The idea that mental states are non-reducible properties of brain states is the central tenant of a theory of mind called property dualism. However, before we can assess the theory we must be aware that the question assumes the existence of mental states and as such we cannot answer this question from some perspectives (e.g. eliminative materialism)
Property dualism proclaims the existence of a single, physical substance (unlike Cartesian dualism), but argues that this single substance has two potential properties: physical and mental states that are not reducible. It is not just that we might talk of mental and physical states in different ways, but that the difference is in ontology as well as language. This is equivalent to historical notions that living things contained some 'vital force'. Essentially mental states are an extra property of matter in the brain.
Property dualists argue that consciousness is an emergent phenomenon of the physical processes of the brain and thus it is important to note that this leads to a belief in asymmetrical causation. Mental properties are caused by physical properties, but have no effect themselves on the physical properties, making the relationship one way.
This can be seen in the illustration below where the same object has both physical and mental properties that exist inextricably alongside each other. The object's physical properties can cause a change in its physical properties, but not the other way around:
The theory of property dualism arose as a defence of consciousness that responded to the key problems of Cartesian dualism (i.e. the problems of location and interaction) caused by the notion of two different substances. Property dualism also...