27 Stetson L. Rev. 559 (1997)

Steven D. Jamar3

© 1997 Steven D. Jamar

The life of the law has not been logic: it has been experience. The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellow-men, have a good deal more to do than syllogism in determining the rules by which men should be governed. The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.

Oliver Wendell Holmes4


This essay seeks to illuminate some of the limits of formal logic in a legal system through exploring some of the logic "problems" in the Religious Freedom Restoration Act (RFRA). Religious freedom is perhaps uniquely apt for examining the limits of logic in the law for two reasons. First, religious beliefs are based on faith and non-logical or extra-logical precepts (though internal logical consistency is often sought once the premises are adopted). Second, developing *560 a coherent, consistent, "logical" jurisprudence of religious freedom has proven to be particularly intractable.

Logic has a favored place in the law, but it is not its only or even its most important structural element. As so eloquently expressed by Justice Holmes well more than a century ago, what the rules of law are or should be owes more to history and human experience than to formal logic. [FN5] One cannot derive the law as it is from the mere application of logic to any particular set of first principles. Even if one could so derive the law, from what source does one logically obtain those first principles?

Two forms of logical reasoning, the syllogism and analogy, are central to the application of rules of law to particular situations. Another form, inductive reasoning, is useful when developing rules to be applied. But none of these forms of logic can be used in the law with mathematical rigor. Neither developing nor interpreting nor even applying the law are strictly logical processes.

Strict logical consistency and mathematical precision are not the stuff of either law or the medium in which it is necessarily expressed, language. [FN6] Indeed, the more fundamental the rule and the greater the interests at stake, the less precisely the interests can be corralled by language and bounded by law. The inherent fuzziness of language, including the language of the law, means that demands for complete precision are doomed to be perpetually unmet. Though one can choose relatively more precise or relatively less precise language to try to express the underlying concept, no expression will ever fully capture the essence, let alone the penumbra, of a right or rule. Since this is so, one ought not demand mathematical precision of the law and ought not condemn a law merely because it is imprecise.

There are, of course, limits. Genuine excessive vagueness and *561 unresolvable contradiction are two of them. But the fact that a law needs to be interpreted and applied in a less than wholly literal fashion is not a proper limit on the validity of a law. And yet this critique has been made by some who disfavor RFRA.

This essay examines RFRA using logic in a fairly formal sense (but not with true mathematical or even philosophical rigor). RFRA has a numberof logic problems, or at least weaknesses, which, if law were a strictly formal logical system, would either invalidate RFRA or would require a rethinking of formal logic rules. Furthermore, if the language used in RFRA is interpreted literally, then these logic problems are more serious. This essay uses these very weaknesses in RFRA to illustrate the limits of the usefulness of treating law as a formal logical system, and by extension, the limits of using formal logic to critique the law in general. [FN7] RFRA should stand or fall not on the basis of its actual or potential logical limitations, [FN8] but rather on the basis of other criteria such as workability, fairness, justice, and, of course, constitutionality. [FN9]

One other aspect of logic in the law is also brought into sharp focus through a consideration of RFRA. Though the logic and order of the law tends to be hierarchical with fairly well-defined levels of authority, e.g., constitution, legislation, administrative rules, executive interpretation and application, and guidelines, this simplistic typology need not always be followed. For example, court decisions are hard to place in just one level in the hierarchy.

More directly related to RFRA is the idea that intermediate or quasi-levels of authority exist within each level in the hierarchy. For example, there are foundational statutes on which subsequent enactments are built. Statutes sometimes create a complete organizational framework. Workers' compensation laws are of this type. Later legislatures may amend that law or later acts may affect that law, but they will also be affected by that foundational law and the rules, principles, and bureaucracies it created. Even seemingly unrelated laws may be affected by the pre-existence of such a foundational law. This phenomenon is ordinary, so ordinary in fact, that *562 we normally do not even notice it.

RFRA is also foundational, but in another sense. It is not just a framework- creating law, like a constitution or a workers' compensation statute. Instead, it seeks to place itself above all subsequent legislation as a meta-level statute to be followed unless displaced by a subsequently enacted law that explicitly refers to it. And even then it is to survive as to all other legislation. As discussed below, this creates a special kind of paradox, but one that can be resolved quite readily if one is willing to grant that strict logic does not control the law.


Law is in no small part a system of rules for deciding things in a relatively formal, structured way. The formality itself draws one toward making analogies to other formal systems, such as logic and mathematics, because the rules of a formal logical system such as arithmetic are also a set of rules for deciding things in a formal, structured way. [FN10] To explore some of the possible implications of analogizing from theorems of logic to the law, a general understanding of some formal logic aspects is required. [FN11] Consequently, this section first articulates some foundational ideas about the law and logic, then introduces some concepts from formal logic, and concludes with a brief reconsideration of law and logic. [FN12]

*563 A. Structural Supports for the Law

Logic is not the core of law and it is not superordinate to the law. Nonetheless, logic is important in the law because it is one of the structural elements of it. But it is not law's sole structural support. [FN13] Other structural elements may be considered to be of two types, experiential and instrumental. These structural supports for law, experiential, instrumental, and logical, can be examined separately and can be used to resolve seemingly- fatal flaws in a result another support might imply. But such resolutions are rarely the result of the application of pure logic; they are more often the result of experience-based judgment.

Experiential supports or sources of law include history, tradition, political beliefs and theories, power relationships in society, and the like.Laws are developed in no small part from society's experience with prior laws and many rules of law owe their continued existence more to tradition and inertia than to reason or purpose. Much of the law is the result of balancing the interests of various groups with power in society, not the result of pure dispassionate reason.

Instrumental supports or sources of structure are more obvious. They include federal and state constitutions, rules of construction, and methods of amendment. These instrumental structural elements stand, as it were, on their own authority (or the authority of the power sources that created them), not on any logical system and are not bound, in a rigorous way, by formal logic.

Logic supports the structure of law in two ways--instrumentally and formatively (or foundationally). This distinction between an instrumental use of logic and the use of logic as a foundational premise for determining legal rules is an important one: the use of logic in the "local" or instrumental sense is entirely appropriate and quite powerful; as a formative or foundational force, logic is also important and useful, but by itself it is insufficiently powerful to determine what the law is or should be.

The formative or foundational aspect of logic as a structural support for law is both subtle and pervasive. The importance of logic for understanding, evaluating, and structuring the law, even law premised on other sources (such as values or morality), is undeniable. Ideas from logic, e.g., the value of consistency, inform our *564 analysis and use of these structural elements, even though they do not ultimately limit them. Because law is inherently neither bound nor boundable by formal logic, to condemn a law because it is illogical in a formal sense, that is, because it contains a logical "flaw" such as inconsistency, contradiction, paradox, incompleteness, or indeterminacy, may miss a greater sense and meaning in the law. A law with a logical flaw may still be useful, valid, workable, and just.

In its instrumental role, fairly formal logic is frequently a useful and even powerful tool for at least three things: (1) as a means of examining a particular rule of law; (2) as a means of solving interpretative problems; and (3) as a means of determining the results of applying a law to a particular set of facts. Often one of the most devastating responses to an opponent's argument is to expose a fundamental flaw in its logic.

Much of legal reasoning is based on deductive reasoning (the syllogism); much is based on inductive reasoning (synthesis, finding, or extracting a rule from several sources, no one of which would be sufficient in itself); and much is based on analogizing. Although these instrumental uses of logic are appropriate and powerful, and although these modes of reasoning are to a great extent logical, even the most formal of them, the syllogism, when applied in a legal setting, loses formality. Indeed, Aristotle considered the differences to be so profound that he even used a different word for the syllogism in rhetoric-- enthymeme. [FN14]

The limited role of logic in legal reasoning is also visible in the use of other means of persuasion in legal reasoning. These other means include substantive appeals to policy and purpose, considerations of practicality or workability of rules, appeals to emotional truth, and persuasion through story- telling. But, even here, with the possible exception of persuasion through narrative, [FN15] once the substantive premises are articulated, the enthymeme or syllogism becomes the dominant form of legal reasoning.

