Section 6
The Inference and Acceptance Models of Legal Change
Peter Suber, Paradox of Self-Amendment Table of Contents

A. Weaknesses of the inference model cured by the acceptance model

Ross's statement of the paradox of self-amendment assumes that the process of legal change is well represented by logical inference. It is important to see that this inference model is just one model of legal change, perhaps the first that common sense would hit upon but also perhaps the least true to the phenomenon.

I will call Ross's model the inference model of legal change and validity. The inference model envisions legal change as a series of deductive inferences. An existing procedural rule for legal change is expressed as a conditional statement ("If A, then B," or "If a procedure is satisfied, then a rule is amended"). That conditional statement is made the first premise of the required inference. The fact of procedural satisfaction ("A is true," or "The procedure has been followed") is made the second premise. The validity of the new rule ("B is true," or "A rule is amended") follows as the conclusion.

If A (procedure), then B (amendment).
A (procedure).
-----------------------------------------
Therefore, B (amendment).

The inference model has the virtue of capturing our sense that law is logical, or at least that it ought to be, that procedures produce outcomes through a structure of rules, and that a violation at any stage would either fail to produce the same outcome or would do so improperly, with a wink, despite the rules. The limitation of the inference model is that it makes legal change exclusively a matter of rule-governed inference, and ignores the legal realities of historical accident, retroactive justification, informal custom, pressure, politics, ideology, inconsistency, and winks. One of the most famous statements of American jurisprudence is on point.[Note 1]

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, institutions or public policy, avowed or unconscious, even the prejudices which judges share with their fellow-men, have a good deal more to do than the 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.

Ross does not defend the adequacy of the inference model; he presupposes it. Indeed, one might say he regards the right of logic to rule and overrule law as an a priori truth. Of course, if one held such a view, no empirical inquiry into legal practices would change one's mind.

Under the inference model the legal validity of a newly changed rule of law derives its authority from the logical validity of the inference (process) that brought it into being. The inference is demonstrably, necessarily, and eternally invalid if the conclusion contradicts a premise (when the premises are consistent with one another). And it seems this will always be the case when an AC changes itself into a form inconsistent with its original form. If so, then Ross is correct to find necessary contradiction in (substantial) self-amendment under the inference model. Unfortunately, he questioned neither the inference model itself, nor the proposition that logical impossibility implies legal impossibility.

If the paradox is real for the inference model, then it must be recognized by any inquirer or discipline that uses formal logic as a standard. While many philosophers have tried to dissolve the paradox even for the inference model, I would like to put those objections aside for a moment (until Sections 10 and 11) in order to introduce the question of the adequacy of the inference model itself, as a model of legal change.

If the legal validity of a newly amended rule of law depends on the logical validity of the deductive inference that models its adoption, then let us concede to Ross (for the time being) that self-amendment is paradoxical and unlawful. But if the validity of new law arises from another source, then the inconsistency of the new law with the old rule of change would no longer be an obstacle. Similarly, if the source of authority could tolerate contradiction, then self-amendment could occur without obstacle. Hart provides a model of law in which this is the case; I will call it the acceptance model.

The acceptance model is more difficult to state than the inference model because it posits a more complex explanans than a logical form (see Section 7). Essentially the acceptance model locates the authority of all law, including newly changed law, ultimately in the acceptance of the people governed by it, and in the practice and usage of the officials of the system. The acceptance model comes very close to a traditional consent theory of law, but it differs from it in several significant ways. The acceptance model requires a much less explicit form of assent than the consent theory and has fewer contractarian overtones. This is because it requires no mutual advantage for the parties, and because acceptance exists even when people are ignorant or indifferent to the laws that govern them. And at least in Hart's version, the acceptance theory is intended to explain authority descriptively rather than prescriptively, or to explain legality, not legitimacy.

An acceptance theory may appeal to acceptance directly for every rule of the system, or only for a few ultimate rules that in turn validate the rest. Hart is often taken to have said the latter. This view has Hart adopt an inference model for all legal rules except the ultimate rule of recognition.[Note 2] Hart's actual position is not so simple.

