Science, Math, and the Essence of All Things

De_revolutionibus_orbium_coelestium2.JPGLast week Thomas Jefferson had Professor James Hackney of Northeastern University School of Law as our last speaker in our colloquium series. His talk focused on his book, Under Cover of Science: American Legal-Economic Theory and the Quest for Objectivity (featured at this past year’s AALS conference) and about his next steps on this topic. The book traces the way that science lurks behind the law and how law and economics has used the appearance of a scientific approach to justify its claims on jurisprudence. As the book’s site puts it “Hackney demonstrates how legal-economic thought has been affected by the prevailing philosophical ideas about objectivity, which have in turn evolved in response to groundbreaking scientific discoveries.” Now Science News reports that the June issue of the European Mathematical Society Newsletter has a debate over whether “new mathematical truths discovered or invented?” (annoyingly, the link to the Newsletter does not have the recent issue available as yet)

According to ScienceNews, one of the participants, Rueben Hersh of the University of New Mexico, “rejects the Platonic view, arguing instead that mathematics is a product of human culture, not fundamentally different from other human creations like music or law or money.” So as Hackney’s work makes a case that law and economics is not as objective as it seems, this group of articles about math suggests that even the science (or here related math) that provides the cover Hackney describes, lacks the objectivity it claims. The recent work on governance by Robert Ahdieh, Orly Lobel, and Mike Madison among others may be a response to the idea that law is not so objective. Rather it may be that the law seeks objectivity but faces complex and less than ideal situations. Governance ideas may fill that gap. We shall see.

Image: Title page of the second edition of Nicolaus Copernicus’ De revolutionibus orbium coelestium, printed 1566

Source: WikiCommons

License: Public Domain

cross-posted at Madisonian

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9 Responses

  1. Hey Deven,

    Frank blogged about Hackney’s book here:

    The quest for objectivity in Western culture in general is a particular interest of mine for some time, and it is central to my dissertation (on pain and pain management). I’d also recommend Lorraine Daston and Peter Galison’s new intellectual history on objectivity:

    (I’m about halfway through it).

    Needless to say, I am exceedingly dubious of the quest — it’s deeply quixotic, as well as ill-advised, IMO.

  2. Patrick S. O'Donnell says:

    I second Daniel’s recommendation of the Daston and Galison book (chock full of wonderful photographs), which I’ve read in full (sorry Daniel, I couldn’t resist!). One of the many provocative stories they relate is how “Sometime circa 1850 the modern sense of ‘objectivity’ had arrived in the major European languages, still paired with its ancestral opposite ‘subjectivity.’ Both had turned 180 degrees in meaning.”

    Unlike Daniel, I think the quest for objectivity (used in the sense of Nicholas Rescher in his Objectivity: The Obligations of Impersonal Reason, 1997), in spite of its excesses or idealizations, has provided the proof in the pudding (indeed, I think this is a reasonable inference to draw from Daston and Galison’s book). But I’m enough of a Daoist not to want to reify this quest, and to atttempt to see the polarity of subjectivity and objectivity on the order of yin and yang (and, thus, like the Daodejing, believe we could benefit from a bit more more yin).

  3. Patrick S. O'Donnell says:

    Regarding the claim “that mathematics is a product of human culture, not fundamentally different from other human creations like music or law or money,” one might consult, for the contrary view, Platonic-like arguments and examples from the field of physics I cited in a comment to a post on the Nobel Prize winner Murray Gell-Mann by Dean Jim Chen over at the Jurisdynamics blog:

    S. Chandrasekhar, Truth and Beauty: Aesthetics and Motivations in Science (Chicago, IL: University of Chicago Press, 1987),

    Ian Stewart’s Why Beauty is Truth: The History of Symmetry (New York: Basic Books, 2007), and

    A. Zee’s Fearful Symmetry: The Search for Beauty in Modern Physics (Princeton, NJ: Princeton University Press, 1999 ed.).

