. perhaps the closer analogy (see below) is Aristotle . *****
Peter Tillers <http://tillers.net/> 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: Peter Tillers [mailto:[EMAIL PROTECTED] Sent: Saturday, February 07, 2004 2:26 PM To: '[EMAIL PROTECTED]'; '[EMAIL PROTECTED]' Subject: RE: [UAI] functional_vs_causal models Dear All, I know -- or believe -- that Zadeh's theory is not Platonic. But there is a loose isomorphism between the Platonic theory of being, Platonic ontology, and Prof. Zadeh's notion of partial truth. In Plato's scheme, things or entities have varying degrees of being. In Zadeh's scheme matters have varying shares or amounts of truth. In Zadeh's partial truth scheme attributes are distributed unequally among things or entities -- or things and entities have varying amounts of an attribute (which is a very Platonic way of thinking about the relationship between concepts and instances or elements) -- and fuzzy logic is a grammar that allows a description of that sort of varying sharing of an attribute. Is Zadeh's way of thinking about the relationship between classes or sets and elements useless? I wonder. In some contexts -- e.g., in the context of reasoning about and interpretation of legal norms and principles -- Zadeh's way of picturing reasoning seems helpful. Is it necessary for Zadeh or proponents of fuzzy sets to show that no other way of reasoning about the relationship between concepts and elements is helpful? I wouldn't think so. Is it necessary for a proponent of fuzzy sets to show that the theory of partial truth teases out implications that other forms of reasoning do not? I would think so. * Professor (emeritus but fully-active) Lothar Philipps of the University of Munich has done a bit of work along this line, suggesting that fuzzy logic can explain some legal results. (To get details, you need to turn to him, and not to me.) But here matters get difficult in contexts such as law -- because of general issues about the appropriateness of using a formal logic or procedure to reason in real-world legal settings about matters such as interpretation of legal rules or, even, about seemingly non-normative factual issues. Sincerely, 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 [EMAIL PROTECTED] Sent: Saturday, February 07, 2004 12:10 AM To: [EMAIL PROTECTED] Subject: RE: [UAI] functional_vs_causal models Greetings :- Thank you, Professor Zadeh, for your reply to my inquiry. Your remarks reinforce my impression that these exchanges would benefit from an authentic definition of partial truth. I confess anew that I am unable to guess the meaning from the examples. "Check-out time is 1 pm," for instance, is laconic but clear. After 1 pm, one has something to negotiate with the inn-keeper. The negotiation may be trivial, and the sign does not say otherwise. The sign simply tells when there need be no negotiation at all. As for the count of tall men in a room with no definition of "tall," then I imagine a situation similar to being asked for the count of men who stand 190 or more cm. with no tape measure. Both problems dissolve if I am supplied with a standard for classification which can actually be applied. Failing that, you will in each task get an estimate, my estimate, rather than the count. If you would prefer to call your estimate in either situation "the count," then go ahead, so long as we both know that you give an unusual meaning to a common word; two common words, in fact, since "the" rarely means "my" in careful speech. I thank Professor Zadeh for moving a bit beyond examples in his discussion suggesting that one might understand "partial truth" by analogy to other partial things. _Partial_ is indeed a fine concept with many varied applications. I do not know what it means in connection with the truthfulness of a proposition. I also do not know what it means in connection with other categorical estates, such as pregnancy, humanness, or left-handedness. That prevents my understanding of partial truth by analogy to other uses of _partial_. I am not denying that there could be a meaning for _partial_ adjoined to any of those things, only saying that the meaning would not be obvious, and so asking Professor Zadeh what his meaning is in the case of partial truth. Please define partial truth, Professor Zadeh.