Logic provides form in another way as well. Legal systems, like logic systems, have hierarchical structures with discrete levels of rules and analysis or evaluation, and, to some extent, the law is modeled on some of the hierarchical structures of logic systems. All *565 systems have at least two levels: axioms and theorems derived from those axioms. Logicians also are concerned with meta-levels and rules that take precedence over other rules. These two aspects of logic that give structure to the law, instrumental use and hierarchical organization, are visible throughout the balance of this essay.

B. Logic

The seeming formality of law, and its nature as being at least in part a system of rules, makes the analogy to formal systems in general, and logic in particular, seductive. To better evaluate the validity and limits of the analogy, some background in logic is necessary.

Certain systems of rules are called formal systems (or axiom systems or axiomatic systems). [FN16] A function of a formal system is to give structure to a given area of knowledge. [FN17] For example, the system known as formal logic gives structure to mathematics.

In mathematics, two kinds of statements could be called rules: axioms and theorems. Axioms are statements that are assumed to be true and are not provable within the system. For example, in arithmetic, the axioms are the rules we learned in elementary school, such as distribution, commutation, and identity. A set of axioms such as arithmetic is called an axiomatic system. Depending on the number and type of axioms that make up a system, an axiomatic system is said to have strength relative to other axiomatic systems.

In mathematics, theorems are those statements that are derived from axioms and can be proven from those axioms. [FN18] In general, theorems are statements that are made within an axiomatic *566 system. Those theorems that are made about an axiomatic system or systems are often referred to as meta-theorems. [FN19] Theorems about meta-theorems are called meta-meta- theorems. This classification can continue without end, thus creating an infinite number of hierarchies of explanation. This distinction between theorems made within a system and theorems made outside of a system is critical and will be explored more fully below. Suffice it for now that this attribute of formal systems implies (1) a formal system will always have relatively discrete hierarchies, and (2) that what one sees depends to no small extent on the frame of reference, on the context, on the level at one is looking, and on just what one is looking for.

In addition to axioms and theorems, there is a third kind of statement in logic called a hypothesis. A hypothesis can be made from within a system or about a system. The difference between a hypothesis and a theorem is that a hypothesis has not yet been proven or disproven. Some hypotheses cannot ever be proven or disproven using only the axioms of the system. One type of hypothesis considered at some length below is the paradox. Rather than discuss paradox here and again below, I have chosen to discuss paradoxes as they arise in the analysis of RFRA in Part III of this essay.

C. Law and Logic

One problem with treating the law as subject to the dictates of formal logic, is that it is not at all clear that the law has a defined or definable set of axioms, and it is certainly true that much of what is regarded as law is not readily provable through whatever axioms are articulated. [FN20] Indeed, it is likely that there is no complete set of axioms for any legal system; one can always find a new premise, concept, purpose, interest, or right that can be deemed axiomatic. The principle of equality of people is an axiom of our legal system today, but it certainly was not always the case. If one postulates axioms of sufficient generality as to be complete, then the very generality of those foundational principles prevent rigorous *567 derivation of functional rules from them. To continue the equality example, fleshing out the content of equality is more a matter of experience and purpose than logic. [FN21]

Even if a rule of law can be proven to be a theorem in a formal or strict sense (i.e., it follows logically from the rigorous application of procedural rules to a set of axioms), it is rare that any particular law could be derived from the application of logic to first principles (axioms) alone. That is, one could well have more than one theorem which is derived from that axiom and ultimately those theorems could well come into conflict with one another, though each one is fully valid as a matter of procedural logic.

For example, if a society values religious freedom, and takes as an axiom that religious freedom is a good thing, this of itself does not lead to any particular form of governmental involvement or non-involvement in religion. Many countries have state-supported religions, but still allow citizens religious freedom. While this state-support approach would not be acceptable in the United States, one cannot really claim that state support eliminates religious freedom. Favoring one religion over another certainly affects everyone, but it does not mean one is not free to believe and, to a large extent, practice as one sees fit. One cannot start from just one or two axioms about religious freedom and create only one rule of law; the same axioms, premises, principles, and values can lead to a variety of different laws within the same system, some of which will be inconsistent with each other, some of which will even require contradictory things, and some of which will be deemed more fundamental or hierarchically more important than others.


RFRA illustrates in several ways the limits of formal logic in the law and the necessity of using other constructs to properly understand and evaluate the law. The three illustrations of the limits of the usefulness of formal logic that are discussed below are (a) truth values, [FN22] (b) the problem of who has the power to establish *568 the ground rules for constitutional interpretation, [FN23] and (c) the intertwined problems of omnipotence and self-reference and the relationship of these problems to hierarchy. [FN24]

A. Truth Values

In formal logic, a statement is either true or false. It is not partially true, sometimes true, conditionally true, [FN25] or variably true. Furthermore, a statement in formal logic is precise. The law is quite different. Although in law one must often decide ultimately using only two truth values, e.g., guilty or innocent, liable or not liable, negligent or not negligent, the tests and rules used to get to that result are generally not so simple. Also, often the decision is a close one, with a good argument both ways, a 51-49 decision, not a 100-0 one. And sometimes the decisions are contrary to the truth because of the standards used for proof. [FN26] This fuzzy nature of language and the law is no surprise. But it does mean that pure syllogistic reasoning, which depends on being able to establish unequivocal sets or classifications, is not really sufficient for the law. The *569 syllogism requires that something either be in the classification or out of it. Binary thinking rules formal logic--true or false, in or out, on or off, one or zero. Legal tests are not so clean and their application not so tidy. Deciding whether a person is in or out of a set or classification often requires a judgment based on more than a formula of words. Deciding whether some action or other operative fact meets a test is similarly fraught with trouble. RFRA illustrates these problems as well.

RFRA adopts three standards to be used to measure whether a statute lawfully infringes on the exercise of religious freedom. None of these standards can be applied in an all-or-nothing fashion; none can be understood or applied using merely two truth values; none can be applied in a mechanical fashion with conclusions being clearly compelled by mere application of the standard. These standards are: (1) substantial burden, [FN27] (2) compelling state interest to permit imposition of that burden, [FN28] and (3) the least restrictive alternative available to meet the compelling state interest. [FN29]

(1) Substantial Burden. There is and can be no universal test to determine whether a governmental action imposes a substantial burden on a person's exercise of religion. Though the state probably should accept without much question or examination a claimant's assertion that the contested state action burdens the claimant's exercise of religion, the substantiality of that burden need not be conceded on just the say-so of the adherent. [FN30] To do so would eliminate the term "substantial" from the test because, to some people, any governmental burden is too much. To so hold would give the adherent a unit veto over the actions of the government. So the substantiality must be based on more than the bald assertion of the claimant. If this is conceded, then the substantialness must be seen as not an all-or-nothing proposition.

In deciding substantialness, one must examine the nature of *570 the person's religious exercise claimed to be burdened, the actual burden on that exercise (e.g., does it ban the exercise completely or does it just limit it to certain times and places?), and other case-specific factors. Indeed, substantialness cannot be determined in the abstract; it must be determined by weighing the compellingness of the government's asserted interest and the availability of alternatives for the government, which might well impose a less substantial burden on the religious exercise. As soon as one weighs interests and multiple factors, one is well past a binary analysis, well past "true or false" or "exists or does not exist" analysis.

