Eh, Pearl’s being a little bit coy. We can typically get away with some very weak/general causal assumptions—e.g. “parameters just happening to take very precise values which perfectly mask the real causal structure is improbable a priori” is roughly the assumption Pearl mostly relies on (under the guise of “minimality and stability” assumptions). Causality chapter 2 walks through a way to discover causal structure from correlations, leveraging those assumptions, though the algorithms there aren’t great in practice—“test gazillions of conditional independence relationships” is not something one can do in practice without a moderate rate of errors along the way, and Pearl’s algorithm assumes it as a building block. Still, it makes the point that this is possible in principle, and once we accept that we can just go full Bayesian model comparison.
I think of these assumptions in a similar way to e.g. independence assumptions across “experiments” in standard statistics (though I’d consider the assumptions needed for causality much weaker than those). Like, sure, we need to make some assumptions in order to do any sort of mathematical modelling, and that somewhat limits how/where we apply the theory, but it’s not that much of a barrier in practice.
Eh, Pearl’s being a little bit coy. We can typically get away with some very weak/general causal assumptions—e.g. “parameters just happening to take very precise values which perfectly mask the real causal structure is improbable a priori” is roughly the assumption Pearl mostly relies on (under the guise of “minimality and stability” assumptions). Causality chapter 2 walks through a way to discover causal structure from correlations, leveraging those assumptions, though the algorithms there aren’t great in practice—“test gazillions of conditional independence relationships” is not something one can do in practice without a moderate rate of errors along the way, and Pearl’s algorithm assumes it as a building block. Still, it makes the point that this is possible in principle, and once we accept that we can just go full Bayesian model comparison.
I think of these assumptions in a similar way to e.g. independence assumptions across “experiments” in standard statistics (though I’d consider the assumptions needed for causality much weaker than those). Like, sure, we need to make some assumptions in order to do any sort of mathematical modelling, and that somewhat limits how/where we apply the theory, but it’s not that much of a barrier in practice.