Philosophy and science are in no way separated: Philosophy is how we turn the light of reason on reason itself. Scientific rigor is how we turn the light of science on science itself.
In philosophy, if we presume that a seemingly "valid" argument holds true in all circumstances, then we have a truism. If we find that there is a circumstance where an argument does not hold true, we have proven the argument false. Hence, we do not count the arguments pro and con: we weigh them. One such idea is democracy.
In science, if we believe something, we have an hypothesis. If we predict of our hypothesis that the outcome of an experiment will always be the same, we have a postulate. But if another researcher shows that it is not necessarily true, then we look at all the variables. Once verified, we reconsider the variables and refine the postulate. Then, once it reasonably holds true, and no evidence of any substance arises to dispute it, then we have a theory. Then, we the researchers, must do everything in our power to disprove our own work. That is called falsification. Some theories, alas, are theories in name only and are not even so well proved as a postulate: evolution, for example, has never once met the tests of scientific rigor yet it is taught as gospel in Middle School and sometimes even High School. Evolution only very rarely occurs in college as there are so many highly credible disputes. Even without thousands of credible disputes, evoloution suffers a complete lack of scientific falsification. Hardly a credible hypothesis, much less a postulate, much less a theory.