Recent advances in genomic research have led to the development of new diagnostic tools, including tests which make it possible to predict the future occurrence of monogenetic diseases (e.g. Chorea Huntington) or to determine increased susceptibilities to the future development of more complex diseases (e.g. breast cancer). The use of such tests raises a number of ethical, legal and social issues which are usually discussed in terms of rights. However, in the context of predictive genetic tests a key question arises which lies beyond the concept of rights, namely, What should we want to know about our future? In the following I shall discuss this question against the background of Kant's Doctrine of Virtue. It will be demonstrated that the system of duties of virtue that Kant elaborates in the second part of his Metaphysics of Morals offers a theoretical framework for addressing the question of a proper scope of future knowledge as provided by genetic tests. This approach can serve as a source of moral guidance complementary to a justice perspective. It does, however, not rest on the-rather problematic--claim to be able to define what the "good life" is.