According to Hutto and Satne, 521–536, 2015), an “essential tension” plagues contemporary neo-Pragmatist accounts of mental contents: their explanation of the emergence and constitution of intentional mental contents is circular. After identifying the problem, they also propose a solution: what neo-Pragmatists need to do, to overcome circularity, is to appeal to a primitive content-free variety of intentionality, different from the full-blown intentionality of propositional attitudes. In this paper, I will argue that, in addition to the problem of circularity, there is (...) another important problem that both neo-Pragmatist accounts, and Hutto and Satnes’s refinement of them, should also deal with: their difficulty to accommodate a host of recent empirical evidence and theoretical developments on the interdisciplinary field of animal cognition. I will call this difficulty the objection from animal minds, and I will present several arguments designed to show that, even though the notion of primitive intentionality, introduced by Hutto and Satne, may be useful to account for some of the most basic ways of dealing with the environment of nonhuman animals, it falls short of providing an adequate explanation of the full-range of cognitive capacities and behavioral dispositions that many animal species display. Thus, their proposal ends up being insufficient to help neo-Pragmatist approaches to overcome the problem of animal minds. Finally, I will suggest that overcoming this objection requires attributing to non-human animals some basic, yet content involving, kinds of intentional mental states. (shrink)