(Interventionist) causality is not about probability, it is about responses to hypothetical interventions. Probability is just there to model uncertainty, it is not at all needed (in fact Pearl’s first definition of causal models is deterministic).
I think it is also a fair claim that “causality is in the mind,” since there does not seem to be any causality in quantum mechanics.
You can use probabilistic models to predict the result of interventions without ever using the word cause.
A deterministic y=f(x) is mathematically just a limiting case of a conditional f(y|x).
I haven’t kept up with the literature for a while, but my PhD was predominantly about embedding causal forward models in a probabilistic framework, and using the network for inference. I was reading both Jaynes and Pearl at the time. The above is always how I considered the relationship between causal models and probabilistic models, and I didn’t run into situations where such a formulation ran into problems.
Interventions do introduce a new variable into an observational model, the intervening action, so one should not be surprised that the observational model may need adjustment when being conditioned on information that was false (the intervention) during the observational period.
I would be interested to hear about how causality and the arrow of time are dealt with in quantum theory, and whether it requires anything more than probabilistic notation. If, as you say, they don’t require some special notions of causality, I’d take it that Hume wins again.
“Really? Has no one made any progress on this?”
(Interventionist) causality is not about probability, it is about responses to hypothetical interventions. Probability is just there to model uncertainty, it is not at all needed (in fact Pearl’s first definition of causal models is deterministic).
I think it is also a fair claim that “causality is in the mind,” since there does not seem to be any causality in quantum mechanics.
You can use probabilistic models to predict the result of interventions without ever using the word cause.
A deterministic y=f(x) is mathematically just a limiting case of a conditional f(y|x).
I haven’t kept up with the literature for a while, but my PhD was predominantly about embedding causal forward models in a probabilistic framework, and using the network for inference. I was reading both Jaynes and Pearl at the time. The above is always how I considered the relationship between causal models and probabilistic models, and I didn’t run into situations where such a formulation ran into problems.
Interventions do introduce a new variable into an observational model, the intervening action, so one should not be surprised that the observational model may need adjustment when being conditioned on information that was false (the intervention) during the observational period.
I would be interested to hear about how causality and the arrow of time are dealt with in quantum theory, and whether it requires anything more than probabilistic notation. If, as you say, they don’t require some special notions of causality, I’d take it that Hume wins again.