Citizen Gödel

Logic v. Experience

Albert Einstein and the economist Oskar Morgenstern accompanied the famous 20th Century logician Kurt Gödel to his U.S. citizenship interview. Gödel fled the Nazis and ended up at Princeton. Einstein and Morgenstern worried that Gödel would blow his interview by being his obsessive, logical self. He almost did.

Judge Philip Forman, then of the Federal District Court for the District of New Jersey and later of the Federal Third Circuit Court of Appeals, interviewed Gödel. Judge Forman knew Einstein from having done Einstein’s citizenship interview. When Judge Forman mentioned that the U.S. Constitution prevented dictatorship, Gödel went off.

Having meticulously examined the Constitution he began rambling about how the logical structure of the Constitution permitted dictatorship because you could amend the Constitution to allow for it. And he was right, even if it’s stupid to contradict a federal judge at your citizenship interview. But he also made a mistake common to the legal logic crowd versus the legal experience crowd - he assumed that logic is dispositive when it comes to law.

From the fact that aspects of law are deductive, it does not follow that the whole of law, or even a large part of it, is deductive. To argue to the contrary is to indulge the fallacy of composition - attributing to the whole the attributes of a part, e.g. because each player on the team is good, the team must be good. Here we use the phrase “the law” to refer loosely to the set of written and unwritten rules, customs, and actions that people generally refer to - uncritically - as the “law,” or the “rule of law.” Let’s avoid that hot definitional mess for a moment because it’s unnecessary to the point here.

The point here is that law at its foundation is a set of socially created constitutive and regulative rules instituted through collective intentionality. It’s not a type of axiomatic set theory. The law requires a certain level of social agreement and thus is a product of social relations. From the set of socially derived rules, you can derive axioms. But not before you’ve got some degree of social agreement on the set of institutional constitutive and regulative rules. In other words the axioms are grounded in external facts and states of affairs from the logical system the axioms exist in. (This is not necessarily the same as social contract theory but that’s another post.) And its a common feature of the law that it never escapes its social origins. The application of any given legal state of affair’s purported propositional content is subject to explicit or implicit ideological capture by whomever is enforcing it. This is the Weimar Judiciary problem, and after almost two decades in federal and state courts across the country, with a couple of forays in the U.K., I think the Weimar Judiciary problem is an inescapable feature of any judicial system. But that’s another post too. Back to the logic games.

Deductive reasoning plays an important, but exaggerated, role in law - and only once you’ve got an agreed upon set of propositions. Which is usually what the battle is about. Lawyers spend a lot of time arguing the validity, scope, and content of legal propositions. Law, among other things, is a battleground over propositions and their applicability. And given two valid sets of propositions that yield deductively contrary results, what’s your criteria for deductively choosing between those two sets that avoids infinite regress? Truth? How do you establish that?

Gödel famously proved that there’s no such thing as a complete, non-trivial, formal, logical system that can internally establish the truth of its propositions while also being consistent in the sense that it avoids all contradictions. No formal logical system exists that can prove the truth of its propositions internally by virtue of the formal system itself; to avoid contradiction you have to ground the truth of your propositions with external propositions. That’s what makes deductive legal formalism so problematic - it’s inconsistent and incomplete. You have to reach outside the system, and that’s where you have issues avoiding the fact that once you reach outside the system you seem to be making an arbitrary choice as to what to use to externally ground your internal truth. This is one of the reasons that coming up with a non arbitrary formula that cleanly distinguishes between what is a question of law versus what is a question of fact is an intractable problem that many famous jurists who’ve wrestled with the problem just give up on. Because its a question of art, not science.

One of the things I love about the law, to speak in anthropomorphic metaphors, is that it’s long implicitly recognized this. Because legal systems didn’t evolve to with the primary function of determining truth - although jurists love to couch the legal process in the language of truth, and its bastard cousin justice. Legal systems evolved to provide an important function for the survival of the species - avoiding endless conflict.

