Several questions from your ever humble law teacher: 1. Are the following two separate responses by Charles Twardy and Joseph Halpern to Lotfi Zadeh consistent?:
Joseph Halpern: >> [Lotfi Zadeh:] In turn, this implies that the assumption that >> causality is a matter of degree should be the point of departure in any >> formalized theory of causality which aspires to provide a body of >> operational concepts and techniques for dealing with causal dependencies >> in realistic settings. >Here again I disagree. Our notion of degree of responsibility (which is a >number between 0 and 1) is simply a refinement of the 0-1 notion of >causality. (A has a positive degree of responsibility for B iff A is a >cause of B.) ... > [Lotfi Zadeh:] What this suggests is that, in realistic > settings, causal dependence is certainly not a matter of yes or no; > rather, it is a matter of degree. >Again, I don't see why it suggests this at all. Although I do agree that >it's useful to speak of degree of responsibility, that's perfectly >compatible with also have 0-1 notion of causality. Charles Twardy: >}[Lotfi Zadeh:] words, we have to assume that causality and related concepts such as >}responsibility and propensity are a matter of degree >I believe that is what "probabilistic causality" has always been about. >Pearl, Halpern, Hitchcock, and others lay a nice foundation for measuring >degrees of influence, considering multiple causes, multiple paths for >single causes, and even retrospectively examining relative blame. No >"yes/no" limits there. 2. Is the reconciliation of the above two positions or explanations something like the following?: The question of whether or not A is a cause of X is bivalent, but the extent to which [event] A increases the probability of [event] X is answered by a calculus that speaks of degrees (but not merely of degrees of _belief_). 3. If the explanation in par. 2 above is correct (and my speculative rendering of the possible explanation for, or reconciliation of, the seemingly-disparate statements in pars. #2 and #3 may in fact be utterly and laughably incorrect) does Joseph Halpern's notion of "degree of responsibility" = "degree to which cause A increases probability of X"? (Forgive me: I haven't yet read the papers that Joseph Halpern referred the readers of the list to. I intend to do so very soon!) 4. If a comprehensive causal explanation of many phenomena is forever (or just for a "long time"?) beyond human reach, does it make sense (in those instances) to draw a sharp line between probabilistic causality and epistemic uncertainty? This question is related to my next question: 5. Is it possible -- I most certainly do not know the answer to this question --, it is possible that it makes sense to use fuzzy or rough set probabilities if we live in a world in which the causes that make our world work the way it does lie (forever?) beyond (full) human comprehension? That is, despite the many victories of the causal explanations found in many of the sciences, is it possible that _scientific_ understanding of some phenomena (or of some phenomena in some settings) is best or (more modestly:) well promoted by a better understanding of the "surface" explanations that human beings often seem to use when they wend through their way in the world? (Is _this_ question part of what the debate between the fuzzy set theorists and the fans of causal interpretations of the standard probability calculus is about?) My sense is that one of the strengths of attempts to model common sense is that human beings seemingly do make their way in the world without a full or even a very good understanding of the causal mechanisms that make the world work the way it does (but, then, yes, this point assumes that conscious common sense reasoning influences & improves practical human decision making). - --For purposes of par. or question #5 (immediately above) I leave aside the question of whether fuzzy set theory or rough set theory does capture (and illuminate and improve) common sense well -- BUT I readily confess that both fuzzy set and rough set theory seem to well capture the intuitions of at least some legal scholars about part (but only part, see below) of what is "going on" in legal reasoning -- for example, the idea of fuzzy and rough (and shifting!) -- here I use these words in their colloquial sense -- classifications is not recent: see Edward Levi's (erstwhile U. Chicago Law professor's, former U.S. Attorney's General) classic little book INTRODUCTION TO LEGAL REASONING (but, from this legal theorist's perspective, one of the oddities of fuzzy and rough set theories is that they have been used, not to model normative reasoning, but processes that, by conventional accounts, seem to involve "factual inference," e.g., the inferences one seemingly must make to run a kiln, a train system, or a camera). Final note (with your patience): Is it interesting to this audience to know that while fuzzy and rough sets seem to describe or evoke how in law classifications shift (or how things seem not clearly to belong in one legal classification/category or another), fuzzy and rough set theories seem (to this law teacher) to be less able to "get under the skin" of such elusive legal categories and explain what induces them, legal categories, to move or shift this way or that: for example, fuzzy sets and rough sets do not in any obvious way portray the kinds of arguments that are made in courtrooms about the meaning or appropriate meaning or interpretation of vague legal categories such as "due process" and "due care"; perhaps, i.e., a fuzzy or rough set theorist could predict the outcome of an appellate argument but (s)he could not function as counsel or advocate in a courtroom, where a _reason_ for a shift of a legal category this way or that way is sought and wanted by the court. Enough said -- or, very probably, much too much -- for today, peter tillers ***
