Riding the Stable Meta-bus

pedagogy, philosophy

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Circular Notarization and Reasoning

I had to go to a lawyer’s office for the first time ever a few days ago. Not for anything serious – I was just gaining complete and absolute control over my parents assets and civil liberties – but in the process of signing the paperwork, found that I needed to have a lawyer notarize my signature. To prove that I’m the person that I really claim to be, or something.

Putting aside the question of why this is necessary (presumably I will have to prove it at time of invocation of any of my new powers, and that my parents wouldn’t have consented to give anyone they didn’t trust such responsibility), it was a small price to pay to not need to worry about having to sort such things out in less favorable circumstances. So I went to the lawyer’s office to get his signature saying that my signature was mine.

Things are loopy in the legal system. This isn’t a surprise to me, but what came next was. The lawyer first gave me a piece of paper to sign, saying that I approved him to have the power to sign saying that he verified my signature. Wat.

Take a second to reflect on just how loopy this is. I needed to sign a piece of paper to say that I trusted him to trust me to sign the piece of paper I originally wanted signed.

Because I am not so fearless as to play a game of silly buggers with very serious lawyers, we can only speculate as to what would happen if I were to refuse to sign the verification of him as my notary (henceforth known as the meta-signature, for brevity’s sake), or for that matter, why such a thing is even necessary in the first place.

OK. With a little squinting I can kind of see why they want to verify my signature in the first place – because they don’t trust me. But then, why on earth would that trust suddenly be created when we step up a meta-level to verification-of-the-verification? If you trust me to verify the notary to verify me, why don’t you just trust me to sign the damned thing in the first place??

The answer to this is probably because then they couldn’t charge me $75 to spend two minutes signing a piece of paper, but monopolies and good economics aside, this is a wonderful illustration of a concept that I’ve been wanting to talk about for a while.

Meta-level Stability

When we chunk concepts into abstractions, or, oppositely, find specific examples of our generalizations, we are traversing meta-levels. Switching between levels of abstraction can get mind-bending confusing (especially if you’re jumping multiple levels at once), so this seems like a good opportunity the practice. I’m a little biased in this respect, however, since I believe that error-free traversal of meta-levels is one of the most useful skills anyone can hone. But I digress.

Meta-level Stability is the principle that things need to broadly behave the same way, regardless of which layer of abstraction at which they are being viewed. The law office is a good example of this: if you don’t trust my signature at the object-level (the least meta), then you shouldn’t trust it on any level. My signature doesn’t magically become more trustworthy just because we jumped up a level of abstraction. Despite being conceptually different, my meta-signature is exactly the same as my object-signature, and as thus should be regarded the same.

This might seem like a silly thing about which to get our collective panties in a bunch, but that’s exactly why it’s a wonderful illustration of meta-level instability. The majority of world (including me, though I’m working on it) makes the same type of mistakes as these dozens of times a day. Unfortunately, it’s so ubiquitous in our thought patterns that it is almost literally undetectable if you don’t know to look for it.

Let’s drive the concept home a little harder since it is so very duplicitous. I attended the first lecture of a philosophy class last term (trigger warning: more philosophy hate) – and dropped it immediately afterwards. The course was “Discussion of Society and Biotechnology”, and the topic at hand during the first lecture was whether or not it was a good idea to genetically recreate dinosaurs in the lab (yes, apparently this is a real thing)1.

To slightly-for-the-sake-of-discussion straw-man the other students participating in the discussion, there were two largely-and-predominantly held views: “extinction is bad – if we can use this technology to prevent extinction, we should”, and “we should not reincarnate extinct animals/dinosaurs”. See any issues with these two opinions?

The issue is this: the opinions are inconsistent with one another. By not reincarnating the dinosaurs (the object-level case), you are further contributing to their extinction, while claiming we should do everything in our power to prevent extinction (the meta-level case). Reincarnation is one of the things in our power to prevent extinction, but we shouldn’t use it. See? Completely backwards.

This is one of those “you can’t have your cake and eat it too” scenarios. Either you pick the “extinction is bad” side, or you side with the “let’s bring dinosaurs back to life” camp. There is simply no room to pick both – it’s like claiming to be both atheistic and god-fearing. I’m not here to which side of the reincarnation debate is right, simply that anyone who says “both sides” is absolutely and necessarily wrong.

Reasoning Has a Bus Pass

Concepts and structure must be preserved when moving between meta-levels. Must must must. Otherwise you’re doing it wrong, and being a hypocrite in the process. And nobody likes a hypocrite. Breaking this principle of meta-level stability is one of the biggest issues in otherwise-cooperative political systems (more on this in a future post). It might sound silly and trivial, but I assure you, it’s a huge reason behind why so many things are broken on this planet:

Yes, you’re allowed to violate the principle of meta-level stability once in a while, but if and only if you have a really really good reason. Personal experience is not a really really good reason. Not every rule is necessarily hard and fast, but your exceptions to the rules indeed should be exceptions and not the rule. Each and every time you violate the principle of meta-level stability, you should feel ashamed. You’re doing something not necessarily wrong, but certainly dirty and unwholesome, Wallow in the regret of your logic violation, and make a promise to yourself that next time you’ll try a lot harder before you abandon the rules.

A natural, diligent question presents itself to be asked here: “why should we believe there are higher meta-levels in the first place? What if this is a fundamentally un-modelable problem?”. To this, I respond that literally every single thing we do or think depends on the assumption that the external world is modelable. Our beliefs about things exist only in our head, and are an infinitely simplified representation of reality. Despite knowing that the apple in front of you is an entirely unique, utterly-incomprehensible, never-to-be-seen-again configuration of atoms, you fully expect it to be juicy and delicious when you bite into it. Indeed, if it were not, you would find yourself very confused, and this confusion arises precisely from the violation of your mental model of the situation. In short, if you want to argue that any problem is un-modelable, you’d better give up on everything altogether.

The principle of meta-level stability is itself a special-case of an even more general principle. In order to be rational – to properly Paint with Thoughts – your beliefs must be internally consistent. Which is to say, that no matter which line of reasoning you follow to come to your conclusion, you must always reach the same conclusion. If your response to the essay topic “Is Wulky Wilkenson a post-utopian?” depends on how you choose to think about the problem, then you are making an egregious cognitive error, and have much bigger issues to deal with than the essay topic at hand.

Formally, this notion of “needing the same answer regardless of how you get there” is known as commuting. If you take the bus to work, there are probably lots of different ways of doing it. In my case I can catch the 9, and then the 25, or I can walk a few blocks and take the train, or presumably I can switch out pieces of the route with others, but the general result is still the same: I am going to get to work.

The metaphor kind of breaks here, because I can also get to places that work via public transit, but the heading was too good to miss. However, if you are evaluating purely between either P or not P, then your reasoning faculties are not allowed to bring you to both, or else your reasoning faculties are broken.

The takeaway message here I think is clear to everyone, and can be summed up as a pithy truism: Don’t break your reasoning faculties; always commute across meta-levels!


  1. I wrote this essay while on a plane, so the links might not be fantaaaastic.