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Within a state-space approach endowed with a generalized potential function, mental states can be systematically characterized by their stability against perturbations. This approach yields three major classes of states: (1) asymptotically stable categorial states, (2) marginally stable non-categorial states and (3) unstable acategorial states. The particularly interesting case of states giving rise to exceptional experiences will be elucidated in detail. Their proper classification will be related to Metzinger’s account of self-model and world-model, and empirical support for this classification will be surveyed. Eventually, it will be outlined how Metzinger’s discussion of intentionality achieves pronounced significance within a dual-aspect framework of thinking.