The formalist theory that legal rules are validated only by other legal rules requires either an infinite regress, an exceptional rule that is validated either by itself or by an extra-legal source of authority such as acceptance. On the simpler reading of Hart, he has chosen the latter path (validation by an extra-legal source of authority), and to that extent differs from Ross only on the permissibility of exceptions and on the authority of the ultimate rule of recognition. But in fact Hart does not adhere to a one-exception inference model of legal change. First, he denies that the rule of recognition is the only rule authorized directly by acceptance, and he gives other examples. For instance, the holdings, and even the jurisdictional basis, of some cases of first impression, and cases in which judges must exercise discretion are not validated by prior law but only (and contingently) by the acceptance they inspire. On this point Hart says,[Note 3]

The truth may be that, when courts settle previously unenvisioned questions concerning the most fundamental constitutional rules, they get their authority to decide them accepted after the questions have arisen and the decision has been given. Here all that succeeds is success....[I]t will often in retrospect be said, and may genuinely appear, that there always was an 'inherent' power in the courts to do what they have done. Yet this may be a pious fiction, if the only evidence for it is the success of what has been done....Here the power acquires authority ex post facto from success....The statement that the court always had an inherent power to rule in this way would surely only be a way of making the situation look more tidy than it really is.

If acceptance is an authority for law, and if it is a fact of social practice more than normative ideality, then it may be created in a society in the wake of a judicial ruling; hence it may come on the scene after the law it authorizes and have its effect retroactively.[Note 4]

Similarly, Hart continues, judges in the United States with powers of judicial review accept certain standards limiting their discretion to nullify statutes, but these standards exist only in judicial usage and are validated only by acceptance.[Note 5]

It is vital to an acceptance theory whether acceptance authorizes only one rule (the rule of recognition) or can authorize any rule. Hart holds the latter, although commentators who disregard the quoted passage have read him the other way. To avoid exegetical quarrels, however, I will call the acceptance theory I will most often contrast with Ross's inference model the direct acceptance theory. It holds that acceptance can authorize any rule of law directly, even if it rarely does so. Acceptance does not authorize only some master rule that validates other laws indirectly. Of course, for the purposes of this essay, it does not matter whether we agree or disagree that Hart himself held the direct acceptance theory. However I will use Hart's discussion of acceptance to show what issues must be raised in making such a theory comprehensive and plausible, since no other acceptance theorist has done nearly so thorough or thoughtful a job.

The rule of recognition does not determine law with the certainty and finality of logical rules. That sort of formalism is repugnant to Hart's entire theory.[Note 6] The open texture or partial indeterminacy of legal rules means that "subsumption and the drawing of a syllogistic conclusion no longer characterize the nerve of the reasoning involved in determining what is the right thing [for a court] to do."[Note 7] In his later essay Hart directly addressed Ross's view that legal change is transacted by logical inferences, and replied,[Note 8]

To this it might be objected that the exercise of legislative powers to introduce new norms is not a deductive inference and it is not clear how this logical principle applies to a legislative act.

However, while Hart clearly intended acceptance to validate more than just the ultimate rule of recognition, he also intended that most rules be validated by conformity to the rules of recognition. The direct acceptance theory allows the acceptance of the people and the practice and usage of the officials to validate any rule not otherwise validated by the rule of recognition, and to invalidate any rule otherwise validated by the rule of recognition. Because acceptance is logically prior to any positive law, in conflicts between informal acceptance and formal recognition acceptance overrules, or at least amends, the rule of recognition. This supplements Hart's position insofar as he did not address the problem of conflicts between actual acceptance and literal recognition.

There are defects in any inference model that admits no exceptions for self-validating rules or some alegal source of authority such as acceptance. The inference model allows formal logic to rule law, and to invalidate whatever fails the criteria of logical validity even while satisfying the courts, the people, and all legal criteria of legal validity. This is one of its most salient weaknesses. By contrast the acceptance model makes the conformity of law to logic contingent for each legal system at each moment; certainly the people and officials can accept a legal act that can only be described with self-contradiction, such as self-amendment, even if they will not accept other types of contradiction such as simultaneously binding inconsistent commands (see Section 21.B).