The mere use of the term "substantial" eliminates any simple true or false approach. The term itself requires a weighing, a judgment, and an evaluation of alternatives. These are not the stuff of formal logic. At the end of the process, one must decide either "yes" or "no" (substantial burden or not), but the process and tests used to get to that decision are not bound by strict, formal logical evaluation. The fact that one will conclude with "true" or "false" (substantial burden or not) does not mean that the forms of reasoning to reach that result are themselves binary. Indeed, the opposite is true. The formal logical requirement of two truth values is not and cannot be met in most legal reasoning.

And yet, the formal logic concept of two truth values pervades the legal system, including RFRA. At the end of the day, one must decide whether the conduct is in or out, whether someone is a member of the class or not, or whether the state action substantially infringes or is acceptable. The result may be binary, but the decisional process is not.

(2) Compelling Interest. Deciding what is a compelling state interest is similarly problematic from a formal logic point of view. To take a binary, all-or-nothing approach to compelling interest would mean that one must decide that for a state interest to be compelling, it either must be compelling for all circumstances, or it is in fact not compelling under any circumstances. (This would tend to be the view of those who want the law to be closer to a logician's formal system than to a messy, pliable, functional ordering system based on shifting power bases, interests, and authority.) To be workable, the standard used to measure the state's compelling interest must be variable and must fit the situation. The greater the burden on exercise, the more compelling the state's interest must be. Zoning to restrict places of worship to certain areas seems a strong interest, at least if judged by the prevalence of zoning used in this way. But is it compelling? The burden on exercise of a group *571 coming together to worship when and where it wants seems minimal, but it is a burden. Is it substantial? Who is to judge? On what basis? Should we consider the amount of the burden at all? Or is there some basis on which to decide when an interest is compelling regardless of the substantiality of the burden and the availability and cost of alternatives? If there is, what is it? National security? Fire codes? Public mobility? Neighborhood homogeneity and traffic patterns? The interests of the community in general against a religious building? And so it would go with any sort of governmental restriction.

These things cannot be judged in a vacuum, separated from a particular situation or from the other factors. The state may have a compelling state interest in developing loyal, strong, and dedicated citizens and it may decide that saying the pledge of allegiance furthers this goal. But Jehovah's Witnesses may consider saying a pledge of allegiance to be contrary to their religious beliefs, and contend that saying it would be a substantial burden to them. But the state interest in insuring loyalty of citizens and in building a sense of nationalism seems compelling at least insofar as it is related to the ultimate survival of and peace within the state. Nonetheless, the courts have allowed Jehovah's Witnesses to not say the pledge of allegiance. That is, the state interest is insufficiently compelling to overcome the identified burden. [FN31] The point is this: the law of the excluded middle is no law in law. Binary thinking simply is insufficiently sophisticated to resolve these difficult problems. This logical messiness in RFRA ought not by itself doom it.

(3) The Least Restrictive Alternative. The state has a compelling interest in educating its next generation of citizens. Nonetheless, there are limits on this interest, including limiting compulsory education to certain younger ages. [FN32] The least restrictive means to achieve the compelling interest is to accommodate the religious claims at some age. But how does one decide at what age? Applying this least restrictive alternative test is, like the compelling interest test, not really a matter of applying the text in its pure form. That *572 is, it is not a matter of purely applying procedural, logical rules to a formula of words, treating them as a code separated from the meaning they stand for. What is the least restrictive alternative? Does the cost to the state enter into the calculus of "leastness?" If so, then the phrase "least restrictive alternative" means something other than purely the least intrusive possible act. It means something more along the lines of the least intrusion given other weighty concerns such as centralness of the practice to the adherent and the cost of the alternative to the state.

Under the compelling state interest test, greater restrictions will be allowed depending upon the weight given to the significance of the religious exercise, to the burden on the religious practice, to the state's identified interest, to the cost and practicality of the alternatives, and so on. A logical or mechanical approach simply will not work. No principle of logic can decide the importance or centrality of a religious belief or a state interest. One can perhaps try to develop another test to determine centrality, apply that test in a syllogistic form, and then compare one case to another using analogical reasoning, but, ultimately, one is stuck with an untestable value judgment.

Even trying to determine what alternatives would be available is not always easy. Similarly, trying to assess which alternative is least restrictive on the adherent is often difficult. And sometimes the least restrictive alternative would not be cost-effective and would have a serious adverse affect on other legitimate and compelling governmental interests. The only way to resolve such a dilemma is with a sliding scale that takes these three concepts into account, i.e., substantiality of the burden, compellingness of the interest, and restrictiveness of the accommodation. For none of these items are the truth-values simply yes or no, true or false, or on or off. Thus, a formal logic with only two truth values is not powerful enough to comprehend law.

This conclusion is unremarkable, but it seems that from time to time some lawyers seek to ignore Justice Holmes' insight and try to treat law and language as if they were in fact binary and precise, and that every statement is either true or false. That is not how it works and it cannot so work.

At some point, the least-restrictive-means approach is not really used by the court; the court balances the alternative against the cost of doing it. At some point, the adherent's or the government's interest becomes attenuated. At some point, even a modest burden can be a substantial one, given the slight weight of the putative *573 state interest.

Lest there be any doubt that Congress intended a balancing test, the statute itself recites a finding that "the compelling interest test as set forth in prior federal court rulings is a workable test for striking sensible balances between religious liberty and competing prior governmental interests." [FN33] Furthermore, in the purposes section, Congress stated that one of the purposes was "to restore the compelling interest test as set forth in Sherbert v. Verner, 374 U.S. 398 (1963) and Wisconsin v. Yoder, 406 U.S. 205 (1972)." [FN34] Both cases involved carefully nuanced consideration and balancing of competing state and religious interests.

The point here is that simple syllogistic logic and simple duality of truth values are woefully insufficient to resolve these fundamental problems of balance, justice, and freedom. Formal logic is not nearly a strong enough tool to decide RFRA claims.

B. Power to Set Standards of Constitutional Interpretation

A second RFRA problem with logical dimensions concerns not the fuzziness of language and not what RFRA is (a piece of duly enacted legislation), but what RFRA does--it seemingly overturns a United States Supreme Court decision [FN35] setting standards of constitutional interpretation for a fundamental right. This seems to upset the hierarchical apple cart of placing the Constitution above statutes. Even though one can restore the apple cart at a higher level of abstraction, at the least it must be conceded that such actions call into question the idea of a strict hierarchy of authority and application.

Overturning a decision of the Supreme Court is not remarkable in itself-- Congress does it whenever it thinks that the Court misinterprets or misapplies a congressional enactment (e.g., the Civil Rights Act of 1991 [FN36] overturned the Wards Cove Packing Co. v. Antonio [FN37] interpretation of Title VII disparate impact claims. [FN38]) What is unusual is Congress substituting its judgment for that of the Supreme Court not with respect to interpreting a statute, but *574 rather with respect to determining the approach or test used to evaluate claims of infringement of the fundamental individual rights guaranteed by the Constitution. [FN39] Though technically RFRA is a statute and provides an independent ground for preserving free exercise of rights, through RFRA Congress essentially seeks to preempt or co- opt the Supreme Court's traditional prerogative of setting the grounds for interpreting First Amendment claims of free exercise of religion. [FN40] It is this aspect that challenges any claim to the legal system having a pure hierarchy.

