The relation between mental states and brain states is important in computational neuroscience, and in psychiatry in which interventions with medication are made on brain states to alter mental states. The relation between the brain and the mind has puzzled philosophers for centuries. Here a neuroscience approach is proposed in which events at the sub-neuronal, neuronal, and neuronal network levels take place simultaneously to perform a computation that can be described at a high level as a mental state, with content about the world. It is argued that as the processes at the different levels of explanation take place at the same time, they are linked by a non-causal supervenient relationship: causality can best be described in brains as operating within but not between levels. This allows the supervenient (e.g., mental) properties to be emergent, though once understood at the mechanistic levels they may seem less emergent, and expected. This mind-brain theory allows mental events to be different in kind from the mechanistic events that underlie them; but does not lead one to argue that mental events cause brain events, or vice versa: they are different levels of explanation of the operation of the computational system. This approach may provide a way of thinking about brains and minds that is different from dualism and from reductive physicalism, and which is rooted in the computational processes that are fundamental to understanding brain and mental events, and that mean that the mental and mechanistic levels are linked by the computational process being performed. Explanations at the different levels of operation may be useful in different ways. For example, if we wish to understand how arithmetic is performed in the brain, description at the mental level of the algorithm being computed will be useful. But if the brain operates to result in mental disorders, then understanding the mechanism at the neural processing level may be more useful, in for example, the treatment of psychiatric disorders.

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