There are degrees of certainties. If for instance one of your beliefs is based on crushing evidence, then changing your mind on that matter will require super-

There are degrees of certainties. If for instance one of your beliefs is based on crushing evidence, then changing your mind on that matter will require super-crushing evidence. If someone comes and assert the contrary of your belief without presenting evidence, you should believe the other person is wrong. Wrong beliefs are often dangerous (an extreme case would be believing that prayers are better than western medicine at curing most illnesses). So your duty is to convince the other person, or at least control the damage. Now of course, if you do see that super-crushing evidence against your previously strongly held belief, then your duty is to change your mind. The most difficult part here is correctly assessing the weight of each piece evidence, and how they interact.