A number of perceptual (exteroceptive and proprioceptive) illusions present problems for predictive processing accounts. In this chapter we’ll review explanations of the Müller-Lyer Illusion (MLI), the Rubber Hand Illusion (RHI) and the Alien Hand Illusion (AHI) based on the idea of Prediction Error Minimization (PEM), and show why they fail. In spite of the relatively open communicative processes which, on many accounts, are posited between hierarchical levels of the cognitive system in order to facilitate the minimization of prediction errors, perceptual (...) illusions seemingly allow prediction errors to rule. Even if, at the top, we have reliable and secure knowledge that the lines in the MLI are equal, or that the rubber hand in the RHI is not our hand, the system seems unable to correct for sensory errors that form the illusion. We argue that the standard PEM explanation based on a short-circuiting principle doesn’t work. This is the idea that where there are general statistical regularities in the environment there is a kind of short circuiting such that relevant priors are relegated to lower-level processing so that information from higher levels is not exchanged (Ogilvie and Carruthers, Review of Philosophy and Psychology 7:721–742, 2016), or is not as precise as it should be (Hohwy, The Predictive Mind, Oxford University Press, Oxford, 2013). Such solutions (without convincing explanation) violate the idea of open communication and/or they over-discount the reliable and secure knowledge that is in the system. We propose an alternative, 4E (embodied, embedded, extended, enactive) solution. We argue that PEM fails to take into account the ‘structural resistance’ introduced by material and cultural factors in the broader cognitive system. (shrink)