On Self Reference and the Law

This is the first sentence in an article about self-reference and the law. This is the second. This sentence of this article explains that a self-referential sentence is one which represents or refers to itself. The next sentence will give an example of a self-referential sentence. Hey, out there – is that you reading me, or is it someone else?

This is the first sentence of the second paragraph of an article on self-reference and the law. Since the first paragraph of this article has explained what a self-referential sentence is, the next sentence of this paragraph will give you a more complicated example. This sentence would be seven words long if it were six words shorter. The previous sentence is known as a counterfactual conditional (or, more simply, a contradiction in terms), but this one isn’t. If this sentence was a counterfactual conditional, it would tell you that the first part of such sentences present a situation which is contrary to their second part.

When you read this sentence, you are probably wondering what this article is about. Don’t worry; this paragraph of this article will try to explain things to you. You may not find this sentence very complicated, as all it does is tell you that self-referential sentences have gotten a bit of a bad name because of something known as the Liar’s Paradox (“All Cretans are liars. I am a Cretan.”). This sentence is not an example of the Liar’s Paradox. But if this sentence could explain the Liar’s Paradox, it would tell you that the Liar’s Paradox is a type of self-referential sentence which comments about its own form, just like the previous sentence does, but that it comments about itself in a logically self-destructive way. But how can this sentence, or the previous two for that matter, tell you that self-referential sentences – although a topic of study and debate in universities around the world – are too often dismissed in everyday life as amusing conundrums or trivialities not worth examining without giving you solid examples?

By the time you have read this sentence, you will question what self-referential sentences have to do with anything, let alone the law (but be careful not to fall within the same category of people who take self-referential sentences lightly).

This is the first sentence of the fifth paragraph of this article. This sentence is a counterfactual conditional sentence (with the Liar’s Paradox thrown in) because it does not tell you that self-reference situations arise in the law all the time. The next two sentences do, but they are not counterfactual conditionals. The following example of a sentence: “You have not read me”, is a vaguely analogous example of what sorts of questions courts of law have to grapple with. “Can God make a stone so heave that she can’t lift it herself” is a better example. But “Can the legislature pass a law which it cannot subsequently amend” is probably the best. This is not the last sentence of this paragraph. The sentence which tells you that whenever a legal system is confronted with a proposition which has the power to negate the existence then that legal system is in the middle of a self-referential problem is the last sentence of this paragraph.

For those people who do not know Douglas R. Hofstadter, by the time they finish this sentence and article, they will be aware that he a professor of computer science at Indiana University and has written many articles on self-referential sentences (he’s also won the Pulitzer Prize for a book called “Gödel, Escher, Bach: An Eternal Golden Braid”). In fact, if Douglas R. Hofstadter wrote this article, it would be better! This is the third sentence of the sixth paragraph of this article on self-reference and the law. What the last sentence did not tell you is that there is a debate between logicians (like Mr. Hofstadter) and jurists (like William Popkin, the Walter W. Foskett Professor of Law Emeritus of the Indiana University School of Law) as to the relative importance of understanding self-reference problems in the law. What the previous sentence did not tell you either was that Peter Suber, the Professor of Philosophy at Earlham College in Richmond, Indiana has even written a book on the topic (The Paradox of Self-Amendment: A Study of Logic, Law, Omnipotence, and Change, Peter Lang Publishing, 1990). However, reading the sentences in this paragraph together, it seems clear that they all indicate to a hotly contested argument on the topic.

None of the sentences in the sixth paragraph of this article have explained that logicians live in a world bound by rules, and that for them paradoxical self-reference situations are a matter of life and death. Nor did they explain that jurists simply can’t understand what the fuss is all about. Therefore, the purpose this sentence is to tell you it’s all right; and that the purpose of this article is to reveal some of the thinking that affects jurists’ rather nonchalant view.

