Cyan, I should perhaps have noted that probabilistic techniques are used in data analysis and the statistical sciences, but I thought it was obvious I was talking about the foundations of the scientific method rather than specific applications of mathematical techniques. Scientists use algebra and calculus and complex numbers and all manner of things and none of them are therefore the foundation of the scientific method (or its "hidden structure" as Eliezer likes to say).

And, no, logic and reason are explicitly not taught, used or applied by scientists. I used scare quotes because the words as generally applied are meaningless anyway. Having been "reasonable" or "logical" means having successfully avoided a set of counterfactual conclusions somebody imagines you could have made. Scientists have no more use for such a perfectly worthless concept than do carpenters or cooks or window cleaners.