Well, since p(rain | grass wet) is high, it seems making the grass wet via a garden hose will make rain more likely.
That's a strawman. The conditional probability we're talking about has a clear (if explicitly unstated) temporal ordering: P(rain in the past | wet grass in the present).
But then you are just reinventing interventions
Talking about conditional probability was widespread long before people started talking about interventions.
It seems to me that the language of interventions, etc. is just a formalism that is convenient for certain types of analysis, but I'm not seeing that it means anything new.
I agree with pragmatist's explanation. But let me add a bit more detail to illustrate that a temporal ordering will not save you here. Imagine instead of two variables we have three variables : rain (R), my grass being wet (G1), and my neighbor's grass being wet (G2). Clearly R preceeds both G1, and G2, and G1 and G2 are contemporaneous. In fact, we can even consider G2 to be my neighbor's grass 1 hour in the future (so clearly G1 preceeds G2!).
Also clearly, p(R = yes | G1 = wet) is high, and p(R = yes | G2 = wet) is high, also p(G1 = wet | R = yes) is...
Yann LeCun, now of Facebook, was interviewed by The Register. It is interesting that his view of AI is apparently that of a prediction tool:
"In some ways you could say intelligence is all about prediction," he explained. "What you can identify in intelligence is it can predict what is going to happen in the world with more accuracy and more time horizon than others."
rather than of a world optimizer. This is not very surprising, given his background in handwriting and image recognition. This "AI as intelligence augmentation" view appears to be prevalent among the AI researchers in general.