>Well, calculus is a bunch of logic propositions and it explains physics pretty well. So clearly some good things can be achieved by formal logic alone.
The idea to use logical rules to infer things about nature was arrived at through the non-logical "gestures and senses" methods that the parent was talking about. If all you had was logic you'd have no way to choose your axioms, or even your rules of inference. The axioms and rules of inference were, ultimately, selected from the vast sea of alternative options based on our observations, which rest on our senses.
The idea to use logical rules to infer things about nature was arrived at through the non-logical "gestures and senses" methods that the parent was talking about. If all you had was logic you'd have no way to choose your axioms, or even your rules of inference. The axioms and rules of inference were, ultimately, selected from the vast sea of alternative options based on our observations, which rest on our senses.