    Cf. too, Nigel Pennick, Sacred Geometry: Symbolism and Purpose in Religious Structures (1980), and, especially, Alfred S. Posamentier and Ingmar Lehman, The (Fabulous) Fibonacci Numbers (2007).

    As I’ve commented here before, Deirdre (as Donald) McCloskey’s books: The Rhetoric of Economics (1985), If You’re So Smart: The Narrative of Economic Expertise (1990), and Knowledge and Persuasion in Economics (1994), are essential in assessing the strengths and in particular the weaknesses of the rhetorical employment of mathematical formalism in economics. I happen to be constitutionally predisposed to finding much of the law and economics literature unavailing, but perhaps it’s only because I find not a little of it incomprehensible when not predictable. It has its place, I just wish it was confined to one small corner of the room.

  4. A.J. Sutter says:

    1. The question of whether mathematical truths are discovered or invented goes back over 100 years to the debate between Brouwer and Hilbert, and the question of whether you have discovered a mathematical object if you have not constructed it. The Hilbert camp, which allows non-constructive proofs such as proofs by contradiction, won out historically. (Ironically, Brouwer’s name appears in textbooks today most often for a non-constructive theorem of his own, in the field of topology.)

    For a concise survey of constructivist theories in science generally, see, e.g., J.-L. Le Moigne, “Les épistémologies constructivistes” (Presses Universitaires de France/Que sais-je, 3d ed. 2007).

    Incidentally, non-constructive proofs are the foundation for many of the mathematical stylings of the Bourbaki school, and, thanks to Debreu, Arrow and others, for the formalism of modern neoclassical economics. They are also popular in the field of game theory, not least in the work of Nash. See, inter alia, Philip Mirowski’s “Machine Dreams” (Cambridge UP 2002) & Roy Weintraub’s “How Economics Became a Mathematical Science” (Duke UP 2002).

    2. As for Prof. Hackney’s book, while I agree with his conclusion that “law & economics” does use a scientistic presentation to give a false lustre to its conclusions, his book does a very poor job of explaining why this is truer of the Chicago school than of other schools. In fact, as Philip Mirowski has shown in “More Heat than Light” (Cambridge UP 1989), it was Samuelson — dean of the politically liberal MIT school of NCE — who was in the vanguard of the scientistic program.

    Hackney ignores Samuelson in his book. He also ignores the work of Mirowski and many other historians of economics who have written about the history and significance of physics theories for NCE. And his ideological contrast between the relativity theories of Einstein (a Socialist, BTW) and the quantum indterminacy of Heisenberg (who worked for the Nazis) is perplexing if not risible in light of, among other things, relativistic quantum mechanics (born in 1928, thanks to Dirac), and the political proclivities of many physicists working in these fields.

    I go into more detail about Hackney’s argumentation in my Amazon review of his book. I wish he’d made a better case for his conclusion than he had, and I think a better case is possible. But to regard his book as a model of intellectual history requires either ignorance of the history of science and the history of NCE, or else being very easy-going in one’s standards of how to support an argument.

    3. Maybe Hackney’s conclusions have shock value because so many law profs have been steeped in the L&E ideology for so long? I admire Patrick O’Donnell for being brave enough to say publicly that he thinks L&E is unavailing (or even that “much” of it is). Adding to his recommended reading, I suggest:

    @ both Mirowski monographs I mentioned above;

    @ two books edited by Mirowski, “Agreement on Demand: Consumer Theory in the Twentieth Century” (Duke UP 2006; co-edited with D. Wade Hands) and a forthcoming book from Harvard UP, tentatively entitled “The Making of the Neoliberal Thought Collective” (2008; an essay on the origins of the Chicago School by R. Van Horn and Mirowski that will be included in this volume has been available online in draft form for a couple of years already); and

    @ the Nobel lecture of Joseph Stiglitz, wih special attention to his remarks about the two welfare theorems of NCE.

    For those of you who are law profs or law students, maybe there is greater moment to read some of these works than to read about aesthetic motivations in science.

