Gödel's Loophole

AuthorF.E. Guerra-Pujol
PositionAssociate Professor, Barry University Dwayne O. Andreas School of Law
Pages637-673
GÖDEL’S LOOPHOLE
F.E. GUERRA-PUJOL*
Judge Phillip Forman: “[Germany] was under an evil
dictatorship . . . but fortunately, that’s not possible in America.”1
Kurt Gödel: “On the contrary, I know how that can happen. And I can
prove it!”2
Jorge Luis Borges: “En algún anaquel de algún hexágono (razonaron
los hombres) debe existir un libro que sea la cifra y el compendio perfecto
de todos los demás: algún bibliotecario lo ha recorrido y es análogo a un
dios.”3
Copyright © 2013, F.E. Guerra-Pujol.
* Associate Professor, Barry University Dwayne O. Andreas School of Law. J.D., Yale
Law School; B.A., University of California, Santa Barbara. This work was supported by a
research grant from Barry University. I thank Professors John Nowak, Juan Perea,
Alexander Tsesis, and Michael J. Zimmer for inviting me to present an earlier draft of this
Article at the Third Annual Constitutional Law Colloquium at the Loyola University
Chicago School of Law in November 2012, and I wish to thank John Nowak, Michael
Freitas-Mohallem, and Yaniv Roznai, in particular, for the their helpful comments on my
Article during the colloquium. I also wish to thank the organizers of the 2013
Southeast/Southwest People of Color Legal Scholarship Conference for inviting me to
present my Article at the University of Arkansas at Little Rock on April 5, 2013, especially
Deleso Alford, Patricia Broussard, Paul Gowder, Jamila Jefferson-Jones, and Isabel Medina
for their insightful comments and queries. In addition, I wish to thank A. Christopher
Bryant for directing my attention to the proposed Corwin Amendment of 1861, and once
again, I must thank my friend and colleague Orlando I. Martinez-Garci a for introducing me,
so many years ago, to the wonderful world of Kurt Gödel and Gödel’s beautiful
incompleteness theorem. Lastly, I thank my wife Sydjia Guerra for her love, support,
kindness, and patience. Any remaining errors in the Article are mine alone.
1 JOHN L. CASTI & WERNER DEPAULI, GÖDEL: A LIFE OF LOGIC 89 (2000). See also
Oskar Morgenstern, History of the Naturalization of Kurt Gödel 3 (Sept. 13, 1971)
(unpublished draft memorandum), available at http://morgenstern.jeffreykegler.com/Home/
files/Morgenstern_onGoedelcitizenship.pdf.
2 CASTI & DEPAULI, supra note 1, at 89.
3 JORGE LUIS BORGES, La Biblioteca de Babel, in FICCIONES 46, 51 (Gordon Brotherston
& Peter Hulme eds., Bristol Classical Press 1999) (1956) [hereinafter BORGES, La
Biblioteca de Babel]. In English, this passage means: “On some shelf in some hexagon [in
the Library of Babel], it was argued, there must exist a book that is the cipher and perfect
compendium of all other books [in the Library], and some librarian must have examined
that book; this librarian is analogous to a god.” JORGE LUIS BORGES, The Library of Babel,
(continued)
638 CAPITAL UNIVERSITY LAW REVIEW [41:637
I. INTRODUCTION: GÖDEL AND THE CONSTITUTION
In the words of the American constitutional law scholar John Nowak,
Gödel’s loophole “is one of the great unsolved problems of constitutional
law.”4 Stated briefly, the mathematician and philosopher Kurt Gödel once
claimed to have found a logical contradiction in the United States
Constitution, a fatal flaw that might transform our existing constitutional
democracy (in which political power is divided among different branches
of government) into a legalistic or military dictatorship (in which power is
concentrated in one individual or one branch of government). Yet, like the
lost proof of Fermat’s Last Theorem, in which the French mathematician
and jurist Pierre de Fermat claimed to have discovered a proof that the
equation xn + yn = zn has no integer solution when n > 2 and when x, y, and
z are not equal to zero,5 no one knows with certainty the particulars of
Gödel’s discovery.
The story of Kurt Gödel’s discovery of a deep logical flaw in the U.S.
Constitution has been retold many times before.6 Additionally, rampant
speculation surrounding Gödel’s lost discovery also abounds on the
Internet7 and has even found its way into a best-selling science fiction
in COLLECTED FICTIONS 112, 116 (Andrew Hurley trans., 1998) [hereinafter BORGES, The
Library of Babel].
