In an earlier message this humble law teacher wrote that fuzzy and rough
sets do not seem to allow us to get "under the skin" of shifting and vague
legal classifications. Now I would like to amend my statement. I think I
jumped to an unwarranted conclusion.
While it may be true that rough and fuzzy set theories do not (by
themselves) lay bare the possible reasons or grounds for rough, shifting,
and vague legal classifications, this "failing" is not necessarily a genuine
failing.
The "failing" of which I spoke, it now seems to me, is akin to a "failing"
of the standard probability calculus: if one believes that either
generalizations or law-like statements do, should, or can play a (good) role
in uncertain inference, one must also concede that the standard probability
calculus "fails" (by itself) to bring such propositions into play. But this
failing, of course, is not a true failing. Probability theory is a
mathematical or logical theory. That theory is susceptible of various
interpretations; and, as David Schum and Judea Pearl have shown (in their
different ways), some of those interpretations put law-like propositions or
generalizations into play.
I see no particular reason why the same sort of strategy could not work for
attempts to use fuzzy and rough sets to dissect the life and evolution of
vague and shifting legal classifications.
***
-- I leave aside for now the broader question of whether fuzzy and rough
sets make _logical_ sense. I do so because I don't want to appear or be
foolish: i.e., before I make any grand pronouncements about this basic
question in the presence of this eminent audience, I want to think out and
formulate my position with a great deal of care, perhaps with more logical
care than I am capable of exercising.
But I would like to say this much (once again) in defense of fuzzy and rough
sets:
(i) in law the phenomenon of "semantic uncertainty" -- the phenomenon of
categories with non-crisp and fluctuating boundaries (or definitions) --
seems both common and quite "real";
and
(ii) While I can _imagine_ that one might use the standard probability
calculus to express one's belief that the boundaries of some legal
classification are such and such -- and the titles of some literature I have
seen suggest that Bayesian analyses of semantic uncertainty are common now
--, this way of thinking about vague language (to my literally na�ve way of
thinking) does not readily capture what lawyers, judges etc. are thinking
when they say or assume that some (or all) legal categories _are_ vague.
Here is an ugly way of explaining what I am getting at in #(ii) above: Legal
professionals -- many of them, in any event -- believe in "stochastic
semantic indeterminacy." This is an indeterminacy that is analogous to the
"real-world probabilistic character" of some natural processes; i.e., vague
legal concepts are a bit like radioactive decay processes; i.e., legal
classifications have indeterminacy in their bones, they are inherently fuzzy
or rough, and they frequently have no "true meaning" on which it makes sense
to bet; i.e., a legal classification has a range of meanings, some of which
seem closer to the core; and some, less so. And so on.
My observations here leave entirely untouched the _really_ big question (in
my mind): how is it possible (and this does seem to be possible) -- how is
it possible to use fuzzy sets to draw inferences, not just about language,
but also about the "material [non-semantic] world"?
I have asked this group whether the theory of fuzzy sets or the cognate
theory of rough sets rests on an ontology that asserts the "reality" of
"surface" phenomena. But so far (apparently) no one thinks my question makes
enough sense to warrant even an attempt at an answer.
The other possible explanation I see for the occasional efficacy of fuzzy
logic in the management of information conveyed by perceptions and other
such things is a background assumption (a necessary background assumption?)
that the evolution and survival of the human species have led human beings
to have thoughts and sorting mechanisms that _somehow_ work and that,
therefore -- if one wishes to advance human understanding of the world -- it
makes sense for human beings to try to figure out how their now-innate
concepts manage to work as well as they do in the cosmos that human beings
inhabit. I wonder if this alternative possible explanation for the efficacy
of fuzzy thinking is as meaningless to this audience as was my conjecture
that an ontology of surfaces underlies fuzzy logic.
I suppose one possible answer to all of my questions is that fuzzy logic is
a poor stepchild to answers framed by the standard probability calculus,
which are the answers we will get if and when we study nature carefully
enough and long enough. (But, then, what should we do and how should we
think "in the meantime"?)
Many thanks for your thoughts,
pt