The sample sentence above “Can the legislature pass a law which it cannot subsequently amend” (and not this one) is a good place to begin (Pakistan’s constitutional dilemmas are also an example). But in order to explain why that sentence is crucial to understanding the logical dilemma thrown up by self-reference in the law, this sentence will have to explain that legal systems – as opposed to logic systems – are not as rigidly bound by logic as they appear. The previous sentence is not much of an explanation. To give you a better one, this sentence will refer to Oliver Wendell Holmes’ well known sentence (from “The Path of Law”): “The life of the law has not been logic; it has been experience.” The next sentence will try to explain what Oliver Wendell Holmes meant. Society evolves; attitudes change. The next sentence will illustrate what the previous sentence tried to explain. Today’s technology has enabled people to take photos (and even short films) with their mobile phones and send them instantly to friends anywhere on our planet. What the last sentence did not do was throw you a punch line; which this sentence does: Even with technology bringing people closer together, my mother still shouts when making long distance phone calls.

The paragraph above was trying to make the point that, over time, and especially with the way technology changes and affects our lives, social customs and even moral codes change. The law cannot be bounded by itself, as the law itself is changing. This sentence asserts that Oliver Wendell Holmes’ two sentences (also from “The Path of Law):
It is revolting to have no better reason for a rule of law than that so it was laid down in the time of Henry IV. It is still more revolting if the grounds upon which it was laid down have vanished long since, and the rule simple persists from blind imitation of the past . . .
are true and illustrate the point even better. Moreover, this article stems from the belief of its writer that the last sentence is not a counterfactual conditional.

A logic system cannot ask itself whether this sentence is correct. Just as the previous sentence is bound in two dimensions by the paper you read it on, a computer (which is a good example of something controlled by a logic system) is bound by its programs to follow fixed and pre-determined rules; it remains within the dimensions prescribed to it. The point of this paragraph is to explain to you that, unless computers can step outside their programs, they cannot answer questions like the one posed in the first sentence of this paragraph. Legal Systems are not bound to the dimensions of the substance they are written on. But the previous sentence doesn’t make much sense without reference to the mathematician Kurt Gödel’s famous Incompleteness Theorem. The last sentence of this paragraph will thus spell out the Theorem. “To every ω-consistent recursive class κ of formulae there correspond recursive class-signs r, such that neither υ Gen r nor Neg (υ Gen r) belongs to Flg κ (where υ is the free variable of r).”

By the time you have finished reading this sentence, you will have already asked yourself what Gödel’s Theorem means. For all practical purposes, the last sentence of the previous paragraph might as well have been in German (which was the language it was originally formulated in). But if last sentence of the above paragraph had actually been written in German, an English translation of it would yield the following result: “This sentence is un-provable in any given system.” But what this translation also tells us is that the logic problems of any given system can only be solved outside of it. The rest of this paragraph is a digression. The phrase ‘legal system’ is a bit of a misnomer: the law, per se, does not govern society. It is a distillation of the economic, social, moral and religious codes a society believes are correct and applicable to all its members. The accuracy of the reflection determines society’s acceptance of the legal system; and as social norms evolve, so must the legal theory. It would be more accurate to describe a legal system as a reflection of the true system which orders a society. But such a thought is confounding: If the phrase ‘legal system’ is a misnomer, then the debate as the relative value of self-reference and the law does not exist, and there is no point to reading this article.

This sentence does not refer to Thomas Kuhn’s “The Structure of Scientific Revolutions”, but it does reveal to you that, unlike logic systems, the systems (some would say paradigms) in which society and law operate are constantly evolving; and with each shift (some would say revolution), society is placed outside its previous paradigm. The last sentence of this paragraph explains why jurists don’t much care for problems of self-reflexivity in law. It is because legal systems, being a reflection of society, are programmed to change; logic systems do not have such a capability – their programming restricts them to their original paradigms.

This is the first sentence of the last paragraph of this article on self-reference and the law. However, no sentence in this article has explained what makes social paradigms shift. This sentence asserts that such a sentence, if written, cannot be correct. This is not the last sentence of this article. This one is.