It is mostly agreed that Popper's criterion of falsifiability fails to provide a useful demarcation between science and pseudo-science, because ad-hoc assumptions are always able to save any theory that conflicts with the empirical data (a.k.a. the Duhem-Quine problem), and a characterization of ad-hoc assumptions is lacking. Moreover, adding some testable predictions is not very difficult. It should be emphasized that these problems do not simply make Popper's demarcation approximate (if it were so, all our problems would be solved!), they make it totally useless. More in general, no philosophical criterion of demarcation is presently able to rule out even some of the most blatant cases of pseudo-science, not even approximatively (in any well defined sense of approximation). This is in sharp contrast with our firm belief that some theories are clearly not scientific. Where does this belief come from? In this paper I argue that it is necessary and possible to recognize the notion of syntactic simplicity that is able to tell the difference between empirically equivalent scientific and non-scientific theories, with a confidence that is adequate to many important practical purposes, and it fully agrees with the judgments generally held in the scientific community.