I believe, from my own experience, the study and mastery of logic while studying philosophy has turned me into a very critical thinker. I've been told several times that I should have been a lawyer. Also, as an engineer, don't you think analysis is critical? Math and logic are united more than quantum mechanics and relativity. I loved logic so much I took to computer programming which became my career. I never studied it formally. I love the study of the philosophy of mathematics. It is mental exercise to make complete sense of all there is. Logic, type theory, category theory, set theory, algorithms, algebra and more abstract algebra.