Gödel, Escher, Bernanke
I have recently been thinking about Gödel's Theorem and the regulation of markets. No, seriously... I know. I can't help it.
It is extremely important to note that I recognize a serious hazard here. It is dangerous to attempt translation across domains of knowledge, and such attempts often go awry, but I believe there is at least a slight chance that there is something real with this idea.
The question is whether the law can be accurately described as a "formal system," which has a mathematical definition. It seem plausible to me to suggest that it can, because all legal questions ultimately seem to boil down to a binary choice: Is action X lawful? That is, given a set of facts, describing the actions of some person, group, or entity, were those actions permitted or prohibited by the law?* In greater detail, the laws and regulations would represent the axioms of the formal system. Furthermore a grammar exists (largely inscrutable to most of us, but natural for lawyers, judges, and such) for constructing assertions or statements in this system, e.g. "Being that, on the Eleventieth of Smarch, Homer J Fonebone did willfully violate article diggity-two, section naughty-five of the state penal code..." (Heh, heh, he said "penal.") Finally, at least in this brief treatment, the grammatically valid statements in this system are ultimately adjudicated as "true" or "false," i.e. a verdict. The law in practice, messy as it is, surely never obtains the status of a formal system, rigorously defined, but in idealized form, this is a reasonable model of what law aims to be.
Now, Gödel tells us, for those who have not visited our friend Kurt recently, that any rigorously constructed formal system must be either incomplete or inconsistent. That is, the system will either contradict itself by producing at least two derived statements that actually contradict each other, OR, if such contradictory statements are prohibited, then the system cannot validate the truth or falsity of all possible statements. That is, there can never be a simple, mechanistic algorithm for determining the truth of any and all possible statements in the system.
If this does, in fact, apply to law, then the signs are certainly all around us. I see two major consequences: First, this renders the idea of "strict constructionism" logically impossible. Various "lower" courts are often arriving at blatantly contradictory conclusions on matters of constitutional law, and since the law, at least in theory, must be consistent, the Supreme Court must resolve the dispute. In doing so, the court sometimes makes new law, which, if I am correct, is not (necessarily) arrogance or hubris, but actually a logical necessity. This is not to say that the Court is always right, or that it does not sometimes exceed its proper bounds, but merely that existing law, as written, will never be both complete AND consistent. This is not quite the same as the classic "the framers couldn't forsee everything" argument, but a statement about logical inevitability.
The other consequence relates to the currently heated "debate" (really at lot more like ad hoc and ad hominem arguments hurled about the chattering political commentariat) concerning regulation and the economy. I have more than once heard prudent, thoughtful people argue that no matter how much we regulate, clever accountants, CEO's, CFO's, and lawyers will find a way to innovate to find "loopholes" that enable some sort of behavior that was intended to be prohibited. I have always found myself nodding, or even exclaiming, my agreement. Now, it seems that this argument may possibly be mathematically true.
Finally, as always, yes, we need regulation. Regulation is just law at the lowest level, and without the rule of law, not only will markets fail to function, but society collapses. But I do believe the Gödelian argument, if valid, points in the direction of so-called "principle based regulation" as an alternative to the minutely detailed proscriptive framework that dominates the modern regulatory landscape. Rather than chasing the mirage of a perfectly tuned and adjusted vast edifice of rules, which will inevitably fail to cover all situations, we should formulate the problem as one of basic principles. Regulate transparency, disclosure, and clarity. Do not, as a rule, try to prohibit any particular contractual arrangement between parties, but rather ensure that the parties fully disclose relevant obligations, and do our best to ensure that disputes about any given contract can later be sorted out effectively and fairly by the courts, for when the shit inevitably hits the fan.
Notes
* I am expressing the problem in language suitable for criminal law, but the reasoning should apply equally well in the civil arena, with suitably adjusted verbiage. Also, the observant, or lawyerly, reader will have noted that I asserted "given a set of facts," omitting the courts' role in actually finding facts. I understand that finding facts is also one of the chief duties of our legal system. This actually makes the argument stronger. Not only are courts needed to find the facts, but they can never be replaced by some mechanisitic framework even taking the facts as given. (Return)
It is extremely important to note that I recognize a serious hazard here. It is dangerous to attempt translation across domains of knowledge, and such attempts often go awry, but I believe there is at least a slight chance that there is something real with this idea.
