How simple minded can you be? Many philosophers would answer: no more simple than a language-using human being. Many other philosophers, and most cognitive scientists, would allow that mammals, and perhaps birds, possess minds. But few have gone to the extreme of believing that very simple organisms, such as insects, can be genuinely minded. This is the ground that the present paper proposes to occupy and defend. It will argue that ants and bees, in particular, possess minds. So it will be claiming that minds can be very simple indeed.