In discussions regarding models of cognition, the very mention of computationalism often incites reactions against the insufficiency of the Turing machine model, its abstractness, determinism, the lack of naturalist foundations, triviality and the absence of clarity. None of those objections, however, concerns models based on natural computation or computing nature, where the model of computation is broader than symbol manipulation or conventional models of computation. Computing nature consists of physical structures that form layered computational architecture, with computation processes ranging from quantum to chemical, biological/cognitive and social-level computation. It is argued that, on the lower levels of information processing in the brain, finite automata or Turing machines may still be adequate models, while, on the higher levels of whole-brain information processing, natural computing models are necessary. A layered computational architecture of the mind based on the intrinsic computing of physical systems avoids objections against early versions of computationalism in the form of abstract symbols manipulation.