RFRA's effect of changing the standard for free exercise claims is plain both from the intent of Congress and from the operation of the statute. In enacting RFRA, Congress explicitly made two findings to support its action. First, Congress found that "governments should not substantially burden religious exercise without compelling justification." [FN41] Second, and even more remarkable for its language, Congress found that "in Employment Division v. Smith, 494 U.S. 872 (1990) the Supreme Court virtually eliminated the requirement that the government justify burdens on religious exercise imposed by laws neutral toward religion." [FN42]

The statute, in effect, operates as a substitute for free exercise claims since it covers the same ground and sets a higher hurdle. If one clears RFRA, one clears the Court's test easily. Congress cannot enact legislation that grants the government greater powers and provides individuals with less protection for their individual constitutional rights than the Constitution requires. But Congress can provide greater protection, at least with respect to the federal government, though not, apparently, with respect to the states if the power is traced to the Fourteenth Amendment. [FN43] And, with respect to certain rights at least, Congress can implement the broad provisions of the various rights memorialized in the Constitution, e.g., *575 the Equal Voting Rights Act of 1965 [FN44] implementing the Thirteenth Amendment. But, can or ought Congress be able to substitute its judgment about the appropriate test to be used to evaluate claims of infringement of certain individual rights?

Though the hierarchial problem of authority gets tangled by the substance of the law itself, the more profound logic problem is at another level, the level of power and authority of the acting bodies, i.e., Congress and the Supreme Court. The logic problem at this level is this: which body is to have the final say in such matters? Though one can recite reasons for one result or another, this is a matter of policy and politics, not of logic. Marbury v. Madison [FN45] did not need to be decided the way it was. [FN46] And that is my point. There is nothing inherently more logical about one approach or the other. Once one adopts certain premises then logic kicks in, but these premises themselves are either axioms or hypotheses (as opposed to being theorems) and are eminently debatable. [FN47]

This is a matter of what Professor Suber calls "global reasoning," not "local reasoning." [FN48] That is, one must step outside the narrow system of legal rules to decide the issue. Syllogisms and legal rules per se are not sufficient. One can and ought to discuss separation of powers, judicial competence, minority protection in the courts from overweening majoritarian influences, democratic decisionmaking, and the like, but one cannot point to a principle that must be accepted as a matter of logic as the guiding principle for this sort of problem. Logic matters only in the sense of trying to reason from whatever principles and premises one considers most forceful. But the underlying explanations are ultimately not logical; they are political. They are, to use Professor Suber's terminology, a matter of reasoning in the sense of discourse over time, not a matter of the application of formal logic.

*576 At this level of discussion, formal logic ultimately fails to provide an answer. The forms of logic can be used to explain one's reasons, but ultimately this is a matter to be resolved through democratic discourse over time or through processes set up by democratic means (e.g., the Constitution and the Supreme Court may be empowered to decide these issue), but this issue is not a matter to be resolved by deferring to a priesthood of logicians.

C. Paradox, Self-reference, Omnipotence, Hierarchies, and Implied Amendment

Perhaps the most precisely definable logic problem in RFRA arises from RFRA's interpretation clause. [FN49] The interpretation clause purports to bind future Congresses to RFRA by stating that future legislation is to be interpreted as being subject to the provisions of RFRA. In effect, RFRA cannot be impliedly amended by later enactments, and later enactments cannot create rights or obligations inconsistent with RFRA without explicitly reciting a congressional intention to do so. To have later legislation not subject to RFRA, any future law that Congress enacts must explicitly state that it is not subject to RFRA.

RFRA is thus a statute that sets itself up as superior to contemporaneous, pre-existing, and subsequent statutes. It is, with respect to its affect on other statutes, constitution-like. This sort of statute messes up the normal, "logical" hierarchy of statutory law in a constitutional system. [FN50] In essence, Congress is creating an intermediate level of law between regular enactments and constitution, sort of a sub-constitution or super-statute.

Just the slightest amount of effort uncovers a paradox here. The paradox is that a standard canon of interpretation states that a later statute takes precedence over an earlier inconsistent one. [FN51] *577 Thus, one could argue that giving effect to the later statute, which ignores RFRA, is correct under one rule of law. Under the rule RFRA purports to make, the later law is to give way to the former--which directly contradicts the canon of interpretation. [FN52]

If one stays just within the system of rules of interpretation, which for these purposes includes both the later-takes-precedence and the RFRA limitation, one cannot decide whether to use the RFRA rule of interpretation or the later-controls-prior rule of interpretation. Both are law. Both are valid. Each leads to an opposite result. As long as one stays within the narrow confines of the universe of interpretation rules themselves, one is stuck with an undecidable proposition, a paradox. To better evaluate whether this paradox is real or illusory, a fairly-detailed digression into certain types of logical paradoxes is appropriate. [FN53]

In formal logic, a paradox is a type of unprovable hypothesis, that is, it is a non-axiom, non-theorem mathematical statement. However, as will be seen, some of these logical paradoxes have relatively straightforward real-world solutions. That is, by stepping out of the artificial constraints of the formal logic system, the problem can be made to disappear, or at least can be resolved in a satisfactory fashion without internally harming the formal system of logic.

There are a number of famous paradoxes. Considered here are Zeno's paradox and four self-referential paradoxes, i.e., the liar's paradox, Russell's paradox, the barber's paradox, and the omnipotence paradox. [FN54] Self- reference means what it says--the statement *578 refers to itself. For example, the sentence "This sentence is in the last sentence in this paragraph in this essay" is self-referential--it refers to itself. [FN55]

There are at least two logical problems that can arise from self-reference: (1) at times self-reference itself creates a paradox, and (2) at times the authority for evaluating the validity of a statement comes from the statement itself, e.g., "this statement is true" is self-referential and makes a value statement about itself (truth). The problem of self-reference can arise in a more convoluted way with one part of a more complex set of rules referring to other parts. In such situations, the self-reference is not in a single statement, but in a group of statements that refer to each other. The "self" is a set, not just a sentence. For example, a statute like the UCC could be considered such a set because the UCC refers to itself, at least in the form of sections referring to other sections, repeatedly.

Self-reference is not in itself a problem. [FN56] Simple cross- referencing, *579 incorporation by reference to other members of the set (e.g., a set of related contracts such as a sales agreement, service agreement, and financing agreement) and simple statements of a thing about itself (e.g., "This contract comes into force on May 1") are not necessarily problematic. But self-referential statements about certain fundamentals such as amendment ("this statute cannot be amended") and validity of the statute itself ("this statute is valid" or "this statute is supraordinate to others" (like RFRA's interpretation provision)) can be paradoxical.

One form of a self-referential paradox is known as the liar's paradox. In its basic form, the liar's paradox is simply: "This statement is false." This paradox is self-referential in that the statement makes an assertion about its own truth value. The paradox plays out as follows: If it is true that the statement is false, then the statement is false. If the statement is false, then it is not true that it is false, so the statement is true. If it is true, then it is false; if it is false, then it is true. This circular conundrum cannot be resolved within the system of the statement itself. Indeed, this particular paradox cannot be resolved at all even by meta-level analysis because no matter how removed one becomes, the core is the same--the statement asserts a proposition about itself that cannot be judged from outside the statement any better than from within the confines of the statement itself.

Other forms of the liar's paradox can have more or less satisfactory resolutions when one steps outside the logic box. For example, if a person asserts, "I always lie," then the paradox can disappear by the simple expedient of recognizing that the person may in fact mean that "I lie most of the time," and assuming that the use of the term "always" is not used literally, but is used poetically for emphasis. Or we can have some level of knowledge about the speaker other than that single statement so that we can use this other knowledge to evaluate the meaning of the statement. But if we take only the statement and the rules of logic as our universe, then it is a real paradox: If the statement is true, then the person speaking it always lies and so the statement itself must be a lie, and hence false. But if the statement is false, then the speaker sometimes tells the truth, and this contradicts the assertion of the *580 statement itself. A statement that is both true and false is a paradox. Like the simplest form of the liar's paradox above, this circle cannot be resolved within the framework of just the one speaker and one statement.