4 Interview with John Nowak, Raymond & Mary Simon Chair in Constitutional Law,
Loyola University Chicago Sch. of Law, in Chi., Ill. (Nov. 2, 2012).
5 See, e.g., E.T. BELL, MEN OF MATHEMATICS 67–72 (1986); SIMON SINGH, FERMATS
ENIGMA: THE EPIC QUEST TO SOLVE THE WORLDS GREATEST MATHEMATICAL PROBLEM 59–
62 (1998).
6 See, e.g., Morgenstern, supra note 1, at 2 (offering a first-hand account); HAO WANG,
REFLECTIONS ON KURT GÖDEL 115–16 (1987) (offering a second-hand account, based in
part on Wang’s personal communications with Gödel). Most reported versions of this
episode, however, are “hearsay,” or th ird-hand, accounts. See, e.g., CASTI & DEPAU LI,
supra note 1, at 88–89; REBECCA GOLDSTEIN, INCOMPLETENESS: THE PROOF AND PARADOX
OF KURT GÖDEL 232–34 (2005); PALLE YOURGRAU, A WORLD WITHOUT TIME: THE
FORGOTTEN LEGACY OF GÖDEL AND EINSTEIN 98–99 (2005); M. Shubik, Oskar
Morgenstern: Mentor and Friend, 7 INTL J. GAME THEORY 131, 134 (1978); John W.
Dawson, Gödel and the Limits of Logic, 280 SCI. AM. 76, 80 (1999). Sanford Levinson has
offered a fourth-hand account. Sanford Levinso n, Shards of Citizenship, Shards of
Sovereignty: On the Continued Usefulness of an Old Vocabulary, 21 CONST. COMMENT.
601, 606 n.19 (2004) (reviewing T. ALEXANDER ALEINIKOFF, SEMBLANCES OF
SOVEREIGNTY: THE CONSTITUTION, THE STATE, AND AMERICAN CITIZENSHIP (2002)).
7 For example, search the phrase “Gödel and the Constit ution.”
2013] GÖDEL’S LOOPHOLE 639
novel.8 In sum, like the infinite library in Jorge Luis Borges’s beautiful
short story The Library of Babel,9 there are many possible branches and
permutations of Gödel’s lost discovery, but the essential facts of this
episode are as follows.
After Gödel applied to become a U.S. citizen in 1947, he prepared for
his citizenship interview by closely studying the Constitution.10 In the
course of his studies, perhaps on the eve of his citizenship hearing, Kurt
Gödel—a “reticent genius”11 and the “greatest logician since Aristotle”12
found a potentially fatal contradiction in the Constitution—what is referred
to in this Article as “Gödel’s loophole.” What was it? This Article offers
the following conjecture: the problem with the Constitution is the
amending power in Article V and the logical possibility of “self-
amendment.” In brief, if the amending clause of the Constitution can itself
be amended, then all express and implied limitations on the amending
power might be overcome through a constitutional self-amendment.
This Article is divided into five parts. Following this brief
introduction, Part II retells the story of Gödel’s lost discovery in greater
detail and attempts to answer a subsidiary question: Why is there no formal
record of Gödel’s constitutional loophole? Part III then reconstructs
Gödel’s loophole in four logical steps: (i) the Constitution contains a finite
number of legal provisions or “constitutional statements”; (ii) one of these
statements contains an amending-power statement, which permits
amendments to the Constitution when certain conditions or procedural
steps are met; (iii) the amending power can be used to amend itself; and
(iv) if the amending clause can amend itself, then all express and implied
limitations on the amending power might be overcome through a
constitutional amendment. Next, Part IV identifies other serious flaws or
“design defects” in the Constitution and explains why these alternatives are
probably not what Gödel had in mind. In summary, these alternative
theories of Gödel’s loophole are off the mark because they ignore his
interest in logical contradictions and the problem of self-reference. Part V
concludes.
8 See RUDY RUCKER, MATHEMATICIANS IN LOVE 295–96 (2006).
9 BORGES, La Biblioteca de Babel, supra note 3, at 46; BORGES, The Library of Babel,
supra note 3, at 112.
10 WALTER ISAACSON, EINSTEIN: HIS LIFE AND UNIVERSE 510 (2007). Unless otherwise
indicated, all references to the Constitution in this Article are to the U.S. Constitution.
11 Dawson, supra note 6, at 78.
12 HAO WANG, A LOGICAL JOURNEY 2 (1996) (statement by Robert Oppenheimer).

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