Here’s a strong claim for you: the primary reason all legal systems evolve is conflict resolution, not truth, justice, or morality. Resolution by mechanisms like adversarial or inquisitorial proceedings in courts, or whatever historical form emerges from a given set of historical state of affairs. That’s the reason trial by ordeal, which to the modern mind seems full of superstitious absurdities, and which put judgment before proof, lasted for centuries. It brought finality and was efficient. Note that this isn’t a teleological process, evolution is a nonteleological process - that’s what’s so radical about Darwin. He provides a nonteleological explanation that destroys the watchmaker theory of the universe. And the nonteleogical destruction is just as applicable to the social ontology of legal systems.

The notion that legal systems’ primary concern is truth, or justice, is problematic for reasons outside of Gödel’s incompleteness theorems. Truth statements in legal systems suffer from subjectivity and narrative framing issues. Do you assess culpability at the moment someone pulls the trigger, or from the moment the “victim” raped the shooter? Dealing with those issues seems to me a reason juries evolved. To make judgment calls in situations with no clear cut truths. And why sophisticated legal systems have multiple avenues for appeal and reversal of decisions.

A lot of damage and injustice occurs in the law because zealots with absolutist yearnings confuse law for science - it’s not. If anything it’s a form of theology or art. Highly contingent and rife with aesthetic judgments masquerading as moral absolutes; to say nothing of social class normativity hiding behind a skein of legal formalism. Our legal system, however imperfectly, implicitly recognizes the problem with arriving at dispositive truth. You can see this when stare decisis is ignored and an old, established precedent, gets overturned. Think Plessy, or Roe. As a rule of thumb, legal history is littered with the corpses of decisions and rules that once functioned as controlling, deductive truths. Again, I’m not arguing that deductive, or even inductive or adductive logic don’t play a role in our legal system - just that the type of legal formalism they embody aren’t as important as certain factions - ones usually motivated by particular ideologies or class - want them to be.

Gödel, like a lot of autistic absolutists, ignored the overwhelming social aspects of the Constitution. “We the People” isn’t as much a logical propositional statement as it is a metaphorical declarative speech act brazenly asserting to speak for the population of North America in a technically illegal act of constitutional restructuring. Logically speaking, the 1787 constitutional convention violated its mandate, it had no congressional authorization to submit a new Constitution to the states. Nonetheless it did, and enough states agreed that the violation of the logical deductive propositions making the acts of the Constitutional Convention technically illegal didn’t matter. Collective social intentionality triumphed over rote legal formalism.

And that’s Gödel’s mistake. He gave primacy to legal formalism over social collective intentionality. Yes, the Constitution can be amended to logically allow for dictatorship. But if enough people want dictatorship, they can impose it without amending the Constitution. They impose it with social force, not logical force. Logical legal propositions, like legal formalism, are just parchment barriers. Legal formalism can be a force for “good”, putting aside the thorny questions involved in defining that word. But it can also be a source of great injustice if society allows it - the irrational and arbitrary United States Sentencing Guidelines are but one example of an arbitrary tragedy of legal formalism. They regularly result in sentencing recommendations disproprotionate to moral culpability for the crime at issue, one reason their binding nature has been rejected by the United States Supreme Court. At the end of the day, collective social intentionality always beat legals formalism in a head-to-head conflict. That’s why the law changes - society moves on.

It’s also why these legal formalist arguments trying to prevent Trump from being President under Section 3 of the 14th Amendment (barring insurrectionists from holding office) fail. First, they’re anti-democractic, and some of the liberals making them are guilty of hypocrisy if not outright fascism (I’m talking to you Erwin Chemerinsky.) Second, not enough people give a fuck for your argument to work. Because it’s social force, not deductive force, that ultimately matters when it comes to the law.

Thanks for reading this. I realize this is murky. Feel free to comment and point out where you think I’m wrong. These posts are sketches for things I’m want to dive into deeper later and any input is appreciated. Even if it’s like Russell’s letter to Frege.