The inference model conceives legal rules to be, as far as possible, as clean and determinate, and as immune to fading away and shading off as the rules of mathematics. Legal rules do differ from mathematical rules, in their origin at certain moments in time by human will, their mutability according to certain procedures and human will, and the spatial limitations on their validity. Sometimes reading Ross one detects a note of wistful regret that legal rules have material content and sully themselves with the complexities, contingencies, and uncertainties of human life. But once enacted, they have single meanings, even if judges fail to discover them, and they cannot validly contradict any other valid law in any way without one of them giving way according to the canons of interpretation and rules of implied repeal. The formal rules of formal deductive inference apply absolutely to all legal rules; whatever can be validly inferred from a valid law is valid law; whatever cannot be validly inferred from any valid law or laws cannot become valid law.

This leads to one of the most radical absurdities of the exceptionless inference model. All change of law would be unlawful. Assuming we had a body of valid law to begin with, we could make no new law nor amend any existing law except by inference from the premises already embodied in law. All rules deducible from those premises would already be law, although perhaps tacitly, and no rules not so deducible could be made law. New enactments could only make explicit that which was already law implicitly. If a proposed rule were not a strict implication of existing rules, then it could not be inferred from them and therefore could not be enacted. From any initial position, therefore, all possible law is already actual, even if we do not know it yet, just as "Socrates is mortal" is already implied when we have asserted "All humans are mortal" and "Socrates is human".

But this absurdity will be avoided by a strict inference model —in the name of a greater absurdity. Law is only changeless if there is law. But a strict inference model implies that there is no law. If legal validity requires that a law be the conclusion of a valid inference in which the premises are already existing valid laws, then we may say more briefly that every valid law is derived from prior valid law. We can take what appears to be present law and locate its authorizing antecedents, but those antecedents are only valid if they have their own valid premises, and so on in an infinite regress. If we allow no exceptions in the inference model, then no rule in the history of authority can be self-validating or validated by an alegal source. The only alternative is an infinite regress of authorities; every valid law requires an infinite genealogy. But no law has an infinite genealogy. Therefore there is no valid law.

The exceptionless inference model must say either that there is no law, or if there is, that it is all immutable. It is no accident that this is what systems of formal logic must say about logical theorems, for Ross reduces legal validity to logical validity. If every step of every inference must be concluded from premises in a prior inference, then we cannot begin with axioms because they have no antecedent authority. Hence we fall into an infinite regress. But if we do begin with axioms, then once the rules of inference are specified, all permissible conclusions are instantly determined, even if human beings never finish discovering what they are.

We may avoid these absurdities only by admitting exceptions in the inference model as applied to law. These may take the form of self-validation, which Ross directly opposes, or an alegal and alogical source of authority, such as acceptance, for at least some rules, which he indirectly opposes.

Note that the alegal source of authority can be many things other than acceptance, such as moral law, military might, or divine command. But it cannot be logic. Ross and the legal formalists represent a new form of natural law theory: one that rests the validity of civic or positive law on logical law rather than moral law. But if formal logic is the alegal source of authority for law, then we encounter the dilemma that laws are only as valid as their premises, and these either recede infinitely or toward some exceptional premise that is self-validating or validated outside the logical and legal systems. This dilemma does not confront the moral version of natural law theory, or an acceptance theory, because these do not make legal validity depend on the logical validity of an inference; hence the pedigree of premises may stop at any point. Natural law theorists and others may nevertheless fall into the trap by searching for the authority of fundamental laws as if for premises of conclusions; but they need not do this. They may say that legal validity comes from moral law, period, or from acceptance, period. If they defend this claim with premises, they will confront the age-old epistemological dilemma of circularity versus infinite regress, but this affects only their theory, like any theory, not the phenomenon of legal validity itself.

The acceptance model does not allow logical rules to interfere with processes determined by legal rules and supervised by mortal judges. Whatever legislators and the people make in the way of new law is new law, if it satisfies the mortal judges and the people themselves; whatever is not regarded by anyone as valid law is not valid law even if it follows infallibly from rules that are accepted as valid law.[Note 9] New law must conform to the rules of making new law, but this conformity is not determined in ideality by logicians reducing the rules to some core of univocal purity. It is determined by judges using a complex web of non-formal methods. While judges try to follow both prior law and their own notions of eternal logic, their errors are as authoritative as their other decisions, unless some other judges overturn them or acceptance wanes through neglect or disobedience.

The inference model blurs the distinction between logic and law, while the acceptance model blurs the distinction between law and history. The inference model subtly identifies logical and with legal validity, or contradiction and illegality, while the acceptance model subtly identifies de jure and de facto validity, or legality and acceptance.

