Wednesday, July 29, 2009
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."
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Jeff, great post. Two related anecdotes: "the formal logicians are very skeptical of attempts to extend metaphors from formal logic into other areas." I took Mathematical Logic in college from Chris Hill, now at Brown, and while I unfortunately remember little of the actual content of the course, I do remember that when we got to Godel's theorem, he was practically jumping up and down as he told us: "Godel's theorem does NOT mean that self-referential statements are invalid!" (I think that's what he was saying. The jumping up and down I remember clearly.)
Second, re: the anonymous reviewer's quote: that seems a variation on an old joke I heard once, again I think from philosophers. Colleague to author: "This is the best article I've ever read about [topic]. Unfortunately, only [person X], [person Y], and you are interested in that topic."
Posted by: Bruce Boyden | Jul 29, 2009 11:10:09 AM
I look forward to more.
The reviewer's comment should prompt the publisher to go forward with your book.
One reason I put together the bibliographies in the Directed Reading series at Ratio Juris was to encourage if not facilitate "working in the space between [at least some] disciplines," so perhaps you won't mind if I publicize it here. Please see: http://ratiojuris.blogspot.com/2008/03/directed-reading.html
Forthcoming anon: a fairly comprehensive compilation for "science and technology" (sections on 'philosophy of science,' 'science, history of science, and science studies,' 'technology,' and the 'ethics of science and technology').
Posted by: Patrick S. O'Donnell | Jul 29, 2009 11:13:18 AM
A couple of small points: I think it's a bit misleading to say that Gödel, was "a member of the Vienna Circle", at least in the way that's normally understood (that he was a logical positivist or accepted their "manifesto", for example.) He was a student of Hans Hahn, a mathematician who was a circle member, and attended many of their meetings, but always insisted that he didn't accept their general outlook and was never a positivist. (I think he probably down-played the influence to some degree, but the general point is right.) He's offend referred to as an "associate" of the Circle, but not normally thought of, by those working on the history of the era, as a member. (Wikipedia seems to disagree with this, but here I'll go with the scholars of analytic philosophy that I know and w/ Godel's own statements, I think.) Secondly, it's probably better to say that Godel's incompleteness proof shows that any system complex enough to establish the truths of arithmetic is either complete or decidable but not both. There are systems that are pretty complex but less complex than that needed to establish the truths of arithmetic that are decidable. (Several sub-sets of the truths of arithmetic, for example, and Godel himself showed that first-order logic is both complete and decidable.) Your way of putting it isn't exactly wrong, but I worry that it lends itself more to the sort of distortions and abuses of Godel's theorem that really need to be avoided.
Posted by: Matt | Jul 29, 2009 1:08:51 PM
A couple of thoughts from a committed interdisciplinarian (who adores complexity theory, to boot):
First, I appreciate that you want to avoid the term "interdisciplinary," but the question you raise is absolutely the quintessential challenge for interdisciplinary studies, wherefrom it derives its power and its privilege:
"If you are constructing a thesis that borrows from many disciplines, how much of an expert in each discipline do you need to be?"
How much, indeed? I think one of the key justifications for an interdisciplinary approach begins by doubting the merit of the classical epistemic modality of atomizing complex systems into individual variables subject to investigation via a precise, refined, and iterative set of disciplinary tools. Indeed, William Newell makes precisely this point in his wonderful 2001 essay on interdisciplinary studies.
Newell argues, persuasively to my mind, that to gain anything approaching an accurate understanding of the behavior of complex adaptive systems, which not coincidentally characterize most human endeavors, attempting to isolate and study individual variables is virtually guaranteed to produce limited and oversimplified understandings. This is because, as I am certain you know, system behavior emerges from interactions between variables; hence isolating them produces distorted views of its role in system behavior.
However, this is not to suggest that disciplines are valueless. Quite the contrary, IMO; mastering a set of methods and literatures is, IMO, critical to the production of knowledge. The problem is not with disciplines per se, it is with the utter dominance of discipline-bounded knowledge modalities to complex systems.
But the scholar who tries to avoid these problems by bringing a range of modalities to understanding a particular set of complex problems risks a very great deal, practically speaking (career, etc., unless they are senior), and epistemically speaking, because it is hard enough to even gain proficiency in any one discipline, let alone multiple disciplines.
This is a difficult question to answer, one which I am trying to answer via my own practices, and one in which I hope a least worst solution emerges (I don't think any convincing conceptual resolution is out there). But FWIW, I have found one means of navigating the minefield is to acknowledge a few approaches/disciplines in which one can legitimately claim either expertise or proficiency. In my case, this is ethics, policy, law, and the history of medicine. I strive to bring the insights and approaches of a great many other "disciplines" into my work -- religious studies, narrative studies, disability studies, feminist theory, medical anthropology -- but I tend to self-identify as an exceedingly friendly outsider, rather than an active and informed practitioner.
Still, I love the questions you are asking and the approach you take (complexity theory? Wittgenstein? Interdisciplinarity? We should talk more).
BTW, Kellert's work is terrific.
Posted by: Daniel S. Goldberg | Jul 29, 2009 1:36:24 PM
Matt, your point on the Vienna Circle is well-taken. On the characterization of what the theorem stands for, also well-taken, and I suspect you are right in implying that more people refer to Godel's theorem than have done even as much as I have, which is to study my way through Nagel and Newman's Godel's Proof, and at the same time try to make sense of the original little pamphlet (which is far more difficult). And I've made it farther along in the undecidability proof than I have in the incompleteness proof.
The point, of course, is whether it has power as metaphor, and I confess to be suckered in by Stephen Hawking's comments to Leonard Mlodinow in the October, 2005 edition of Discover magazine to the effect that Godel's proof is one of the reasons he no longer thinks there's a theory of everything. And if you can't believe Hawking on this, who can you believe (if you're not an expert?)
Posted by: Jeff Lipshaw | Jul 29, 2009 3:24:08 PM
No worries at all on my part, Jeff. I saw those just as small nits to pick and not necessarily important to your project. On the "theory of everything" idea, I'm not sure what, exactly, Hawking had in mind, but I do think that Godel's ideas probably do rule out some approaches to such a project. Russell, for example, had hopes of going on from Principia Mathematical to "axiomatize" physics (I have to admit to not really being sure what that was supposed to mean), building up from the work in Principia. But, I take it, Godel's proof rules out the very possibility of this sort of project. If Hawking had something like that in mind, the Godel's work probably does rule it out in a fairly straight-forward way.
Posted by: Matt | Jul 29, 2009 3:42:15 PM
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