I think Judea Pearl would answer that the do() operator is the most reductionistic explanation that is possible. The point of the do calculus is precisely that it can't be found in the data (the difference between do(x) and "see(x)") and requires causal assumptions. Without a causal model, there is no do operator. And conversely, one cannot create a causal model from pure data alone- The do operator is on a higher rung of "the ladder of causality" from bare probabilities.
I feel like there's a partial answer to your last question in that do-calculus is to causal reasoning what the bayes rule is to probability. The do calculus can be derived from probability rules and the introduction of the do() operator- but the do() operator itself is something can not be explained in non causal terms. Pearl believes we inherently use some version of do calculus when we think about causality.
These ideas are all in Pearls "the book of why".
But now I think your question is where do the models come from? For researchers, the causal models they create come from background information they have of the problem they're working with. A confounder is possible between these parameters, but not those because of randomization etc. etc.
But in a newly born child or blank AI system, how does it acquire causal models? If that is explained, then we have answered your question. I don't have a good answer.
I myself think (but I haven't given it enough thought) that there might be a bridge from data to causal models though falsification. Take a list of possible causal models for a given problem and search through your data. You might not be able to prove your assumptions, but you might be able to rule causal models out, if they suppose there is a causal relation between two variables that show no correlation at all.
The trouble is, you don't know whether you can rule out the correlation, or if there is a correlation which doesn't show in the data because of a confounder. It seems plausible to me that children just assume they can rule out the correlation and assume one of the remaining causal models until new evidence proves them wrong again, and so enter into an iterative process eventually leading to a causal model. But again, this idea isn't well developed.
I think Judea Pearl would answer that the do() operator is the most reductionistic explanation that is possible. The point of the do calculus is precisely that it can't be found in the data (the difference between do(x) and "see(x)") and requires causal assumptions. Without a causal model, there is no do operator. And conversely, one cannot create a causal model from pure data alone- The do operator is on a higher rung of "the ladder of causality" from bare probabilities.
I feel like there's a partial answer to your last question in that do-calculus is to causal reasoning what the bayes rule is to probability. The do calculus can be derived from probability rules and the introduction of the do() operator- but the do() operator itself is something can not be explained in non causal terms. Pearl believes we inherently use some version of do calculus when we think about causality.
These ideas are all in Pearls "the book of why".
But now I think your question is where do the models come from? For researchers, the causal models they create come from background information they have of the problem they're working with. A confounder is possible between these parameters, but not those because of randomization etc. etc.
But in a newly born child or blank AI system, how does it acquire causal models? If that is explained, then we have answered your question. I don't have a good answer.
I myself think (but I haven't given it enough thought) that there might be a bridge from data to causal models though falsification. Take a list of possible causal models for a given problem and search through your data. You might not be able to prove your assumptions, but you might be able to rule causal models out, if they suppose there is a causal relation between two variables that show no correlation at all.
The trouble is, you don't know whether you can rule out the correlation, or if there is a correlation which doesn't show in the data because of a confounder. It seems plausible to me that children just assume they can rule out the correlation and assume one of the remaining causal models until new evidence proves them wrong again, and so enter into an iterative process eventually leading to a causal model. But again, this idea isn't well developed.