B. Ross's solution: the invisible, immutable amendment clause

Ross concludes that the contradiction of self-amendment means that valid amendments to ACs cannot derive their authority from the ACs themselves. Either they are merely accepted, which to Ross is to be legally unauthorized and invalid, or they derive their authority from a tacit rule transcending the constitution posited to validate precisely such changes. Logically Ross has no grounds to choose between these options, but he prefers the second, as if acknowledging that amendments to ACs do occur (which he never explicitly admits) and must be explained. Hence, attempts to amend an AC are not invalid exercises in futility, but neither when they succeed are they cases of self-amendment. Amendments to ACs derive their authority from a tacit rule, transcending the legal system, which states that the AC may be used to create its own successor, but that the successor is made valid only by the tacit, transcendent rule. This is a rudimentary theory of types. The highest positively enacted rule of change in the system is evidently mutable, but logically it cannot change itself or be changed by any other positive rule of change. Hence it cannot really be supreme and must have a tacit superior. The tacit rule of change might be called a tertiary and the constitutional AC a secondary rule, but of course Ross does not use these terms.

The positing of higher levels could go on forever in principle except that Ross sees no need to think of the transcendent rule at the first tacit level (the tertiary rule) as mutable. If it were mutable we would have to go to the second tacit level (to a quaternary rule) to find the authority for changing the tertiary. But if the first tacit rule is immutable, then the tacit series stops with only one transcendent rule, necessarily immutable, and conveniently "discovered" transcending every mutable constitutional AC.

In short, Ross avoids infinite regress by an arbitrary halt at the first tacit level above the constitution, and he avoids self-amendment through the theory of types and an immutable rule. Ross even gives us the content of the tacit, immutable rule:[Note 10]

Obey the authority instituted by [the express AC], until this authority itself points out a successor; then obey this authority, until itself points out a successor; and so on indefinitely.

It follows that ACs can be amended only if they are not actually supreme, and then they can be amended only by superiors. Therefore, the supreme rule of change will always be immutable. Actual constitutional ACs are not supreme, but inferior to the tacit transcendent rule of change that he has discovered.

Why should we believe that this tacit rule exists as a legal rule in every legal system? The only reason is to make amendments to ACs lawful without resort to self-application, which Ross thinks is resort to self-contradiction. Avoiding contradiction may be a good reason to make a law, but not a good reason to think such a law already exists. It is no more a good reason than, as Bentham said, "hunger is bread".[Note 11] The logician may discover gaps and inconsistencies, but only judges and legislators can cure them, and will only do so if they care to.

Ross's fundamental principle is "that from the validity of a norm it is impossible to derive the validity of any norm in conflict with [it]."[Note 12] This principle is obviously taken from logic, not law. It implies that a norm or rule cannot authorize its own change into a form inconsistent with its original form, for any such substantive self-amendment would comprise the derivation of a conflicting norm from a valid norm. Ross's first principle, then, precludes the possibility of substantial self-amendment a priori.

He does not justify the principle except as a principle of logic, in which guise it is unassailable. If the richness and historical contingency of the world of law does contain rules that permit the derivation of conflicting rules, then Ross has adopted a principle that prevents him from seeing that fact and that actually requires him to deny it. He is guilty of the arrogance of a priori thinking about an empirical subject. There are no errors in his reasoning, only in his choice of premises, and in his presumption that what logic forbids, law must forbid. If the existing legal rules seem to permit what logic forbids, then the philosopher or logician is within her rights to complain and to suggest what seem to her to be improvements. But if she is bent on explanation, then the makeshift of a tacit, transcendent, immutable rule, universal across all systems, authorizing exactly what must be authorized, is comical and unscientific, blind to the legal concept of legal validity.

