| Sumario: | Scientists and philosophers alike debate whether various systems such as plants and bacteria exercise cognition. One strategy for resolving such debates is to ground claims about nonhuman cognition in evidence from mathematical models of cognitive capacities. In this article, I show that proponents of this strategy face two major challenges: demarcating phenomenological models from process models and overcoming underdetermination by model fit. I argue that even if the demarcation problem is resolved, fitting a process model to behavioral data is, on its own, not strong evidence for any cognitive process, let alone processes shared with humans.
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