As someone who does social science causal inference for a living, I have to say that I didn't really enjoy "The Book of Why". Full disclosure: I mostly practice the Neyman-Rubin potential outcomes form of causal inference rather than the Pearl do-calculus / DAG ("directed acyclic graph") form of causal inference, but the two are in many cases equivalent.
The reason I didn't like the book is that I found it insufficiently rigorous to really engage with the "how" of doing causal inference, but excessively mathematical as a theoretical introduction to causality.
"Causality: A Primer" (also written by Pearl) is a very short book that I think does a good job of surfacing some of the same theoretical background while also explaining how to use Pearl's causality. If you exhaust that, I'd recommend moving to the full "Causality" book.
But otherwise I'd recommend actually looking into the counterfactual / potential outcomes view of causality. The set of questions it answers are about 80% overlapping (although both Pearl and POs have their own 20%), but I find the vocabulary a little more intuitive. Canonical books include Morgan and Winship "Counterfactuals and Causal Inference" or Imbens and Rubin "Causal Inference for Social Scientists".
As to the blog post, Pearl is correct that causality requires qualitative assumptions about design to justify assumptions required to do causal inference. In Pearl's work this is often motivated as qualitative knowledge informing the structure of the DAG before any estimation. But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. By contrast, I agree with Gelman that Pearl is an irritating writer and that in "The Book of Why" he gives a sloppy intellectual history of causation.
The reason I didn't like the book is that I found it insufficiently rigorous to really engage with the "how" of doing causal inference, but excessively mathematical as a theoretical introduction to causality.
"Causality: A Primer" (also written by Pearl) is a very short book that I think does a good job of surfacing some of the same theoretical background while also explaining how to use Pearl's causality. If you exhaust that, I'd recommend moving to the full "Causality" book.
But otherwise I'd recommend actually looking into the counterfactual / potential outcomes view of causality. The set of questions it answers are about 80% overlapping (although both Pearl and POs have their own 20%), but I find the vocabulary a little more intuitive. Canonical books include Morgan and Winship "Counterfactuals and Causal Inference" or Imbens and Rubin "Causal Inference for Social Scientists".
As to the blog post, Pearl is correct that causality requires qualitative assumptions about design to justify assumptions required to do causal inference. In Pearl's work this is often motivated as qualitative knowledge informing the structure of the DAG before any estimation. But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. By contrast, I agree with Gelman that Pearl is an irritating writer and that in "The Book of Why" he gives a sloppy intellectual history of causation.