C. Solutions from the model of direct acceptance

The newly changed AC need not derive its authority from the old AC or a tacit, transcendent, immutable, universal rule. It may, for example, derive its authority from the acceptance and usage of the people. An analogy may clarify this possibility. Contracts often contain the equivalents of ACs, and often contain no-revocation clauses. The parties to a contract may amend the contract's AC or revoke and replace the no-revocation clause, without paradox, because the new clause derives its authority not from the old clause but from the agreement of the parties to supersede the old and abide by the new. This is possible because the agreement of the parties is the source of the contract's authority[Note 13] and supersedes the particular written provisions. Similarly, a constitutional AC may derive its authority from a source outside the legal system such as the acceptance of the people if (under the acceptance theory) that acceptance is a genuinely higher or more encompassing authority. Hart argues that it is and must be. An AC derives its authority from the constitution of which it is a part, which leads us to the ultimate question of the authority of the constitution. Just as parties to a contract supersede the old by appeal to their own will, not to their old words, so the people of a society might supersede their old AC by appeal to their own will, not to their old words.

But note what has happened here. If acceptance is an authority external to the constitution and system of positive law, and if a change of ACs is authorized by acceptance, then the new AC may contradict the old AC but it will not contradict the authority that makes it law. Even according to Ross, the contradiction is only fatal when the authority for the amendment is the old AC, and when the conclusion of the inference that is supposed to make new law is the inconsistent new AC. Ross's inference model would not recognize acceptance as a source of authority; but if we do so, and then apply the most rigorous logical standards, no logical scruple will force us to say that the contradiction in self-amendment prevents its legality. For either acceptance prevents the need for self-amendment and hence contradiction, or else it validates self-amendment, contradiction and all.

The acceptance theory, then, provides two solutions to the paradox of self-amendment:

  1. If an AC is changed by self-amendment, then a contradiction in the process (even if Ross is right that it is there) would not invalidate the result if the result is accepted by the people and officials, for acceptance and not formal logic is the final arbiter of legality.

  2. If an AC is changed without appeal to itself as a rule of change, then no self-amendment occurs, and no contradiction; such amendment without self-application can be validated directly by acceptance.

Under the former solution, the old AC is the authority for the new AC and under the second solution the new AC is directly authorized by acceptance. In both cases we may admit with Ross that the new AC formally contradicts the old AC. Under the second solution this contradiction is irrelevant, because the new AC does not contradict the authority by which it is law. But under the first solution, the new law does really contradict the authority by which it is law; but this contradiction has no power to nullify the new law because the new law is accepted and the contradiction tolerated or overlooked.

Of these I prefer the first, although there is no need to choose. However, I will argue that strict self-amendment is permissible in any case, even if Ross's contradiction is ineliminable.

The two solutions are compatible, and may be invoked alternately as circumstances require. If an AC is amended by appeal to its own procedures, then even if this creates a contradiction, it may nevertheless create a valid new AC, if the necessary acceptance is obtained. On the other hand, if the AC is amended by procedures that it does not itself specify, the same conclusion follows: if accepted, the product can be valid law, although it would not in that case be self-amendment. If an AC is followed, self-amendment has occurred and the contradiction is overruled by acceptance; if the AC is not followed, self-amendment has not occurred and the new AC would be unauthorized unless directly authorized by acceptance.

As a matter of fact, the people and officials are much less likely to accept an amendment of an AC that did not follow the AC's procedures. This is a fact about law only because it is a fact about acceptance, not because it is a fact about logic. Even Ross admits that an amendment to an AC that did not follow the AC's own procedures would not usually be accepted, although he denies that acceptance can confer validity. Ross admits this because he attributes to ordinary citizens the belief that an AC may be amended by its own procedures and, if the AC is to be amended at all, that it must follow its own procedures. Then he chastises the ordinary citizen for the contradiction latent in this belief.[Note 14] According to Ross, if we want to amend an AC, then applying the AC to itself in self-amendment is a necessary condition of doing so plausibly or acceptably, but it is a sufficient condition of doing so invalidly or illegally.

ACs and other rules of change may as well be thought self-applicable for the acceptance model. The legal validity of self-application is to be judged by the acceptance it inspires, not the contradictions it entails. An indissoluble contradiction is powerless to nullify a legal act in the face of sufficient acceptance. The paradox of self-amendment exists only for the inference model, or some other concept of law that allows logical tests to overcome legal and social tests of legal validity. If the paradox of self-amendment exists only for the inference model, then changing models will dissolve the paradox, at least for law. The paradox of self-amendment has forced us to choose between fundamental philosophies of law.

