2003. (Downloadable: http:// www-bisc.cs.berkeley.edu/zadeh) Insofar as the realm of law is concerned, a basic question is: Do bivalent logic and bivalent-logic-based probability theory provide adequate tools for a formalization of legal reasoning? In my view, legal reasoning is much too complex to lend itself to an analysis within the conceptual structure of bivalent-logic and bivalent-logic-based probability theory. Warm regards, Lotfi - -- Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC) http://www.cs.berkeley/~zadeh
