<p>Artificial intelligence technologies are becoming an increasingly prominent part of our everyday lives. We frequently rely on these technologies to provide us with advice, assist us in our decision-making, and perform tasks in high stakes contexts that can range from healthcare to warfare to finance. But is it possible to <i>trust</i> artificial intelligence technologies in these different ways? And, if it is possible, should we design these technologies to be <i>trustworthy</i>? There is a growing body of interdisciplinary literature that has sought to answer these questions. But with a few exceptions, surprisingly little attention has been given to philosophical theories of trust that have been developed. This is problematic because these theories can provide important insights into whether it is possible, feasible, or even desirable to develop trustworthy artificial intelligence technologies. This paper fills this important research gap in three important ways. First: it introduces a prominent philosophical theory of trust developed by Annette Baier. Second: it extrapolates three definitions of trustworthiness from that theory of trust. Third: it argues that while it is possible to develop trustworthy artificial intelligence systems according to each of these definitions, it is undesirable to do so because it makes us uniquely vulnerable to them. The key upshot of this paper is that we ought to develop artificial intelligence technologies that are merely reliable, rather than trustworthy, because this will limit the extent to which we are vulnerable to them.</p>