In Lord of the Flies, what is the paradox of the boys' attitude toward the beast?

The boys' attitude is paradoxical in that the object of their fear does not exist in the outside world but, rather, within themselves. Their fear is perfectly justified, so there is indeed an underlying truth to this paradox. But instead of being afraid of some mythical beast, they ought to be afraid of what is inside themselves, their own innate capacity for barbarism.
Jack is not afraid of this inner savagery; on the contrary, he revels in it. But he cynically realizes the value of using the boys' fear of the beast as a means to consolidate his power over them. So long as the boys are fretting themselves sick over some nonexistent creature, they will be more likely to turn to Jack for protection. Furthermore, if the boys are mired in superstition, that means that they will be less amenable to going along with Ralph and his system of order.
In subjecting themselves to Jack's control, the boys are unleashing their own atavistic impulses, repressing their capacity to reason and think for themselves. They do not yet know it, but this will prove to be a far greater threat than any so-called beast could ever be.

In literature, a paradox is when two contradictory concepts or beliefs are juxtaposed to reveal a significant, underlying truth. In the novel Lord of the Flies, there is a paradox attached to the boys' attitude toward the beast. The beast does not exist, but the boys fear it nonetheless. Their attitude towards the fictional beast reveals their actual fear of the unknown. They try to rationalize their fears by discussing the identity and existence of the beast. While Ralph, Jack, and Piggy maintain that there is no such thing as the beast, the boys remain fearful. The underlying truth in this paradox is that the boys fear what they do not understand. Their fear of the beast represents their fear of the unknown, which is a significant trait shared by all humans. We as humans tend to fear the unknown, and Golding illuminates this common fear in the boys’ attitude towards the beast throughout the novel.