More on the law, with apologies if the interest in these matters is slight.
A number of further examples that are designed to show, I think, how "legal reasoning" may be advanced by differing formal methods have been offered. I don't think they show that. Rather, they demonstrate as I previously suggested that the arguments among different approaches to ambiguity and uncertainty don't have obvious implications for the law. Some of them also demonstrate a lack of understanding of how the law operates. A few brief comments on the examples: > > A simple example which clarifies the difference is one that > > I used before. If Robert is half- German and half- French, and I say > > that Robert is German, then what I say is half-true, with no uncertainty > > involved. On the other hand, if I am not sure whether Robert is German > > or not German, then the probability that he is German may be 0.5. In > > the first case, we have partial truth and no uncertainty ,while in the > > second case we have partial certainty of full truth. A. If Robert is half-German and half-French, whether he is one or the other depends on the purpose for which the question is asked. That, in turns, depends on substantive law. If Germany or France has a statute that makes a person a citizen if they are "half" one or the other, then for purposes of German law Robert is German and for purposes of French law here is French. And so on. Suppose the statute of either state was ambiguous, so that it wasn't clear on its face what the definition of citizenship is. This might appear to generate an interesting question about "partial truth" and so on, but it doesn't. If faced with the question whether Robert is German, given the ambiguous German statute, the ambiguity will be solved by reference to substantive criteria concerning such things as legislative intent, statutory purpose, canons of construction, social objectives, and the like. No court in the United States at least (and actually I am only making claims about US courts) would consult any formal probability or mathematical theory to resolve such a case. There are many works on legal process and statutory interpretations, and I would be happy to provide the standard canon for anyone who would like to see them. One will see in them many interesting points, but one of them will not be that substantive determinations about the meaning of law should be determined by reference to differing conceptions of uncertainty and ambiguity. B. If we consider uncertainty, we reach an analogous conclusion. It may be uncertain whether Robert is German or French. Here the law provides rules for decision under uncertainty. Here there may be some scope to argue that the nature of that uncertainty is better captured by one formal approach over another, but there are no practical consequences to doing so (not to diminish the achievement in other respects). To take just a simple example, in the US civil litigation is designed to affect errors in one way or another. That, again, is a substantive determination that is independent of how probability is conceived. No matter how it is conceived, the same error rule will be applied, making the probability debate epiphenomenal. Here, by the way, standard probability theory has a decided advantage over fuzzy sets in its ability to articulate clearly the consequences of different choices. Before an even remotely plausible argument for fuzzy sets could be sustained in this context, the decision rule that would optimize social interests would have to constructed that has the same formal properties with respect to errors as the .5 rule understood as a conventional probability. Perhaps fuzzy set theorists have worked this out, and I would be glad to learn of it. Nonetheless, at the end of the day, it is the errors that matter rather than the characterization of the nature of uncertainty. > > > > In the realm of law and legal reasoning, most assertions are > > both partially true and partially certain. > > > > l. The tall Swedes problem: Most Swedes are tall. What is > > the average height of Swedes? > > > > 2. Usually it is not very cold ,and usually it is not very > > hot in Berkeley. What is the average temperature in Berkeley? The two questions above demonstrate precisely the misunderstanding about the nature of legal processes that I referred to in my earlier email. If either of these questions mattered, they would be resolved through investigation. And, interestingly, a quick google search yielded answers to both. The point, which obviously I failed to make clear previously, is that legal processes are not formal processes that are stuck with the first articulation of a problem. They are organic processes that can respond in various ways, and in these two by finding out the answer or doing the primary research necessary to find out the answer (if it is not preexist the question). > > > > 3. The Robert example: Usually Robert returns from work at > > about 6 pm. What is the probability that Robert is home at about 6 :l5 pm? When? Always? Generally? A particular day? Why does it matter? Again, this question simply reflects a misunderstanding of litigation. The answer above more or less applies here. The difference would be in the nature of the investigation. > > > > 4. The balls- in- box problem: A box contains about 20 > > black and white balls. Most are black. There are several times as many > > black balls as white balls. What is the probability that a ball drawn at > > random is white? Again, what difference does it make? without knowing that, one can make nothing of this hypothetical. And are we talking about a sequence or a single event? Were there witnesses, etc., etc., etc. Most generally, if the question is whether a plaintiff has proved that the ball is white under these circumstances, where that is what he must prove, the answer is plainly no if this is all the evidence there is. It is more controversial if the same answer is yes if he has to prove the drawn ball is black, but that is almost surely the correct answer. Whether it is or not has to do, again, with how one conceives the purposes of the system of litigation, and the incentives, generally speaking, that one wants to create for the production of information at trial. None of that will be affected by resolving debates over various ways to characterize this problem. Best regards to all. Ronald J. Allen Wigmore Professor of Law Northwestern University Phone: 312-503-8372 Fax: 312-503-2035