In general, when we have an external speaker, i.e., someone saying something about him or herself, rather than the statement itself saying something about itself, we automatically bring a world of context, nuance, and subtlety to bear on what at first blush seems an unsolvable logical problem. If we treat the problem as a purely logical one, this form of the paradox, and other more complex forms, [FN57] are inherently unresolvable due to the self- referential nature of the statements. Such statements are not understandable in purely formal terms, though they look like they should be. The syntax is right, they just do not mean anything. As noted above, one constant feature of these pure examples of the liar's paradox is that resort to meta-level analysis is not helpful. No matter how many steps removed from the initial statement one is, the truth or falsity of the assertion runs into the same wall.

More complicated than the liar's paradox is Russell's paradox, named after the philosopher and mathematician Bertrand Russell. This paradox involves a concept of a set, which is a collection of elements. Sets can contain anything: e.g., the set of all even numbers or the set of all pens in the mug on my desk. Sets can also contain other sets, e.g., the set of all sets of pens. Some sets can include themselves. For example, consider the set of all things that are not in the mug on my desk. That set includes itself because that set is not in the mug on my desk. This is a form of self-reference in which a set defines a member of itself as including itself.

Russell's paradox arises in the field of sets of sets that may contain themselves. Consider the set "S" that is defined as "all sets that are not members of themselves." Russell's paradox is this: If S is a set that is a member of itself, then S is a set that is not a member of itself. Conversely, if S is a set that is not a member of itself, then S is a member of itself because S is the set of all sets that are not members of themselves. Though this sounds like the liar's paradox (most paradoxes seem to sound somewhat alike), it is a different type of paradox. The liar's paradox shows that statements can *581 look sensible, but cannot be determined to be true or false. Though Russell's paradox is concerned with the truth or falsity of a statement, it is not the statement that is referring to itself that is the problem, it is the undecidability from within a system of whether something is in or outside of a set.

Russell's paradox shows that when dealing with formal systems involving sets, a set can be constructed that cannot be determined to be in or out ofthe system from within the system. That is, some sets can be well-formed that the formal system cannot account for. Russell's paradox demonstrates that any attempt to create a set theory that is fully complete and free of such paradoxes is doomed to failure. [FN58] These sets are self-referential and it is that quality that makes them so problematic for formal logic and formal systems.

However, for most legal sets, Russell's paradox is not too significant. [FN59] Most self-referential problems in the law are more in the nature of a statement making a statement about itself (truth, validity, or power) rather than an assertion about being in or out of a set. But one can find many statements in the law that create sets where those set-creating-statements refer to themselves. For example, a law which boldly declares that it is the criminal law code creates a set (everything in that code is a criminal law) and refers to itself. This sort of self-reference is normally not paradoxical because the authority for the validity of the statement is not really the statement itself, but the power and processes that enacted it, the legislative bill endorsed by the executive.

There are other types of paradoxes for which solutions are found by moving to a meta-level or by changing the frame of reference. For example, Zeno's paradox posits that one can never cross a room. In fact, one could not even start out. Zeno's paradox is this: To get to the other side of the room, one must first get half-way across. Now, to cross the remaining portion of the room, one must *582 again first get half-way across that remaining portion and so on indefinitely. Since any finite space can always be cut in half, one will never reach the other wall. This same logic keeps one from even starting: To get to the half-way point of the room, one must get half-way there. And to get to that half-way point, one must first get to the half-way point to it, and so on until one cannot even move. There is no "logical" refutation to the paradox. You must go through the midpoint of the room to get to the other side. Pure logic simply does not reflect reality in this case.

The solution to Zeno's paradox is simply to step out of the confines of the formal logic system and prove that motion is not geometric, but linear, and so one can indeed cross the room. That is, Zeno's paradox is an inaccurate description of physical reality and, as soon as one moves out of the system to the larger system of physical reality, the paradox disappears and simply becomes a curious misstatement of motion. The point is this--if one viewed logic as a full reflection of physical reality, there would be no way out. [FN60]

As intimated above, this same sort of erroneous use of logic can tie one in knots in the law. If one treats logic as the supraordinate organizing principle of law, then any illogical or paradoxical problem analogous to Zeno's paradox renders the legal system impotent or invalid. If one looks only to formal logic to resolve disputes of power between Congress and the Court, then the "can't start" paradox arises. Similarly, if one wants to use purely formal true-false logic in applying RFRA, one can hardly even begin before "improper" results happen. But, as in the case of Zeno's paradox not describing physical reality, so logic alone is inadequate to the task of being the full measuring stick or ordering principle of the law.

Another paradox that, like Zeno's paradox, has a solution when one steps outside the system, but, unlike Zeno's paradox, is in fact self-referential (like the liar's paradox), is the barber's paradox. A barber lives in a town and makes the following claim: "I shave the beards of all the men and only those men in the town who do not *583 shave themselves." The statement is self-referential because the speaker's statement is making an assertion (albeit indirectly) about the speaker (the barber) himself. The paradox arises when considering who shaves the barber. If the barber shaves himself, then he shaves a man who shaves himself, so he does not shave all and only those men who do not shave themselves. If he does not shave himself, and someone else does, then he does not shave all those who do not shave themselves, because he does not shave himself. And if he lets his beard grow, then he still does not shave all those who do not shave themselves.

Solving the barber's paradox requires "stepping out" of the system. One could find solutions such as the barber is a woman or, as with Zeno's paradox, simply point out that there is in fact no such town and no such barber and so this logical game does not conform to reality.

However, sometimes one need not step all the way out of formal systems to find a solution. Another way of "stepping out" of a system is to look for a different or expanded formal system in order to find a place for the barber. Or one can treat the formal system as authoritative and then evaluate the seeming paradox within that system.

To solve the problem of the barber in this way, one can treat the statement by the barber as a tentative statement to be tested, i.e., a hypothesis, rather than as an assertion of extant facts, i.e., a true statement. Then, testing the hypothesis with the formal system's rules of logic, one must conclude that such a barber cannot exist because the contradiction (the barber both does and does not shave himself) proves the falsity of the original statement. Thus, the paradox is an illusory one: it is not really a paradox, but merely a false statement.

Within the facts of the original paradox, you are stuck with a barber that not only does not fit into the system, but the existence and non-existence of which are a proven contradiction and, therefore, he does not exist. This solution may be tenable for artifically bounded formal logic systems, but cannot be used to solve many legal paradoxes of a similar ilk because, unlike the hypothetical barber, the law really exists; logical contradiction cannot refute existence of what actually is anymore than Zeno's paradox keeps me from crossing the room. Nonetheless, when interpreting a law, the use of hypothesis and testing the hypothesis for logical contradiction can be useful. One could choose to reject the interpretation that creates the contradiction. Or, if a law truly were to require two *584 contradictory behaviors at once, then it must be invalid and unenforceable unless rectified by amendment or interpretation to remove the contradictory obligations.

Another paradox of the barber-type is illustrated in the title of this essay. The title asserts that this article has no footnotes. If the title "This Article Has No Footnotes" is true, then footnote one of this essay must not be a footnote. Indeed, if one believes the title, one ought not even look for footnotes. But assuming one is familiar with the convention of law review article footnotes and upon seeing the footnote marker in the title one looks for, finds, and reads the footnote, then one is confronted with the assertion by the footnote that the title is false. The paradox arises because the title and the footnote cannot both be true, and, as long as the observer stays just within the system of the two assertions that refer to each other, one cannot tell which is true. If one believes the title, then what seems to be a footnote is not. If one believes the footnote, then the title is false. One denies the existence of the other; the other asserts something about the truth value of the former. (Note that this paradox combines the truth-value aspect of the liar's paradox (the statement in the footnote about the truth of the title) with the existence-value aspect of Russell's paradox (the statement in the title about the members of the set of things included in this essay.)) From within the closed, two-statement system one cannot decide which to believe. [FN61]

As in the barber's paradox, one can find a solution by bringing the barest of real-world information to the problem. If the title is treated as a hypothesis, the truth of which is to be tested, then *585 depending upon the "real- world" test used, it is either true or false. By choosing to read the essay according to some truth value related to importance or time, i.e., either hierarchically or temporally, one can resolve the problem. Using a hierarchical approach, one can consider a title as superior to a footnote and thus believe the title. This solution is logical, but wrong--there are footnotes. Or one can choose to believe what is read first rather than later. This may be logical, but again would lead to a wrong result.

