Fuzzy Logic and Fuzzy Thinking in Law

I have been thinking about Lotfi Zadeh and his fuzzy logic. Indeed, I have been thinking, off and on, about Zadeh's fuzzy logic for decades. The law is full of fuzzy thinking. If there is a precise way to think about fuzzy ideas, legal scholars, judges, etc., should use it. On reflection and re-reflection and re-re-reflection etc., I do believe that Zadeh has given us important tools for radically better ways of thinking about fuzzy thinking.

It has often been said that the standard probability calculus can do all that fuzzy logic does. But such claims sometimes have the air of gratuitous dicta: one wants to see the proof in such probabilistic pudding. The fuzziness and vagueness of legal concepts (and many other types of concepts) usually can only awkwardly be characterized in terms of uncertainty. Legal principles, concepts, etc., often employ vague notions. There is a difference between a vague concept and an uncertain proposition. Probability theory sometimes deals well with uncertain propositions - but not so well with vague and fuzzy concepts.   In many of its iterations, Zadeh's fuzzy logic does not seem to reach beneath the surface of our fuzzy thinking (e.g., our conventional legal thinking), but seems just to accept the fuzziness of ordinary thinking. It might be said that fuzzy logic, in some its iterations, just describes the natural behavior of fuzzy terms, operators ("and" "or" etc.), and the like, and does not attempt to identify the causes, bases, or foundations of the fuzzy ideas we have and use.  This creates a puzzle: How can a logic that does not purport to identify the foundations, sources, or causes of fuzzy thinking give us useful new thoughts? (This question assumes that fuzzy thinking is a sort of disease.)  

The answer, I think, lies in the notion of tacit knowledge. There is genuine knowledge buried in some or much of our "ordinary" fuzzy thinking. (If that were not the case, few of us would survive even for one day.) Fuzzy logic's proven successes suggest that fuzzy logic may offer a way to uncover, or display, much "innate," or tacit, human knowledge.

These are admittedly deep and possibly murky waters, and I confess I do not have the ability to swim through them easily. I console myself with the thought that the acquisition of knowledge is a collective human enterprise and that there will be others who may be able to build on some of the paltry number of insights I may have acquired over the years. But if it turns out I have not learned much of enduring value about fuzzy thinking, the efforts I have made may have been worth the candle - because people can learn by studying other people's errors. &&&     The dynamic evidence page
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Physics, Soup & Legal Reasoning

Anyone with the slightest appreciation of the character of enormous events such as black holes (which might be said to be enormous non-events), see

NYTimes article on the biggest and baddest black hole yet 

and

Wikipedia article on black holes

and 

Hubblesite on black holes (highly recommended)

understandably hesitates to say anything that might reek to the slightest degree of absurd deconstructionist talk -- such as talk about "decentering gravity" (see the Sokal hoax). With this in mind, I pose several comments and questions seriatim (comments and questions I first posed on Google+):

First: A participant in the BISC list (Berkeley Initiative for Soft Computing list) asked an interesting question: Is human knowledge of causality fuzzy or is causality itself (also) fuzzy?

Second: Is it possible or desirable to combine the precision of, say, special relativity (ignore quantum mechanics, please) with fuzzy logic and probability?
Third: It is fair or accurate to say, yes?, that some or many or all models generated by "real physics" -- models such as Newtonian mechanics and special relativity -- make sense only as universal models (at least in our universe, i.e., putting aside a possible multiverse and the like)? If so, is it logically coherent to imagine (only to imagine, I say!) that such models are mechanisms, processes, or structures that exist in an ocean, or soup, of fuzziness? Or is such an image (an image of quantitatively-specifiable islands in a murky and elusive soup) too close -- fatally too close -- to the excesses and absurdities of deconstructionism, postmodernism, and all that (see the Sokal hoax and ridiculous talk about matters such as "decentering gravity")? Does "real physics" allow for the existence of soup, soup with an ontological status, i.e., "real (fuzzy?) soup"?
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[I repeat, here:] Even if I am just speculating, should I be embarrassed to be speculating in this fashion? (N.B. I repudiated Hegelianism, neo-Hegelianism, and all that, decades ago!)
My probable motivation for the speculation found here: I am groping for a way to explain and defend sloppy, soupy (and non-numerical) reasoning (which is prevalent in legal discourse and argument).