Hopefully the following clarifies my position.

In what follows, "Pearl's causal theory" refers to all instances of Pearl's work of which I am aware. "DAG theory" refers only to the fragment which a priori assumes all causal models are directed acyclic graphs.

Claim 1: DAG theory can't cope with the gears example. False.

For the third time, there exists an approximation of the gears example that is a directed acyclic graph. See the link in my second comment for the relevant picture.

Claim 2: Pearl's causal theory can't cope with the gears example. False.

If the approximation in claim 1 doesn't satisfy you, then there exists a messy, more computationally expensive extension of the DAG theory that can deal with cyclic causal graphs.

Claim 3: Pearl's causal theory describes all causal systems everywhere. False.

This is the only claim to which quantum mechanics is relevant.

The problem of causality in the system of gears reminds me of this comment, comparing a control system model of the stepwise algorithm "measure, compute correction, apply correction, repeat" versus the continuous reality of a centrifugal governor for a steam engine. I didn't fully understand the discussion there, but perhaps there is some relation. (I think of arguing that the governor can be seen as the limit of increasing the update rate of the algorithmic solution; and that limit is merely best analyzed by different tools than the algorithm, not fundamentally different — but as I said, I haven't studied the discussion, and the limit still has a cycle in it so this isn't directly relevant to your problem.)

I don't follow.

You made a claim of the form "For all causal systems, this theory ought to describe them." I demonstrated otherwise by exhibiting an explicit assumption Pearl makes at the outset, and that because of this assumption the theory applies only to a subset of causal systems. Gears are classical objects, and so a simple example involving gears doesn't elucidate the weaknesses of assuming all processes are Markov.

Then, I alluded to how one can hack around cycles in causal graphs by approximating them with "ladders".

As far as I can tell you're assuming some narrative between these points; there isn't one.

The theory is supposed to describe ANY causal system.

No, it's not.

In particular, most of Pearl's work applies only under some sort of assumption that the underlying process is Markovian. The common criticism of Pearl is that this assumption fails if one assumes quantum mechanics is true. He addresses this in Causality, around chapter two or three. He also addresses extensions to possibly-cyclic diagrams, but the technicalities become annoying.

If you are okay with discretizing time, then Timeless Causality shows a "ladder"-like directed acyclic graph that will approximate the causal system.

The system you describe can't be given by a directed acyclic graph, so why is it surprising that the theory breaks?

I'm not at all a fan of Hegel, and Heidegger I don't really understand, but I linked to a paper that describes the interaction of Heideggerian philosophy and AI which might answer your question.

I still think you don't have your categories straight. Philosophy does not make "claims" that are proved or disproved by evidence (although there is a relatively new subfield called "experimental philosophy"). Think of it as providing alternate points of view.

To illustrate: your idea that the only valid utterances are those that are supported by empirical evidence is a philosophy. That philosophy itself can't be supported by empirical evidence; it rests on something else.

I think you are making a category error. If something makes claims about phenomena that can be proved/disproved with evidence in the world, it's science, not philosophy.

Hmm.. I suspect the phrasing "evidence/phenomena in the world" might give my assertion an overly mechanistic sound to it. I don't mean verifiable/disprovable physical/atomistic facts must be cited-- that would be begging the question. I just mean any meaningful argument must make reference to evidence that can be pointed to in support of/ in criticism of the given argument. Note that "evidence" doesn't exclude "mental phenomena." If we don't ask that philosophy cite evidence, what distinguishes it from meaningless nonsense, or fiction?

I'm trying to write a more thorough response to your statement, but I'm finding it really difficult without the use of an example. Can you cite some claim of Heidegger's or Hegel's that you would assert is meaningful, but does not spring out of an argument based on empirical evidence? Maybe then I can respond more cogently.

I think you are making a category error. If something makes claims about phenomena that can be proved/disproved with evidence in the world, it's science, not philosophy.

So the question is whether philosophy's position as meta to science and everything else can provide utility. I've found it useful, YMMV.

BTW here is the latest round of Heideggerian critique of AI (pdf) which, again, you may or may not find useful.

A few points:

• Philisophy is (by definition, more or less) meta to everything else. By its nature, it has to question everything, including things that here seem to be unuqestionable, such as rationality and reductionism. The elevation of these into unquestionable dogma creates a somewhat cult-like environment.

• Often people who dismiss philosophy end up going over the same ground philosophers trode hundreds or thousands of years ago. That's one reason philosophers emphasize the history of ideas so much. It's probably a mistake to think you are so smart you will avoid all the pitfalls they've already fallen into.

• I agree with the linked post of Eliezer's that much of analytic philosophy (and AI) is mostly just slapping formal terms over unexamined everyday ideas, which is why I find most of it bores me to tears.

• Continental philosophy, on the other hand, if you can manage to make sense of it, actually can provide new perspectives on the world, and in that sense is worthwhile. Don't assume that just because you can't understand it, it doesn't have anything to say. Complaining because they use what seems like an impenetrable language is about on the level of an American traveling to Europe and complaining that the people there don't speak English. That said, Sturgeon's law definitely applies, perhaps at the 99% level.

• I'm recomending Bruno Latour to everyone these days. He's a French sociologist of science and philosopher, and if you can get past the very French style of abstraction he uses, he can be mind-blowing in the manner described above.

I used to TA a class whose covert purpose was teaching students how to think. The class encouraged everyone to use resources like Wikipedia whenever they didn't know something, so that it could focus on things more interesting than merely gathering information. That class tried to get everyone to think about things, to use their existing knowledge to solve types of problems they'd never seen before, and to learn in a way that went way beyond memorizing facts and regurgitating them on the test. If the class covered probability, it would make students analyze card games or the lottery. If it reviewed trigonometry, students would have to derive some identities. In the labs, they had to write computer programs. And so on.

Many (most?) of the students were actively pissed off by this. Why were their questions to the professor answered with helpful links to Wikipedia or someone's lecture slides, or a web page? Why did the class refuse to tell them exactly what they'd need to commit to memory to get a good grade on the tests? It went against everything they'd come to expect from "education". And the computer programming was especially maddening; they couldn't just pattern-match their way through it without thinking.

It was a required class for all freshmen in electrical engineering, and a lot of the graduating seniors said it had been one of the most valuable classes they'd taken. Not because of the material it covered, but because it had shaken them out of the bad habits they'd been given in high school "to prepare them for college." It was an uncomfortable process for them at the time, though.