As soon as we bring our meta-level, outsider analysis to the problem, two things are instantly obvious: (1) there are footnotes of the exact type one expects to see in a scholarly legal essay (though perhaps fewer of them and some are a bit quirky); and (2) the title (or at least part of it) is false. By moving out of the artifically closed system of the title and the first footnote, the apparent problem instantly disappears. One cannot use formal logic within the system to resolve the dilemma; one must use other approaches including experience, tradition, and expectations.

We can now see the paradox in the interpretation provision of RFRA. There are two authoritative statements both of which seem to control: RFRA says it controls later legislation; a canon of interpretation says the opposite. Just like the title-footnote problem. And just like the title-footnote problem, the solution to the RFRA interpretation provision is not to be found in logic. As with logical paradoxes that have real-world solutions, so the RFRA problem has a real-world solution: courts can simply decide to give effect to one rule of interpretation or the other and can decide on the basis of some premise or set of premises they take from RFRA and from outside RFRA. [FN62]

One important type of paradox for RFRA in particular and self-amendment in general is the omnipotence paradox. [FN63] The omnipotence paradox usually is framed in terms of a deity who is defined as omnipotent (or self-defined, in which case the paradox is also self-referential): Can an omnipotent being make an object that even that being could not move? The canard of the unstoppable force meeting the immovable object is a form of this paradox. If a being *586 is omnipotent, then that entity should be able to make something that is immovable, even by that entity. But if the entity is truly omnipotent, then it could move the immovable object. In law, this can show up in several forms: Can a current legislature forever bind all subsequent ones? Or can a legislature validly vote itself out of existence and delegate all of its powers to a "President for Life?" How does one judge the validity of such an act? By a constitution? By popular acquiescence? By "might makes right"? By logic?

The omnipotence paradox lurks in RFRA with respect to RFRA's assertion regarding its amendability, or more precisely, its lack of implied amendability. Can a sitting Congress limit a future Congress's action? Does Congress have the power to limit its successors or is each successor not bound by such attempts to make supraordinate law? The problem would be greater if the act provided that it was unamendable or required a supermajority for amendment or some such. (For the sake of clarity, there is no doubt that a later Congress can amend RFRA itself.) This would raise the omnipotence paradox in a stronger form than the statute raises it now. But the omnipotence paradox still exists in a weakened form: The question is, assuming that Congress could not get the votes to amend RFRA, and tried simply to ignore it, would later acts be subject to RFRA? The stronger form is also present, though not in the strongest form: the RFRA Congress seeks to limit a later Congress's ability to amend or modify by implication. Many later statutes might be inconsistent with RFRA and, under ordinary interpretation, the later would control the former, but here RFRA says Congress cannot do that.

But as with some of the other paradoxes, as soon as one steps out of the narrow, self-referential system of rules, the problem is resolvable by appeals to extra-logical values. That is, a set of values can be chosen that would make one or the other choice (the RFRA Congress controls or the later Congress does) preferable--and the choice of values is not really a matter of logic. For example, if one values free exercise over the power of a representative democratic Congress, one would choose to uphold the RFRA limitation on future laws. But if one places a premium on the value of current democratic expression of will, then the later-enactment-controls rule will be given force. The main point is that neither of these positions is required by logic and that both of them are tenable as a matter of the viability of the legal system. Neither position is "illogical."

One could also appeal to another rule of construction that says *587 that any explicit act of Congress controls a more vague general rule of law. In this setting, the RFRA provision could be considered the narrow, explicit rule that would control the general rule of law later enacted. But one could also argue that RFRA is the general law, that applies broadly across the entire realm of potential governmental conduct (it is hard to get much broader than that), so the other law is the narrow one. How does one decide which is general and which is specific in this setting? Howsoever one decides, this sort of solution is hierarchical, that is, one set of rules is held to be superior to others because of another rule that explicitly sets one above the others in terms of precedence.


This analysis of logical values, including two truth values, hierarchical structural forms, and self-referential paradoxes, and their application to RFRA merely illustrates that logic in the law has limits. The validity of RFRA should not be decided on purely logical grounds, but rather on the grounds of workability, policy, and extra-logical values. The logic problems can all be solved, or merely accepted as a part of the nature of the law so long as action is not stymied. I concur with Suber that the law can tolerate paradox, inconsistency, contradiction, and self-reference, but it cannot tolerate ossification and omnipotence. [FN64] Since RFRA can be amended, the problem of ossification is avoided and the omnipotence is of a limited kind.

Although the law in general should strive for consistency, and ought not loose itself from the current modest constraints of logic, both formal and informal, one ought not reject a law, a legal structure, or a legal system merely because one can find a logical problem with it. The vast reservoir of resources available to resolve the inconsistencies and to give effect to seemingly problematic laws ought to continue to be used. Experience, tradition, values, history, power, and justice all properly hold a place in structuring the law. In the law, logic is important, but it is not supreme.

1. The title of this article is false.

2. Religious Freedom Restoration Act (RFRA), 42 U.S.C. § 2000bb to - 4 (1994).

3. Professor of Law and Director of the Legal Research and Writing Program, Howard University School of Law. I am greatly indebted to Rosalind Manson (J.D., Howard University, 1996) for her many contributions to the substance of the logic portions of this Essay, for her insights and comments on various drafts, and for her writing of several pages of an early draft.

4. THE COMMON LAW 1 (1881).

[FN5]. See generally Peter Suber, Legal Reasoning After Post-Modern Critiques of Reason, 3 LEGAL WRITING 21, 22, 41 (1997) (distinguishing "local reasoning," which he defines as using law to solve discrete legal problems (primarily through using fairly formal modes of reasoning such as analogizing and applying rules of law syllogistically) from "global reasoning," which he ultimately defines as the "dialogue of free people over time" (used to decide what the law should be)).

[FN6]. See generally DOUGLAS R. HOFSTADTER, LE TON BEAU DE MAROT (1997). Hofstadter examines the problem of translation in general and of machine translation and artificial intelligence in particular. Hofstadter elegantly exposes the lack of neatness of language and the many-layered meaning of words. Though law strives for greater precision than does ordinary language, mathematical precision is neither possible nor desirable.

[FN7]. The assertion that the utility of logic is limited does not mean it is not both relevant and powerful, which indeed it is. It simply means that the power of a critique based on logic is limited and a formal logical flaw ought not in itself be fatal to the validity of the law.

[FN8]. This is not to say that RFRA and RFRA-like state laws could not be drafted better to avoid or reduce some of the logical and interpretive problems.

[FN9]. See Boerne v. Flores, 65 U.S.L.W. 4612 (U.S. June 25, 1997) (No. 95- 2074). See infra note 39 for a discussion of Boerne.

