Section 5
Peter Suber, Paradox of Self-Amendment Table of Contents

A. Ross's paradox of self-amendment

Let us now explore the horn of the dilemma that affirms the self-applicability of the rules of change. On this horn either an individual rule applies directly to itself and authorizes its own amendment or repeal, or a set of rules applies directly to one of its members. The paradox which Alf Ross believes results from such assumptions may be simplified as follows.[Note 1]

Suppose a constitution has an amending clause, cited as AC.1, which provides that an amendment to the constitution will be valid law if and only if condition K.1 is met. K.1 specifies a procedure such as ratification by three-fourths of the states within seven years.

We want to amend AC.1. Our proposed amendment, call it AC.2, provides that an amendment to the constitution will be valid law if and only if condition K.2 is met. We would not want to amend AC.1 if K.1 and K.2 were the same. Hence, suppose that K.1 and K.2 make valid amendment turn on different conditions. Suppose further that they are inconsistent in the sense that each permits something that the other forbids and forbids something that the other permits.

The essence of Ross's statement of the paradox is his belief that an act of amendment may be set out as a deductive inference such as the following:

  1. If condition K.1 is met, then the proposed amendment (AC.2) becomes valid law.
    • Reason: Article AC.1
  2. The proposed amendment (AC.2) has been passed in accordance with condition K.1.
    • Reason: contingent fact, certified by an official
  3. Therefore, the proposed amendment is valid law.
    • Reason: steps 1 and 2, by modus ponens[Note 2]

But consider the inference when we propose to use AC.1 to amend AC.1, replacing it with AC.2. It is not surprising that AC.1 and AC.2 are inconsistent rules; their inconsistency is a desired byproduct of the original desire to amend AC.1. But their inconsistenty raises a problem. If we make AC.2 the proposed amendment in the inference above, then the conclusion contradicts the first premise. The first premise asserts the legal validity of AC.1 and the conclusion asserts the legal validity of AC.2. If the two clauses are inconsistent with each other (by hypothesis), then each excludes the other. Hence, the first premise asserts the exclusivity of condition K.1, and the conclusion asserts the exclusivity of condition K.2; by hypothesis these are inconsistent assertions.

This inconsistency makes the inference invalid. An inference in which the conclusion contradicts a premise, when the premises are consistent with one another, is demonstrably invalid. If logically valid deductive inference is a good model of legally valid amendment, then no amendment can be valid whose corresponding inference cannot be rendered valid.

That is the paradox. Whenever the amended AC will contradict the original AC, which will almost always be the case in self-amendment, then the inference that models the act of self-amendment will be invalid.

The most common objection to make at this point is to observe that AC.1 and AC.2 were never in effect at the same time, and that there is no contradiction in saying AC.1 has a certain period of validity and AC.2 has another distinct from the first. But even if true, that does not suffice to avoid the contradiction. AC.2 receives its authority or status as valid law from AC.1. It is precisely this transference of authority that the deductive inference is intended to model. According to this concept of law, a legal rule is valid if and only if it is validated by prior law through a valid inference. If AC.2 and AC.1 are never in effect at the same time, then they may not contradict one another as simultaneously binding laws. But their inconsistency as propositions outside time and law invalidates the inference by which alone AC.2 is to become valid law. AC.2 would not be valid law if it were not the conclusion of a valid inference; but it cannot be the conclusion of a valid inference as long as AC.1 is the reigning amending clause and must take a place in the premises.

There are many ways to refine the time-based objection to Ross, and many ways to refine the Rossian reply. The family of objections based on time will be explored in more detail in Section 10.

If Ross is right, then an AC that is already valid law cannot amend itself without contradiction. If it is the only lawful means of amending the set of rules of which it is a member, then it cannot be amended by any means whatever. Hence it will be immutable. If the rule of change were not supreme, it could be amended by a higher rule, but still could not amend itself. Self-application for non-supreme rules of change leads to contradiction as clearly as for supreme rules of change.

Ross's analysis stops after he locates this contradiction. But we may easily extend it from contradiction to paradox for any AC thought to be omnipotent. If self-amendment is self-contradictory, then self-limitation of a legally omnipotent AC is as paradoxical as the self-limitation of an omnipotent being. If a constitutional AC cannot limit its own power irrevocably (immutably), because the required self-amendment is self-contradictory, then there is a constitutional amendment it cannot enact; but if it can, then there is a constitutional amendment it cannot amend or repeal. Either way, it cannot be omnipotent in the naive sense (able to enact any law at any time).