The question is whether the law can be accurately described as a "formal system," which has a mathematical definition. It seem plausible to me to suggest that it can, because all legal questions ultimately seem to boil down to a binary choice: Is action X lawful? That is, given a set of facts, describing the actions of some person, group, or entity, were those actions permitted or prohibited by the law?* In greater detail, the laws and regulations would represent the axioms of the formal system. Furthermore a grammar exists (largely inscrutable to most of us, but natural for lawyers, judges, and such) for constructing assertions or statements in this system, e.g. "Being that, on the Eleventieth of Smarch, Homer J Fonebone did willfully violate article diggity-two, section naughty-five of the state penal code..." (Heh, heh, he said "penal.") Finally, at least in this brief treatment, the grammatically valid statements in this system are ultimately adjudicated as "true" or "false," i.e. a verdict. The law in practice, messy as it is, surely never obtains the status of a formal system, rigorously defined, but in idealized form, this is a reasonable model of what law aims to be.
Now, Gödel tells us, for those who have not visited our friend Kurt recently, that any rigorously constructed formal system must be either incomplete or inconsistent. That is, the system will either contradict itself by producing at least two derived statements that actually contradict each other, OR, if such contradictory statements are prohibited, then the system cannot validate the truth or falsity of all possible statements. That is, there can never be a simple, mechanistic algorithm for determining the truth of any and all possible statements in the system.
If this does, in fact, apply to law, then the signs are certainly all around us. I see two major consequences: First, this renders the idea of "strict constructionism" logically impossible. Various "lower" courts are often arriving at blatantly contradictory conclusions on matters of constitutional law, and since the law, at least in theory, must be consistent, the Supreme Court must resolve the dispute. In doing so, the court sometimes makes new law, which, if I am correct, is not (necessarily) arrogance or hubris, but actually a logical necessity. This is not to say that the Court is always right, or that it does not sometimes exceed its proper bounds, but merely that existing law, as written, will never be both complete AND consistent. This is not quite the same as the classic "the framers couldn't forsee everything" argument, but a statement about logical inevitability.
The other consequence relates to the currently heated "debate" (really at lot more like ad hoc and ad hominem arguments hurled about the chattering political commentariat) concerning regulation and the economy. I have more than once heard prudent, thoughtful people argue that no matter how much we regulate, clever accountants, CEO's, CFO's, and lawyers will find a way to innovate to find "loopholes" that enable some sort of behavior that was intended to be prohibited. I have always found myself nodding, or even exclaiming, my agreement. Now, it seems that this argument may possibly be mathematically true.
Finally, as always, yes, we need regulation. Regulation is just law at the lowest level, and without the rule of law, not only will markets fail to function, but society collapses. But I do believe the Gödelian argument, if valid, points in the direction of so-called "principle based regulation" as an alternative to the minutely detailed proscriptive framework that dominates the modern regulatory landscape. Rather than chasing the mirage of a perfectly tuned and adjusted vast edifice of rules, which will inevitably fail to cover all situations, we should formulate the problem as one of basic principles. Regulate transparency, disclosure, and clarity. Do not, as a rule, try to prohibit any particular contractual arrangement between parties, but rather ensure that the parties fully disclose relevant obligations, and do our best to ensure that disputes about any given contract can later be sorted out effectively and fairly by the courts, for when the shit inevitably hits the fan.
Notes
* I am expressing the problem in language suitable for criminal law, but the reasoning should apply equally well in the civil arena, with suitably adjusted verbiage. Also, the observant, or lawyerly, reader will have noted that I asserted "given a set of facts," omitting the courts' role in actually finding facts. I understand that finding facts is also one of the chief duties of our legal system. This actually makes the argument stronger. Not only are courts needed to find the facts, but they can never be replaced by some mechanisitic framework even taking the facts as given. (Return)
Labels: business, economics, government, markets, math, policy
posted by wRONgainey at 11:58 AM
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