In an address I am giving in early January -- in a talk or lecture called "Trial by Mathematics - Reconsidered" -- at a conference in Munich I will make roughly the following comments at the end of my address:
My thoughts about the possible purposes of formal analysis of factual inference and proof have a variety of causes and sources. But among the most important influences on my thinking about the purposes of formal theorizing about factual inference were my (feeble) efforts to discern the possible implications of fuzzy probability for uncertainty in law. Lotfi Zadeh's revolutionary way of looking at uncertainty struck me as both a powerful window and an inadequate one. In trying to puzzle out the reason for these opposing sentiments, I realized that fuzzy probability (to the extent that I understand it) addresses some types of uncertainty in law in an extremely enlightening way but that it does not address some other types of uncertainty in a way that I find useful or enlightening. For example, I found that I could imagine that fuzzy logic, with the appropriate semantic data, might someday usefully describe and predict -- to some degree -- the behavior of some legal concepts and words in the real judicial world, but I had a much harder time imagining -- and I still do -- how fuzzy logic could serve as a reasonably complete guide to argument directed at a court about the appropriate interpretation of some legal word or concept.1 [1. However, the distinction between predicting the behavior of legal concepts and making arguments about legal concepts in forum such as a courtroom is neither sharp nor simple. For example, there is the simple fact that predictions about the behavior of legal concepts are usually an important part of legal argument addressed to a legal decision maker such as a judge.] This awareness (though quite possibly rooted in a mistaken premise) made me more acutely aware of the variousness of the ways in which the standard probability calculus (and other types of formal theory) might be used to deal with uncertain inference in law.
Another matter has strongly influenced my thinking about "trial by mathematics." Although in this talk [this paper] I have not said which of the possible purposes of formal analysis that I previously mentioned are most likely "viable," I do wish to suggest that it may be very fruitful to develop conceptual tools that combine the function of inference support with the function of increasing the transparency of inference. There is a reasonable chance that human beings can use formal analysis to (i) make more transparent to themselves some of their own cognitive or mental processes and (ii) thereby improve (at least occasionally) the workings of "the logic or logics that are immanent, or present, in existing ordinary inconclusive reasoning about uncertain factual hypotheses that arise in legal settings." If one shares my view that much human reasoning is subconscious but that there are degrees of awareness (rather than a crisp disjunction between awareness and non-awareness),2 [2. The important work of Timothy van Gelder draws on this insight. See his web site (with references and discussion) at http://timvangelder.com/] there is some reason to believe or hope that some formal conceptual tools (such as diagrams of arguments) can lead human beings to better understand what they think subliminally (to some degree) and thereby put them in a position to evaluate, critique, and improve some reasoning of theirs that was previously largely subliminal. Of course, even if we have such tools, there is no guarantee that "facilitated human awareness" will improve the accuracy of human inference in legal proceedings such as trials. That's in part because some human mental processes will forever -- or at least for the foreseeable future -- remain inaccessible to introspection. Nonetheless, human progress in the sciences (and in some other "intellectual fields"?) suggests that a hope that rigorous introspection can and will improve the accuracy of human factual inferences is not irrational. And with such a rational hope, I think, we can and should be content.