The paradox need not be cast in terms of the direct amendment of the AC. If a constitutional AC cannot add an immutable provision to any part of the constitution, then there is is a legal rule that it cannot enact; if can add such a provision, then there is a rule that it cannot amend or repeal. Either way, it fails to be omnipotent in the naive sense.

Finally, Ross would add, if self-amendment is a contradiction logically, then it is impossible legally. The last conclusion depends on the view that legal change is transacted by logical inferences and that no legally valid change can occur through a logically invalid inference. If we deny this model of legal change and allow lawful amendment at least sometimes in the face of logical invalidity in the corresponding inference, then we must still confront the fact that, apparently, self-amendment involves contradiction. If legal change is not prevented by contradiction, then it tolerates contradiction, which must itself be faced squarely and explained.

It appears, then, that self-amendment is contradictory. If it is impermissible for that reason, then we must explain why logic rules so imperiously over this domain of human affairs where inconsistency seems to abound. If self-amendment is permissible anyway, then we must explain how law can tolerate this contradiction while forbidding many other things in the name of consistency.

A third alternative is that there is no real contradiction in self-amendment, only an apparent one that can be explained away. Attempts to make this work are considered, and ultimately rejected, in Sections 10 and 11.

B. Some distinctions

In order to facilitate discussion of the paradox some distinctions must be introduced. First, the paradox arises equally (if at all) from direct and indirect self-amendment. Direct self-amendment is the sort presented above: the application of an AC directly to itself just as to any other clause of the constitution. Indirect self-amendment is the replacement of a valid AC by a different one through an act that replaces the whole constitution of which it is a part. Indirect self-amendment is usually performed by constitutional conventions. It requires not only that the new constitution contain a new and different AC, but also that the new constitution and AC become law under the authority of the old AC (see Section 12.A).

Again, the paradox arises equally (if at all) from immediate and mediate self-amendment. These terms are taken from classical logic where an immediate inference is one that reaches a given conclusion validly in one step, whereas mediate inference requires extra premises or steps to arrive at a given conclusion from a given premise. If an AC is written as a single rule, then its self-amendment would be the direct or indirect application of that rule to itself, sufficing to amend in that one step by that one rule. This is immediate self-amendment. The AC may be written as many sub-rules, however. If each is an entire rule sufficient to authorize amendment, then applying a sub-rule to itself is also immediate self-amendment. If the sub-rules must work together to amend, then self-amendment becomes the application of a set to a member or a subset. That I will call mediate self-amendment.

One of the most important distinctions relating to the paradox of self-amendment and the paradox of omnipotence is borrowed from Hart's discussion of the omnipotent sovereign. An omnipotent parliament, he says, may limit its power to make law, without paradox, if its omnipotence is "self-embracing", and may not do so, at least without paradox, if its omnipotence is "continuing".[Note 3] Self-embracing omnipotence is unlimited power to make law, including power to affect that power. It may be used against itself and lost or limited irremediably. Continuing omnipotence is unlimited power to make law, but not including power to limit that power, thereby insuring that the omnipotence of the entity continues. Self-embracing omnipotence is unlimited but limitable power; continuing omnipotence is limited only to insure that it is (otherwise) illimitable. Self-embracing omnipotence is the power to make law on every subject, and therefore includes laws that diminish this power irremediably, whereas continuing omnipotence is the power to make law at every moment, and therefore excludes laws inconsistent with this very continuity. The self-embracing character of self-embracing omnipotence is mutable and even mutable irrevocably; the continuing character of continuing omnipotence is immutable, or at best mutable only revocably.

Beings of continuing omnipotence are doomed to life, power, and even doomed to freedom, while beings of self-embracing omnipotence are free to resign, abdicate, and self-destruct. Pliny the Elder said mortals were freer than the gods because mortals could commit suicide.[Note 4] He obviously thought that divine freedom was continuing, and that continuing freedom was inferior to self-embracing freedom. By contrast, Jesus is depicted in 1 Corinthians 15:27 as having continuing omnipotence:

For he hath put all things under his feet. But when he saith all things are put under him, it is manifest that he is excepted, which did put all things under him.