  5. A.J. Sutter says:

    I apologize if the tone of my previous comment seems a bit high-handed, as it does to me on re-reading; I can wax a bit too rhapsodic when running a fever with flu, as I am now. But I’m also impatient at the (here I go again) apparent parochialism among legal theorists, especially when it comes to ignoring the history of economics per se when discussing L&E. You don’t need to extrapolate from freshman physics or to invoke the post-modern theory of objectivity to see that the Chicago School has had a political ideological motivation since its inception; old-fashioned archival research has shown that to be so.

  6. Patrick S. O'Donnell says:


    Would you recommend S.M. Amadae’s Rationalizing Capitalist Democracy: The Cold War Origins of Rational Choice Liberalism (2003)?

  7. A.J. Sutter says:

    Patrick, thanks for mentioning this book. I hadn’t heard of it before, so I scanned a few pages on Amazon. Obviously that’s too little basis even for one as ornery as I to comment on the book, but I can distinguish it from the two Mirowski monographs; they may be complementary.

    @ It takes Mirowski two books to cover the time period Amadae’s book seems to cover in one. In particular, other than his discussion of Samuelson, “More Heat Than Light” (MHTL) doesn’t discuss the post-WWII era, while “Machine Dreams” (MD) concentrates on this era. BTW Amadae’s book seems to have been in press when MD appeared, since Amadae comments only on MHTL.

    @ Amadae’s book seems to focus on social choice theory, while both MHTL and MD focus more on the scientific and mathematical metaphors in NCE. Maybe that makes Amadae’s book more interesting for an L&E specialist, but Mirowski addresses the very foundations of the whole NCE shebang. There are certain topics both are interested in, e.g. the RAND Corporation; one of Mirowski’s main themes in MD is who was funding the Cowles and MIT branches of NCE, so there is some overlap in this regard. (Neither Mirowski book discusses the Chigago School at length; that will be more the focus of his edited volume to be published later this year.)

    @ There are some important and interesting folks discussed at length in MD but not in Amadae. Gerard Debreu is especially important because the two welfare theorems he and Arrow proved are the only justification for NCE’s fondness for markets (other than the Chigago School’s fondness, which is based on politics, not theorems). Mirowski doesn’t critique the welfare theorems directly but he gives you a lot of background for the critique. (Reading Arrow’s and esp. Stiglitz’s Nobel lectures will help finish them off.) Debreu is absent from Amadae’s index. Also, MD talks a lot about game theory and John Nash in particular — plus the oft-forgotten fact that von Neumann himself abandoned the theory after a few years, moving on to cellular automata (now the basis of “complexity economics” and other simulations, such as espoused by Vern Smith, the Santa Fe Institute and others). Again, judging by the index, I don’t find as much attention to these topics in Amadae.

    @ I can’t be sure from what I can see on Amazon, but from the snip of the bibliography I can access, it looks like Amadae’s book is based on published sources only. MD is based extensively on archived correspondence and other unpublished manuscripts.

    @ I can definitely see that in terms of writing style, Mirowski’s MD is much funnier and more enjoyable than Amadae.

    So while Amadae may be a good book (and one that I will check out), it looks to be more of a complement or supplement to the two Mirowski books, rather than a substitute. I can’t recommend the Mirowski books highly enough. His whole research project helps to show that when it comes to the ‘E’ in L&E, there is much less than meets the eye.

  8. Patrick S. O'Donnell says:


    Thanks so much for that quite informative reply to my question. I have Machine Dreams and have skimmed through it, but I certainly will want to read it more thoroughly now! You appear to have an uncannily good grasp of the Amadae book without having read it! And thanks generally for your helpful (because knowledgeable) comments.

    Best wishes,


  9. Patrick S. O'Donnell says:

    I should have mentioned that I’ve always suspected, without the requisite expertise to confirm the suspicion in a manner that might convince others that, as you say, “when it comes to the ‘E’ in L&E, there is much less than meets the eye.”