Living Outside the Paradigms

Two different pieces got me thinking again about issues of depth and breadth, or alternatively, working in the spaces between disciplines.  (I'm loath to call it either inter-disciplinary or cross-disciplinary, because, to some extent, those terms already tinge the meta-thinking about it.)  I was explaining this yesterday to my father-in-law, who is visiting us here in Michigan.  He's a really bright guy (a lawyer), and loves ideas, but he's not a scholar by any means, and so I'm obliged to use plain English.  It went like this.  If you are constructing a thesis that borrows from many disciplines, how much of an expert in each discipline do you need to be?  Moreover, if it's really original work, who is going to be able to judge whether the work constructively pushes the inquiry along, or is simply bullshit?*  In other words, if you are going to write in law and phrenology, do you have to have the equivalent of a professional certification (whatever that is) in both disciplines?  And if you do, have you been sufficiently co-opted by both disciplines so as to kill off whatever inclination you may have had to do "out of the box" thinking?  That's the dilemma, and I don't think it's any more resolvable by way of a silver bullet than most other long-standing irresolvable debates (like "Tastes Great" or "Less Filling").

At the recommendation of frequent commenter, A.J. Sutter, I recently started a book by Hamline University philosopher of science, Stephen Kellert, entitled Borrowed Knowledge:  Chaos Theory and the Challenge of Learning Across Disciplines.  At the same time, Brian Leiter linked the other day to my friend Rob Kar's recent review (in the Notre Dame Philosophical Reviews) of Brian's Naturalizing Jurisprudence.  The fun in reading something like Brian's work, or Rob's review of it, is the deep dive into a long-standing dialogue; in this case, the jurisprudential debates over the last century or so over the possibility of explaining, philosophically, scientifically, sociologically, or psychologically, how judges go about making law, and more fundamentally, what law is.  Nevertheless, if your intuition happens to be that looking at what judges do is like looking backwards through a telescope (i.e., not wrong, but focused on a very particular instance of how humans manage to order their affairs in the whole scheme of life, law, norms, and business), then you keep bouncing out of it with something of a "so what?"  The "so what?" is likely the reaction of most normal people to most of what philosophers, historians, literary critics, and other sojourners in the humanities do anyway, but I'm a lawyer-practitioner who somehow plopped into the academy, for God's sake, and like Guy Noir, trying to find answers to life's persistent questions.  I thus feel compelled to figure out what might bridge us from the relatively pure jurisprudence of a Leiter or Hart or Raz to what I spent more than a quarter century doing in the real world, which was legal work, but most of the time not involving judges.

More below the fold on the opposite of the deep dive - borrowing from one field to another.

A couple of years ago, I got hung up on Gödel's Theorem, which is one of the groundbreaking instances of pure thought in the last century.  For the uninitiated, Bertrand Russell and Alfred North Whitehead purported to reduce all of mathematics to a set of foundational axioms and rules of inference, focusing primarily on sets and numbers (cardinal, ordinal, real).  Kurt Gödel, a member of the Vienna Circle, constructed a lengthy proof, the purpose of which was to show that any complete complex system of formal logic, like arithmetic (particularly as encapsuled by Whitehead & North's Principia Mathematica), contained propositions that were formally undecidable within the system (i.e., that they could not be proved either true or false using the axioms and rules of inference).  In other words, the system could be either wholly consistent or complete, but not both.  The proof method involves a formal version of the Liar's Paradox, in which the following phrase translates into numbers:  "[Is not provable] is not provable."  In other words,  we get to the point where the system loops on itself, and tells us in formal terms, that the  proposition "is not provable" we've postulated within the system, and then working only from the system's basic axioms and rules of inference, and thus appearing to be provable, is not provable.  That's what makes it a theorem.

This is a mind-bending thing to contemplate, and Douglas Hofstadter's Gödel, Escher, Bach is perhaps the most famous attempt to derive metaphors from it.  But is it an effective metaphor for reducibility or limitations on knowledge, or other epistemological or metaphysical insights?  Gödel himself, like many mathematicians, was something of a Platonist. 

When I was fiddling around with this (and there's a lot of fiddling in this area - do a Lexis or Westlaw search in law reviews on "Gödel"), Larry Solum, ever wise, voiced the cautionary message:  the formal logicians are very skeptical of attempts to extend metaphors from formal logic into other areas.  But are the logicians entitled to define the extension of the metaphor?  That's what Kellert's book is about, but more generally as to all disciplines (including a discussion of the question "what's a good metaphor?").  In particular, he looks at metaphors to chaos theory, something HE knows about, in economics, law, and literature.

Well, I'm just diving into this, so more to come later.

* I may have a special interest in this.  I have a book proposal under review with a major university press.  The following comment from one of the anonymous reviewers is one that I kind of cherish:  "It is clear the author has a special range of interest and expertise, and this book weaves the author’s unique range of interests together with purpose.  The problem is that not many people share the author’s range of interests."