Shakespeare's Richard II views his own sovereignty as self-embracing. Hence, he could not be deposed; he could only abdicate. He emphasizes this to Bolingbroke, who mistakenly thinks of himself as Richard's overthrower:

Now mark me, how I will undo myself: [...]
With mine own tears I wash away my balm,
With mine own hands I give away my crown,
With mine own tongue deny my sacred state,
With mine own breath release all duteous oaths.[Note 5]

When John Stuart Mill said, "[i]t is not freedom to be allowed to alienate [one's] freedom,"[Note 6] he was defining freedom to be a continuing power, and his disagreement with those who would permit people to sell themselves into slavery, become drug addicts, or otherwise freely choose unfreedom, is not so much on the desirability of these acts as on the logic of self-application.

The distinction is very useful, and by extension we may speak of self-embracing and continuing powers to amend. Self-embracing amendment power may amend, limit, or repeal itself, irremediably, while continuing amendment power may not apply to itself, at least to diminish itself irrevocably.

Continuing omnipotence and amendment power are not maximally omnipotent, for there is one family of things they cannot do, namely, limit themselves, violate their immutable limitation and continuity, bind themselves for the future, and so on. But this should not lead us to think that continuing omnipotence and amendment power can augment themselves. For the only way to do that is (1) to repeal their limitation and become self-embracing, or (2) to become capable of repealing their limitation, which is already to be self-embracing. But these would contradict their continuing character and are impermissible for them.[Note 7] That is why this is the paradox of self-amendment, not merely the paradox of self-limitation. Because continuing omnipotence and amendment power can only affect themselves in ways that neither limit nor augment themselves irrevocably, they are restricted to relatively trivial acts of self-amendment. For example, an AC of continuing omnipotence could rearrange and renumber the articles of the constitution, including itself, without affecting the extent of its power (see Section 12.C).

While continuing omnipotence cannot become self-embracing, the converse is not true. Self-embracing omnipotence can become continuing omnipotence and may even become "partipotence" or of merely finite power (see Section 11).

It may seem that the distinction between continuing and self-embracing omnipotence solves the paradox of self-amendment (and the paradox of omnipotence generally) straightaway. Either the power of an AC is continuing or self-embracing. If it is continuing, then it simply may not amend itself to limit or augment its power; and if is self-embracing, it simply may. However, I will argue in Section 11 that the paradox reappears on each side of the distinction even when we are careful to avoid equivocation and keep the two senses of ominpotence distinct.

C. Lawfulness of self-amendment

At this point it is well to note that self-amendment is undoubtedly lawful in the United States. The federal AC has never been amended, directly or indirectly (Appendix 1). It may have been amended in more unorthodox and unofficial ways, depending on what is counted as amendment (Part Two). But by contrast, 47 states have histories of unambiguous self-amendment at the constitutional level, and in many cases more than one instance (Appendix 2). In one case (New Mexico) self-amendment was the result of pressure from the federal government.

No state or federal court has explicitly upheld the permissibility of self-amendment, except in unfocused obiter dicta that simply state that any clause of a constitution may be amended, or that there are no implied limits on the amending power. No court faced the question directly because the constitutionality of self-amendment has never been challenged. Not a single act of self-amendment has been called contradictory or paradoxical, not by losing plaintiffs in court nor by scholars in journals (except by Alf Ross[Note 8]), and none has been struck down by any court for any reason. Many scholars have proposed and opposed self-amendment, but none of them has noticed a paradox or contradiction in the idea (Appendix 1). Opponents of certain proposed self-amendments either have not seen the apparently paradoxical nature of it, or have deliberately refrained from using it as a legal objection, despite their incentive to multiply arguments.

I interpret these signs as proof that self-amendment is legal by most tests of legality, and illegal by none; it is commonplace; and if it is also paradoxical, then the paradox is legally irrelevant. To anticipate my conclusion, I will argue that the logical case that self-amendment is paradoxical is strong and resists all obvious solutions; but I will conclude that law can absorb and tolerate even a real (unsolved and undissolved) logical paradox because law is what is accepted as law, not a logical system afflicted with entangling content.

D. Self-reference

Ross objects to self-applicability on a second ground. Self-applicability is impossible without self-reference; and self-reference, he believes, is always meaningless.