The acceptance model is just one alternative. A second alternative, developed to a degree in Section 10, may be called the procedural model. The procedural model allows the outcomes of any valid procedure to be valid law even if there is a formal contradiction between the outcome and the antecedents of the procedure. The direct acceptance theory, however, is sufficient to escape Ross's paradox, and in Hart's version of it sufficiently complex to take up our time. But by acknowledging that other models may exist and suffice, we must be careful to avoid affirming the truth of the direct acceptance theory just because it circumvents the conditions of the self-amendment paradox, although we are clearly entitled to deny Ross's inference model because it fails to do so. For the merits of the direct acceptance theory, beyond the demerits of the inference model and the paradox of self-amendment, see Section 21.D. What follows is a slightly more complete account of Hart's acceptance theory, long enough to show its weak points, but short enough to prevent our being diverted from the main track of our discussion.

Notes

1. Oliver Wendell Holmes, Jr., The Common Law, Little, Brown, and Co., 1881, p. 1. [Resume]

2. There is some support for this view of Hart's theory in his The Concept of Law, Oxford University Press, 1961, pp. 92, 93, 97, l06, 205, and 229. One of the most formalistic statements of Hart's theory is to be found in John M. Farago, "Judicial Cybernetics: The Effect of Self-Reference on Dworkin's Rights Thesis," Valparaiso University Law Review, 14 (1980) 371-425, at p. 377-78.n.3:

We might view Hart's model as an instrumental application of deductive logic to jurisprudence... Thus, the rule of recognition provides a single undefined assumption, against which we can evaluate the various axioms (rules) of our system. Propositions of law are demonstrably true (or false) by application of the rule of recognition and the primary and secondary rules. The rule of recognition itself provides a recursive rule for determining whether any given proposition is a theorem of the system. [Resume]

3. Hart, op. cit., at pp. 149-50 (emphases in original). [Resume]

4. Joseph Raz prevents an infinite regress of authorities with a similar theory. Arguing more against Kelsen than Ross, Raz says,

The authors of the first constitution [or the constitution without a prior authority] have legislative power, which is not given to them by law, to make the first constitution. The first constitution is law because it belongs to an efficacious legal system (a fact which cannot be determined until some time after the constitution is first issued)....[L]aws can indirectly authorize their own creation.

Joseph Raz, The Concept of a Legal System: An Introduction to the Theory of Legal System, Oxford University Press, 1980, at p. 138; emphases added. [Resume]

5. Hart, ibid., at p. 142. See also Stoliker v. Waite, 101 N.W.2d 299, 305 (1960) in which the Michigan Supreme Court said that the obstacle in the state AC to rapid and easy amendment is "secure from judicial profanation, though its security is measured only by the tradition of the law, our sense of self-restraint." [Resume]

6. Hart, ibid., at pp. 121-50. [Resume]

7. Hart, ibid., at p. 124. [Resume]

8. Hart, "Self-Referring Laws," Festskrift Tillägnad Karl Olivecrona, Stockholm: Kungl. Boktryckeriet. P.A. Norstedt & Söner, 1964, pp. 307-16, at p. 315. [Resume]

9. This claim amounts to saying that inferences by modus tollens are not generally valid in law; it is defended at greater length in Section 21.B. [Resume]

10. Alf Ross, "Self-Reference and a Puzzle in Constitutional Law," Mind, 78 (1969) 1-24, at p. 24. [Resume]

11. Jeremy Bentham, Anarchical Fallacies, in Bowring ed. of his Works, vol. 2, pp. 501. See also his Pannomial Fragments, vol. 3, p. 221. Quoted by H.L.A. Hart in "1776-1976: Law in the Perspective of Philosophy," in his Essays in Jurisprudence and Philosophy, Oxford University Press, 1983, pp. 145-58 at p. 147. [Resume]

12. Ross, ibid., at p. 21. [Resume]

13. We may regard this agreement as a sufficient authority by itself or as an authority only by virtue of a rule of public law that gives agreement this status. Some of the difficulties of the latter position are discussed in Sections 7 and 20. [Resume]

14. Ross, ibid., at p. 6. [Resume]

This file is one section of the book, The Paradox of Self-Amendment. Return to the Table of Contents.

[Blue Ribbon] Peter Suber, Department of Philosophy, Earlham College, Richmond, Indiana, 47374, U.S.A.
peters@earlham.edu. Copyright © 1990, Peter Suber.