Lubet Replies to Edelman: Mistakes? What Mistakes?
1998; Northwestern University School of Law; Volume: 93; Issue: 1 Linguagem: Inglês
ISSN
0029-3571
Autores Tópico(s)Legal principles and applications
ResumoIt appears that Professor Paul Edelman disagrees with me about relative importance of forests and trees.1 I wrote an Essay on general subject of problem solving, trying to draw some lessons from calculus that might be helpful in understanding law.2 That's forest. Edelman plucks out a couple of particulars, claiming that my language was insufficiently precise. Those are trees. (And besides, I was not nearly so wrong as Edelman believes; more on that to follow.) Suffice to say that readers of my Review of David Berlinski's A Tour of Calculus3 will recall that modest intention of Essay was only to show that there are some parallels between way that mathematicians think about calculus and way that lawyers think about trials.4 In this, I think I was reasonably successful, and neither of Professor Edelman's cavils have convinced me to contrary. Edelman first complains that I misunderstood history of development of calculus in my discussion of Leibniz's early reliance on idea of infinitesimal numbers. These numbers, smaller than any other, were used by and later rejected by others as a basis for calculus. According to Edelman, anyone with mathematical training would have realized that Leibniz was right-and he quotes a footnote of Berlinski's to make his point.5 Curiously, Edelman omits Berlinski's final sentence. entire note is as follows, with Edelman's unacknowledged elision in italics: development of [non-Archimedean] fields by logician Abraham Robinson in twentieth century has made possible development of calculus entirely along lines anticipated by Leibnitz [sic]. But at a very great price in plausibility.6 So there seems to be some dissension, even among trained mathematicians, as to standing of infinitesimals.7 But disagreement, whatever its extent, actually strengthens my original point, which was to demonstrate that systems of thought mature over time.8 In 1666 had one view of infinitesimals, by 1734 Bishop Berkeley had attacked very idea.9 Centuries later Abraham Robinson revived infinitesimals, either righteously (per Edelman) or implausibly (per Berlinski). Using history of calculus as a parallel, I demonstrated that legal doctrine also progresses-with ideas being adopted, rejected, revived and refined. If a field so certain as math is subject to cyclical development, the: legal scholars ought to be hesitant indeed before proclaiming that they have any definite answers. One more turn of calculus wheel apparently brings infinitesimals back into play. Precisely! Edelman's second point is based upon my fundamental confusion about what means to compute area under a curve,10 as is accomplished in integral calculus. But he does little to clear up whatever confusion there may be, telling us only that it is difficult to be precise about what exactly area is.11 In any event, my use of integral calculus was explicitly metaphorical, offered as an example of accretion of detail in search of ineffable truth: The best that we can do is to strive for a method-a calculus-that can help us accrue knowledge and minimize mistakes.12 In my humble opinion, analogy holds. It does seem that Professor Edelman's ultimate complaint is that I ventured to write something about math notwithstanding my lack of serious mathematical training,'3 thus highlighting the danger of relying on secondhand knowledge of a field quite different from one's own. …
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