His primary argument against self-amendment is that it is self-contradictory. But that argument only applies to amendments that change the AC into a form inconsistent with the original form. Therefore, it does not forbid all self-amendment, but only all substantive or significant self-amendment. However, the argument from self-reference would apparently forbid all self-amendment.

A sentence such as the Liar's, "This very statement is false," appears to be true if false, and false if true. This paradox can be avoided if we can say it is neither true nor false. To call it meaningless is attractive for that reason. But is it meaningless? The words "this very statement" form the subject of the sentence, but Ross argues that they do not denote anything. They refer to the string of words "this very statement is false," but that referent itself refers to the string of words "this very sentence is false," and so on ad infinitum. When we try to fill the subject of the sentence with meaning we find that it is an infinite and incompleteable task.[Note 9]

Even though the string of words is an object of experience, and therefore an existing object fit for thought and, it seems, for meaningful reference, it violates a rule that Ross and others regard as a sine qua non of meaning: that the words describing the subject of the sentence be replaceable without loss by the name of their referent. "The third planet from the sun bears life" is meaningful under this rule because the words describing the subject of the sentence may be replaced by the name "Earth" without loss of meaning or truth-value. Let us call the sentence "this very statement is false" by the name "TVSIF", its acronym. By substituting the name of the subject for its description we get "TVSIF is false". But within the name "TVSIF" there is a reference to TVSIF that should be replaceable by "TVSIF", giving us "TVSIF-IF is false". But the subject of the latter sentence also contains a description that should be replaceable by a name, giving us "TVSIF-IF-IF is false", and so on ad infinitum. The referent of these sentences is not a thing but an infinite path to a thing which eternally eludes determination. As Ross says, "one is never told what proposition is subject to the qualification of being false."[Note 10] In a miracle of conciseness Hart calls the resulting infinite regress an "asymptotic stutter."[Note 11]

We can certainly cavil with Ross's conclusion here. If "TVSIF" is a name, there is no reason to interpret its first three letters as another description requiring replacement by a name. But if we do, and meaning requires the subject of a sentence to be replaceable by a name (another contestable principle), then TVSIF is meaningless. The reason the very last sentence is meaningful, however, is that it refers irreflexively to meaning and to TVSIF, not directly to itself or solely to something (TVSIF) with no fixed name-replacement.

Hart argues that sentences which say, e.g. "Nothing in this section shall be amended, including this section" are meaningful, even by Ross's standard, because they refer to things other than themselves as well as to themselves.[Note 12] By referring to something other than itself, with respect to which the referential series is finite and terminating, the sentence has made itself something determinate as opposed to an asymptotic stutter; because it is determinate, it can be referred to by an auxiliary self-reference that will therefore have a determinate referent. Hart is clearly right on this. Ross cannot answer him, and when he tries to respond to critics who urge the meaningfulness and harmlessness of sentences such as "this sentence is in English", Ross's response is to modify his flat ban on self-reference until it forbids only those self-referential sentences without additional, completeable references.[Note 13]

Even if the ban on asymptotic stutters should stand, Ross's qualified prohibition no longer affects self-amendment and may be ignored for the purposes of this essay. If an AC explicitly said of itself that it could amend itself, that self-reference would be meaningful because the rest of the AC would consist of irreflexive references that would prevent the asymptotic stutter. This is true a fortiori when the AC is silent on self-applicability, and therefore contains no self-reference and is simply applied to itself. In this respect it is noteworthy that no AC I have ever seen explicitly addresses the permissibility of self-application. The only self-reference in ACs that could affect self-amendment is in entrenchment clauses (see Section 9). Other, harmless self-reference abounds, such as clauses on the lines of "this Constitution may be amended by...", "all amendments shall be parts of this Constitution for all intents and purposes...", "no convention called under this Article may be limited...", "no amendment to this Constitution shall be valid unless adopted pursuant to the procedures of this Article...."

Finally, of course, even if self-reference makes an AC meaningless, it may still be used in the adoption of valid amendments. If the self-reference in an AC made the AC meaningless, then it would prevent self-amendment as well as normal irreflexive amendment. One of the premises in the inference which results in amendment would say something like, "The Congress, whenever two-thirds of both Houses shall deem it necessary, shall propose amendments to this Constitution..." (Article V). By Ross's standards that may be meaningless, and therefore incapable of grounding the inference that results in amended law. But ACs are used for amendment and self-amendment all the time without regard to any self-reference in them.

