Actually, empirical observation depends on the correctness of basic logic, which must therefore precede it. You can't do experiments without having a logical f

Actually, empirical observation depends on the correctness of basic logic, which must therefore precede it. You can't do experiments without having a logical framework that allows you to interpret their results. You can certainly find people who've convinced themselves that they need to empirically check math. i.e. check that 30x100 = 3x1000 by rearranging beans on their kitchen floor. I wouldn't hire anyone who did that to paint my bathroom, though.