The downside to logical reasoning is that it only deals with absolutes. If you mistake an uncertain trend in the world for an absolute fact then logical reason

The downside to logical reasoning is that it only deals with absolutes. If you mistake an uncertain trend in the world for an absolute fact then logical reasoning also suffers from garbage in garbage out. All models have prerequisites, and logic requires propositions, which are either true or false. If you are trying to talk about models themselves (which is what most of math is), then logic is useful because it's easy to come up with propositions about models, and then you can explore what else must be true, or what else can't be true. Probability and statistics are much more useful for explaining the world than logic. But we use logic to prove things about the models that we use in probability and statistics. Logic is correct, you aren't going to find something logically true and then see it violated empirically. You are going to instead discover that the real world thing can't be neatly modeled as propositions. The error will be in producing the inputs to the model, not the model itself.