Here again Ross is guilty of a priori reasoning about an empirical subject. As long as legislators and judges and citizens can find meaning in an AC, they will have found enough to permit amendment for the purposes of law. If courts never prevent or nullify amendments that rely on self-referential rules of change, which is the case, then the latter are undoubtedly legal, even if they shock the conscience of logicians.

In general, if we let courts determine what is lawful and let scholars and lay users of the language determine what is meaningful, then we should never face a conflict between them. Even when the scholars and folk agree that judicially validated language is meaningless (probably for different reasons), the courts are saying merely "but it is law."


1. This account is based on Ross's fullest exposition of the paradox, "Self-Reference and a Puzzle in Constitutional Law," Mind, 78 (1969) 1-24. See Section 1, note 17. [Resume]

2. Inferences by modus ponens take the form, [(A B).A] B, or, in English, "if a conditional statement is true, and its antecedent is true, then its consequent is also true." Inferences by modus ponens are demonstrably valid. Therefore, when their premises are true, their conclusions must be true. [Resume]

3. H.L.A. Hart, The Concept of Law, Oxford University Press, 1961, p. 146. [Resume]

4. Quoted in Montaigne, "Apology for Raymond Sebond," The Complete Essays of Montaigne (Original 1580, 1588), trans. Donald M. Frame, Stanford University Press, 1958, at p. 393. [Resume]

5. Richard II, Act IV, Scene 1, lines 203-210. David Hume uses a similar view of royal sovereignty as an analogy to the self-subversion of reason:

Reason first appears in possession of the throne, prescribing laws, and imposing maxims, with an absolute sway and authority. Her enemy, therefore, is oblig'd to take shelter under her protection, and by making use of rational arguments to prove the fallaciousness and imbecility of reason, produces, in a manner, a patent under her hand and seal. This patent has at first an authority, proportion'd to the present and immediate authority of reason, from which it is deriv'd. But as it is suppos'd to be contradictory to reason, it gradually diminishes the force of that governing power, and its own at the same time; till at last they both vanish away into nothing, by a regular and just diminution.

David Hume, A Treatise of Human Nature (original 1739), ed. L.A. Selby-Bigge, Oxford University Press, 1888, pp. 186-87. [Resume]

6. John Stuart Mill, On Liberty (Original 1859), Hackett Pub. Co., 1978, p. 121. [Resume]

7. I owe this observation to Jaakko Hintikka, "Remarks on a Paradox," Archiv für Rechts- und Sozialphilosophie, 44 (1958) 514-16 at p. 514. [Resume]

8. See also John Hicks, "The Liar Paradox in Legal Reasoning," Cambridge Law Journal, 29 (1971) 275-91. Other scholars who argue that an AC cannot be used to limit its own power base arguments on policy grounds, not the specter of paradox. See e.g. Douglas Linder, "What in the Constitution Cannot Be Amended?" Arizona Law Review, 23 (1981) 717-33, passim and esp. at p. 733: "[A]rticle Five cannot be amended so as to create any new limitations on the amending power." Linder does not defend this proposition in its full generality, but only to the extent that "new limitations" take the form of entrenchment clauses (clauses that explicitly protect some legal rules from amendment). Linder assumes without argument (and, I will argue, wrongly) that entrenchment clauses imply self-entrenchment and that self-entrenchment clauses are immutable; from these premises he argues that entrenching the AC through self-amendment would make immutable rules that are undemocratic in a way which courts must act to prevent. See Sections 8 and 9. [Resume]

9. Ross, op. cit. at pp. 7-17. [Resume]

10. Ross, ibid., at p. 9. [Resume]

11. H.L.A. Hart, "Self-Referring Laws," in Festskrift Tillägnad Karl Olivecrona, Stockholm: Kungl. Boktryckeriet. P.A. Norstedt & Söner, 1964, pp. 307-16, at p. 310. [Resume]

12. Hart, ibid., at p. 312. [Resume]

13. Ross, op. cit., at pp. 13-17. [Resume]

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

Ribbon] Peter Suber, Department of Philosophy, Earlham College, Richmond, Indiana, 47374, U.S.A. Copyright © 1990, Peter Suber.