Actually, empirical observation depends on the correctness of basic logic, which must therefore precede it.  You can&#x27;t do experiments without having a logical framework that allows you to interpret their results.  You can certainly find people who&#x27;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&#x27;t hire anyone who did that to paint my bathroom, though.