[FN10]. One commentator implies that a single law can be understood as a system of rules. See Stuart Banner, Please Don't Read the Title, 50 OHIO ST. L.J. 243, 246 (1989) (noting that some legal decisions create systems of decisions, in which each new decision is designed to decide the previous decision, but instead the new decision simply leads to creating a new decision). Mr. Banner's notion of rules, meta-rules, and meta-meta-rules, ad infinitum can be analogized to talking to a small child. If this child asks a question, frequently the child's response to your answer is "Why?". If you provide another answer, a "meta-answer," the child responds, "Why?". Each question and appropriate response takes the conversation to a level higher than the original question. See id. at 255. However, the law is not so strictly hierarchical, and the interrelationship of laws and opinions is not so tidy.

[FN11]. For an extensive discussion of these concepts written for the non- mathematician, see DOUGLAS R. HOFSTADTER, GODEL, ESCHER, BACH: AN ETERNAL GOLDEN BRAID (1979). For a more mathematical discussion, see GEORGE S. BOOLOS & RICHARD C. JEFFREY, COMPUTABILITY AND LOGIC (3d ed. 1989).

[FN12]. Other concepts are introduced and discussed as appropriate in Part III of this essay.

[FN13]. See Suber, supra note 5, at 45, 49.

[FN14]. ARISTOTLE ON RHETORIC 40-47, 186-215 (George A. Kennedy trans., 1991).

[FN15]. However, the power of a narrative to persuade depends on the resonance with the audience of the premises underlying the story and so narrative itself ultimately relies on both analogy and enthymeme, as well as purely emotional factors, to persuade.

[FN16]. I am greatly indebted to Ms. Rosalind Manson for her thoughtful efforts drafting early versions of the next several paragraphs.


[FN18]. One must be quite precise with language here. A mathematical theorem is a proposition that can be proven true or false using only the axioms of the system. A scientific theory (not theorem) is a proposition that is testable and demonstrable or perhaps disprovable, but is generally not provable in the same way that a mathematical theorem is provable within a particular axiomatic system. This distinction is often lost in the debates surrounding the theory of evolution. "Theory" used in this sense is not merely a hypothesis or conjecture. The theory of relativity, the theory of plate tectonics, and the theory of quantum dynamics are all powerful and generally accurate descriptions of how parts of the physical world works. A theorem in logic and mathematics is a bit different. Even here, one can see how problematic language is and the impossibility of strict, formal logic ever capturing human discourse.

[FN19]. The prefix "meta" comes from ancient Greek and means "beyond." RANDOM HOUSE DICTIONARY OF THE ENGLISH LANGUAGE 1206 (2d ed. 1987).

[FN20]. For instance, see Roy L. Stone-de Montpensier, Logic and Law: The Precedence of Precedents, 51 MINN. L. REV. 655 (1967). In Banner's words, the Stone-de Montpensier article "treat[s] the legal system as if it were a formal system, with silly results." Banner, supra note 2, at 244 n.4.

[FN21]. There are some rather significant consequences of this observation for the affirmative action debate, but that is far beyond the scope of this modest essay.

[FN22]. Unlike most of formal logic, the law often has more than two truth values (things are not merely true or false with no partial truths or uncertainty). Furthermore, values other than truth are also involved in the law, e.g., justice and fairness. I recognize that logic systems are being developed which incorporate "fuzzy logic" and the use of probabilistic reasoning, but those systems are beyond my personal knowledge. To the extent logicians are trying to build logic systems with more than two truth values, this is a welcome recognition of the limits of traditional formal logic. Also, insights of the branch of mathematics concerned with chaos theory has a number of useful insights about predictability of results, e.g., for some sets it is very difficult if not impossible to predict whether an item is in or out of the set without doing the calculations or, given some set of conditions, one cannot confidently predict what the system will be like after a time period lapses. The reason given is that even the slightest change of conditions alters the ultimate result significantly. The law is, in this sense at least, chaotic. See IVARS PETERSON, THE MATHEMATICAL TOURIST 144-73 (1988).

[FN23]. This question is unanswerable from within the system using merely formal logic. The decision to choose one branch or another may be reasonable or logical, loosely speaking, but the decision is driven by politics. To the extent it appears to be driven by logic, that appearance is strictly formal, not substantive. Logic is present through the application of logical forms of reasoning to the problem, through the use of logic as an instrument of reasoning, but the critical choices relate to the premises from which one is reasoning, and those are "extra-legal" premises, e.g., the judiciary should protect an individual's rights from the tyranny of the majority. This may be true, but it is not self-evident (axiomatic) nor is it a rule of law per se.


[FN25]. There are conditional statements in logic, e.g., if p, then q. The statement as a whole is either true or false, but the statement, though a condition, is not itself conditionally true.

[FN26]. For example, O.J. Simpson was guilty of murdering two people. But the legal standard was proof beyond a reasonable doubt, and a jury found reasonable doubt to exist so a guilty man walked. Though the evidence, such as I understood it from press reports, convinces me of his guilt, I can easily understand how a reasonable jury could consider the case not proven beyond a reasonable doubt.

[FN27]. See RFRA, 42 U.S.C. § 2000bb-1(a) (1994).

[FN28]. See id. § 2000bb-1(b).

[FN29]. See id.

[FN30]. In rejecting this test as one to be used in applying the First Amendment, the Court wrote "that it 'is not within the judicial ken to question the centrality of particular beliefs or practices to a faith, or the validity of particular litigants' interpretations of those creeds."' Boerne v. Flores, 65 U.S.L.W. 4612, 4613 (U.S. June 25, 1997) (No. 95-2074) (quoting Employment Div., Dep't of Human Resources v. Smith, 494 U.S. 872, 887 (1990)). Applying the words in an absolutist sense would lead to a kind of unit veto with each person being a law unto him- or herself. That would not be workable; consequently, some sort of balancing would be required.

[FN31]. Perhaps a term different from "compelling" would have been advisable or perhaps it would have been better to include a more explicit statement that the "compellingness" of the state's interest is to be weighed considering other factors such as the centrality of the claimed religious belief, the effect on others of accommodating that interest, and so on.

[FN32]. See generally Wisconsin v. Yoder, 406 U.S. 205 (1972) (holding states may not compel children after a certain age to attend schools).

[FN33]. 42 U.S.C. § 2000bb(a)(5) (emphasis added).

[FN34]. Id. § 2000bb(b)(1) (italics added).

[FN35]. See Employment Division v. Smith, 494 U.S. 872 (1990).

[FN36]. 42 U.S.C. § 1981 (1994).

[FN37]. 490 U.S. 642 (1989).

[FN38]. See H.R. REP. No. 102-166, at 26 (1991), reprinted in 1991 U.S.C.C.A.N. 549, 566.

[FN39]. The Supreme Court invalidated RFRA in part by holding it unconstitutional as applied to the states. See Boerne v. Flores, 65 U.S.L.W. 4612, 4620 (U.S. June 25, 1997) (No. 95-2074). The Court held that Congress could not, under the Fourteenth Amendment, impose on the states a more onerous duty than the First Amendment itself requires, as the First Amendment has been interpreted by the Supreme Court. See id. The statute was not held to be an authoritative interpretation of the scope of the First Amendment. See id. It was treated (properly) as a statute. See id. at 4612.

[FN40]. Though the statute no longer applies to the states, it may well still be applied to the federal government, unless the Court were to interpret it as a usurpation of its authority by Congress and invalidate it under the doctrine of the separation of powers.

[FN41]. 42 U.S.C. § 2000bb(a)(3) (1994).

[FN42]. Id. § 2000bb(a)(4) (italics added).

[FN43]. See Boerne, 65 U.S.L.W. at 4613; supra note 39.

[FN44]. 42 U.S.C. §§ 1971-1973gg-10 (1994).

[FN45]. 5 U.S. (1 Cranch) 137 (1803).

[FN46]. But it was rightly decided as a matter of policy, if the witness of so many new democracies in creating constitutional courts, which have the function of determining the constitutionality of legislative enactments, is to be believed.

