The first two sections of this chapter are strictly related to some seminal Peircean philosophical considerations concerning abduction, perception, inference, and instinct which I consider are still important to current cognitive research. Peircean analysis helps us to better grasp how model-based, sentential and manipulative aspects of abduction have to be seen as intertwined. Moreover, Peircean emphasis on the role of instincts in abduction provides a perfect philosophical introduction to the problem of animal hypothetical cognition in the remaining part of the chapter.