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.
My claim was that, if we simply represent the gears example by representing the underlying (classical) physics of the system via Pearl’s functional causal models, there’s nothing cyclic about the system. Thus, Pearl’s causal theory doesn’t need to resort to the messy expensive stuff for such systems. It only needs to get messy in systems which are a) cyclic, and b) implausible to model via their physics—for example, negative and positive feedback loops (smoking causes cancer causes despair causes smoking).
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.
Thanks, that is helpful.
My claim was that, if we simply represent the gears example by representing the underlying (classical) physics of the system via Pearl’s functional causal models, there’s nothing cyclic about the system. Thus, Pearl’s causal theory doesn’t need to resort to the messy expensive stuff for such systems. It only needs to get messy in systems which are a) cyclic, and b) implausible to model via their physics—for example, negative and positive feedback loops (smoking causes cancer causes despair causes smoking).