[FN47]. In this respect, the RFRA debate echoes the arguments made in 1925 in the Scopes trial with William Jennings Bryan and the State of Tennessee arguing for majoritarianism--the right of the legislature to control the teaching of evolution in the schools--and with Clarence Darrow arguing from the individual rights perspective. See EDWARD J. LARSON, SUMMER FOR THE GODS: THE SCOPES TRIAL AND AMERICA'S CONTINUING DEBATE OVER SCIENCE AND RELIGION 99-101, 265 (1997).

[FN48]. See Suber, supra note 5, at 41.

[FN49]. See 42 U.S.C. § 2000bb.

[FN50]. This problem with hierarchy is different from that described in the preceding section insofar as it does not displace other levels. Instead, it seems to add a level, and does so mostly on its own authority.

[FN51]. Canons of interpretation are notoriously pliable. In perhaps the most analogous string of cases, the Supreme Court has held that a foundational statute can indeed be interpreted as superior to later statutes in a broad extension of the general principle that implied repeal is disfavored. See Hagen v. Utah, 510 U.S. 399 (1994). See generally Rector of Holy Trinity Church v. United States, 143 U.S. 457 (1892) (demonstrating further how statutes can be interpreted in ways different from how some would interpret their language rigidly since this immigration statute should be read in light of unstated, but "understood" congressional intent, despite seemingly clear language that would have required a different application). But inconsistent later acts may not be impliedly repealing. Instead, they may simply be construed to be controlling to the extent of the inconsistency. Implied repeal would not apply in its typical form in RFRA because few statutes would be intended to repeal, expressly or impliedly, the general interpretive thrust of RFRA. However, a neutral, later-enacted statute, which would infringe on religion does conflict with the RFRA standard and either the RFRA standard controls or the later standard controls. By interpreting the later standard as subject to RFRA, the conflict disappears, but the paradox remains--how is one to decide which to give force to--RFRA or the later-enacted statute?

[FN52]. Note that this clause does not create the strong paradox of the type Suber discusses in his book under which it may be possible to create a law that cannot be amended. See SUBER, supra note 23, at 175-76. Here, Congress can amend away the problem or can avoid the problem just by noting that the subsequent law is not subject to RFRA.

[FN53]. And even if not appropriate, it is fun (at least to some of us).

[FN54]. The omnipotence paradox is not necessarily self-referential. It becomes self-referential when the assertion of omnipotence is made by the one who would be referring to itself. If the assertion of omnipotence is made by an outsider, or if just made in the abstract, then the paradox is not really self- referential. But in law the omnipotence problem, i.e., the statement that something is all powerful (e.g., a constitution) often is self-referential.

[FN55]. Interestingly, self-reference is becoming endemic in television and other art forms today. The play within a play in Hamlet may be an early form of this (though the self-reference is indirect), but it is commonplace today to see television shows deriving humor by self-reference, especially in cartoons like "Animaniacs," "The Simpsons," and "The Tick."

[FN56]. Not all self-referential statements lead to paradoxes or contradictions within a formal system. Some statements that are self- referential are an illustration of Godel's Incompleteness Theorem. Godel's Incompleteness Theorem states, in essence, that in any axiomatic system of certain strength, it is inevitable that a hypothesis can be made within the system that is a statement made about the system and the truth or falsity of that statement cannot be determined from within the system. Interestingly, for at least some such propositions, by stepping outside the system one can determine that the statement is true and that it is a theorem, not merely an unprovable hypothesis.

Unlike the paradoxes discussed above, hypotheses that are illustrated by the Incompleteness Theorem do not create an inconsistency within the system, they simply show that no formal system of sufficient power can be complete. (Though this is quite commonplace in legal circles, it came as quite a shock to mathematicians trying to create complete, self-contained, axiomatic systems.) The most famous of these hypotheses is the Continuum Hypothesis. There are proofs showing that this statement about mathematics cannot be proven nor disproven.

In contrast to the incompleteness Godel exposed, the barber's paradox creates an inconsistency: either the barber exists, and one must live with this contradiction within the formal system, or the barber cannot exist. See infra pp.582-84. A part of RFRA illustrates this feature of not being able to be fully validated from within the part of the law derived from logic, but of not creating an inconsistency. Other parts of RFRA do not give rise to such inconsistencies. But, as with the barber's paradox, the inconsistencies can be managed by stepping outside of the logical part of the legal system to the other structural supports, i.e., tradition, experience, history, and power. To add, for the moment, one more twist to the braid, if those non-logical parts of the legal system are included among the axioms of the legal system, then we are not stepping out at all, we are just using different structure-giving axioms to decide the otherwise problematic logical conundrums. See HOFSTADTER, supra note 11, at 272.

[FN57]. A more complicated liar's paradox can be constructed by having two paired statements that refer to each other: (1) Statement (2) is true. (2) Statement (1) is false. (We leave to the reader to sort out the paradox.)

[FN58]. To the extent the law is a classification scheme (a system of sets, e.g., the set of criminal laws) that includes self-referential sets, Russell's paradox shows that the system cannot ever be fully complete. This may give pause to Hart-type jurisprudential scholars, but further consideration of that problem is far beyond the scope of this essay.

[FN59]. Classification in the law, the creation of sets, is problematic for another reason--the fuzziness of language. Determining whether someone is in the classification of people to be protected by the rule of law may be very difficult because of the facts, the law, or the purposes of the law, but rarely will the difficulty arise from a logical problem under which a person would be both in and out of the same set at the same time. Though this could happen.

[FN60]. There is a larger problem of mathematical modeling lurking here. Mathematical models are useful and powerful analytic tools, but cannot capture reality and do not ever fully reflect reality. This is an inherent limit in modeling, e.g., drawing maps to scale. The universe will never be reducible to simple, or even complex, mathematical formula. See Shawn Carlson, The Amateur Scientist Algorithm of the Gods, SCI. AM., Mar. 1997, at 121, 121 (explaining a "close enough" solution for inherently difficult problems); John L. Casti, Confronting Science's Logical Limits, SCI. AM., Oct. 1996, at 102, 102-05 (explaining some of the inherent limitations of mathematical modeling).

[FN61]. The title-footnote dilemma illustrates other problems with the language of the law and logic. Formal logic requires strict, non-ambiguous definitions and usage; ambiguities abound in real language and in the law. Similarly, formal logic involves two truth values: true or false; and one must view a whole statement as true or false. The title of this essay is only partly false (the no-footnote part). The other part (referring to RFRA and logic in the law) is in fact what this essay is about. Now how are we to judge the truthfulness of the footnote? Under formal logic, if the colon in the title is an "and," then, since one of the conjoined parts of the title is false, the title as a whole is false. If the colon is an "or," then the fact that one of the parts of the title is true makes the title as a whole true, and the footnote false. If the title is treated as two sentences, then one part of the title is true and the other false and the footnote is both right and wrong, or more accurately, perhaps, partially right and partially wrong. If the title refers only to the portion before the colon and the second part is defined as a subtitle, then by definition only the part before the colon is referred to by the footnote and the footnote is correct. The point of this somewhat extended analysis is this: Language and the language of the law do not conform well to dictates of formal logic.

[FN62]. Personally, I see no problem with courts giving effect to such a provision, and the Supreme Court has given effect to a similar provision in another law. See Hagen v. Utah, 510 U.S. 399, 410-13 (1994).

[FN63]. See SUBER, supra note 24, for a thorough consideration of the weak and strong forms of the paradoxes which arise from self-amendment. One major concern is the problem of omnipotence which Suber discusses at some length. See id. at 73-105.

[FN64]. See id. at 288-303.