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In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to use elements of a non-classical logic. Specifically, a model is proposed here, according to which causality can be considered to be spatio-temporally graded. It is outlined how this can be described using the formalism of fuzzy sets theory, with the degree of causality varying between 1, that is no separation between causes and effects, and 0, that is perfect separation between causes and their effects as in classical 'billiard balls' models of physical systems, namely such based on the notion of ideal mathematical point. Our model posits that subjective moments of time are like fuzzy sets, with their extension determined by local degrees of causality, resulting from information integration processes extended gradually in space and time. This, we argue, is how a notion of causality could be, to a certain degree, spared and reconciled with a variant of Bergsonian duration theory as formulated in the theory of continuous change. Relation of the proposed viewpoint to other theories, as well as possible solutions it suggests to various problems, in particular the measurement problem, are also discussed.