Dear Lotfi, Thank you again for your cordial and constructive response.
>...Underlying our exchanges is a basic difference in our views >regarding the sufficiency of standard probability theory, call it PT, >to deal with uncertainty and imprecision. In your view, which at >present is an overwhelmingly majority view, PT is sufficient. Excuse me? I would very much appreciate your not ascribing positions to me that I have on more than one occasion explicitly and to your face declined to state. I can recall on a number of occasions being pressured, by people in one or another camp of the "uncertainty wars," to state a firm position on whether I believe probability theory is sufficient to deal with all forms of uncertainty and imprecision. I always decline to do so. I respond that I find it most natural to think about problems I encounter in decision theoretic terms, but I recognize that not everyone shares my view of what is most natural. Whenever I have been presented with a problem in which someone claims fuzzy sets, belief functions, or any other formalism for that matter, is "better than" decision theory, I have always been able either to construct a decision theoretic argument for why the technique performs better than a decision theoretic approach, or to come up with a decision theoretic approach that beats it. In the former case, as I argued in a previous posting, a decision theoretic argument would in fact favor the technique that works "better." In the latter case, I would not state that decision theory is "better," but only that I have come up with a decision theoretic approach that has beat the best alternative anyone has devised to date. As a scientist, the most I am willing to state is that the approaches on which I have bet my career have thus far not been unseated by any challengers, and indeed seem at present to be gaining strength and adding followers. But all our scientific theories are provisional and stand ready to be challenged. Otherwise we are practicing religion, not science. I have no problems with anyone practicing religion, but if that's what it is, let's not call it science, please. The above is a sketch of the decision theoretic argument by which I justify devoting my career to decision theoretic methods. I most assuredly would *not* argue that *everyone* should devote him or herself exclusively to decision theory. Each of us must make our own career choices. You and I have had this conversation on several occasions, both in email and in person. I therefore find it difficult to understand why you continue to misstate my position on the matter. >In my >view, which at present is an overwhelmingly minority view, it is >not. In order to convince me to devote my energies elsewhere, one must argue not only that decision theory is inadequate to the problem at hand, but that the alternative is superior, or at the very least, not inferior. I have not seen an argument that convinces me. Others, as I noted above, may draw their own conclusions. >An exposition of my view may be found in the paper entitled >"Toward a Perception-Based Theory of Probabilistic Reasoning with >Imprecise Probabilities," which appeared in a special issue on >imprecise probabilities of the Journal of Statistical Planning and >Inference, Vol. 105, pp. 233-264, 2002, (downloadable at >http://www-bisc.cs.berkeley.edu/BISCProgram/Projects.htm). Your use of the term "perception" in this context mystifies me. Probability theory provides an excellent account of the physical processes by which perception operates. Indeed, probability theory has been stunningly successful at describing any physical process humanity has yet encountered. Indeed, quantum physics, a theory based fundamentally on probability, has predicted the existence of as-yet-unobserved physical processes that were subsequently confirmed by experiment. Any scientist who studies the biology and physiology of perception makes essential use of probability theory in his or her work. The examples you give seem to have more to do with the use of linguistic terms than with perception. Thus, I would think the label "linguistic imprecision" might be more apropos. Linguistic terms have whatever meaning the speakers of the language collectively attach to them. A community of speakers is perfectly free to define a language that operates by the rules of fuzzy logic. Such a language would tend to persist, according to the theory of evolution, to the extent that those in the community adopting it are able to communicate with each other sufficiently well to perform functions needed to survive and thrive. Perhaps fuzzy logic will turn out to have long-term survival value; perhaps not. If I had to attach a probability to which will last longer, probability or fuzzy logic, my bet would go to the former. On the other hand, those who study fuzzy logic have contributed to humanity's understanding of the process of reasoning under uncertainty. Cordially, Kathy Laskey
