## Wednesday, January 23, 2013

### 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.
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