The present article offers an introductory vision to the political philosophy of science. The political philosophy of science is a new field of study where the philosophy of science and political philosophy converge. We will see the main contents of this field. We will also note that it depends on the construction of a model of rationality where science and politics can meet each other. Finally, the article tries to outline such a model of rationality. In order to do so, we will review the relationship between Karl Popper's scientific and political philosophy. I suggest to read Popper's critical rationalism in terms of a kind of prudential rationality.