What does it mean, in practice, to perform an intervention over variables representing abstractions over reality? When does such a notion even make sense?
I, Luigi Gresele, and Sebastian Weichwald (co-first author of Rubenstein et al.) have a pre-print that goes deep into this question, although we certainly do not answer it. I think this problem is one of the main reasons that the Pearlian framework is probably not gonna be a good mathematical framework for agency.
I don’t think the issue is unique to the Pearlian paradigm. You have the same problems whenever you talk about counterfactual statements like ‘if X were the case, then Y would be the case’. There are many possible worlds where X may be the case, and we have no principled way to figure out what fraction of those worlds make Y true (and how different worlds should be weighted). The Pearlian framework makes it appear as if this problem does not exist, but the problem does not go away.
Super interesting post! Thanks for writing it.
I especially like the point that you raise here:
I, Luigi Gresele, and Sebastian Weichwald (co-first author of Rubenstein et al.) have a pre-print that goes deep into this question, although we certainly do not answer it. I think this problem is one of the main reasons that the Pearlian framework is probably not gonna be a good mathematical framework for agency.
I don’t think the issue is unique to the Pearlian paradigm. You have the same problems whenever you talk about counterfactual statements like ‘if X were the case, then Y would be the case’. There are many possible worlds where X may be the case, and we have no principled way to figure out what fraction of those worlds make Y true (and how different worlds should be weighted). The Pearlian framework makes it appear as if this problem does not exist, but the problem does not go away.