Comment by kqr
> People didn't always use statistics to discover truths about the world.
And they were much, much worse off for it. Logic does not let you learn anything new. All logic allows you to do is restate what you already know. Fundamental knowledge comes from experience or experiments, which need to be interpreted through a statistical lens because observations are never perfect.
Before statistics, our alternatives for understanding the world was (a) rich people sitting down and thinking deeply about how things could be, (b) charismatic people standing up and giving sermons on how they would like things to be, or (c) clever people guessing things right every now and then.
With statistics, we have to a large degree mechanised the process of learning how the world works, and anyone sensible can participate, and they can know with reasonable certainty whether they are right or wrong. It was impossible to prove a philosopher or a clergyman wrong!
That said, I think I agree with your overall point. One of the strengths of statistical reasoning is what's sometimes called intercomparison, the fact that we can draw conclusions from differences between processes without understanding anything about those processes. This is also a weakness because it makes it easy to accidentally or intentionally manipulate results.
Discovering that two different-seeming statements reduce to the same truth is new knowledge.