Whilst all of the theories looked at so far present different pictures of dualism, they at least have one thing in common in that they treat mental events as non-physical. In other words, they mental events exist as a completely separate substance (Cartesianism, Occasionalism, Parallelism and Platonism), a by-product of physical substance (Epiphenomenalism) or the property of some other intermediate substance (Double Aspect theory). As such, all of the above theories represent modifications of Cartesian dualism. However, there remain other theories that, whilst being dualistic, present a different view of the substances or properties involved in the relation of mind and body.

An example of such a theory is that of the philosopher E. J. Lowe who attempts to show in what way a non-Cartesian dualism can exist. He does this by redefining the nature of the mental, arguing that the concept of an immaterial substance does not make sense (for traditional reasons - problem of interaction, etc.).

However, to understand the rest of the theory it is necessary to analyse the concepts of "self" and "identity". Let us, for instance, take the idea of a car. I may replace certain engine parts, wheels, etc., and yet still say that it is the same car as it was. The collection of parts that make up the car may have changed slightly, but the car is still a car. On the other hand, if take all of the original parts and make a completely different type of machine out of it - such as a petrol-driven electricity generator - although the parts are exactly the same, the car no longer exists. Therefore, Lowe concludes, the thing that gives something its "identity" or "self" is not collection of parts - or any one part - of which it is made up.

When we relate these ideas to the concept of an individual, we discover that similar analogies can be drawn. A person is not the mere collection of limbs and organs that constitute it, nor is it a single part - such as the brain. Therefore, the person or self, although it is material - in that it relies on the existence of a body - is not identical with it.

This rather subtle and ingenious form of dualism is quite a long way from that of Descartes and Plato.

Firstly, the notion of self is not independent of the physical body and although Lowe might call the self a material substance, it is only in as much as it is another way of looking at the physical (i.e. there is no special independent substance or material soul).

Secondly, this notion of dualism seems to deny the possibility of immortality or existence of the self before or after birth - ideas that were so important to Descartes and Plato.

Thirdly, this theory seems to imply a form of determinism in that, since there is no overriding centre of decision making - such as the mind or the "I" - the material self is open to the same material influences as any other material substance (and therefore arguably determined by them). Lowe's counter-argument to this tries to show that it is possible that the will is a complex interaction of social and physical processes whereby no one cause is responsible for events. So, because the self contains all of these "parts" - social, physical, mental, emotional, etc. - decisions and actions are brought about by the arrangement of these parts in a certain way (in the same way that a spider's web allows the spider to move by both restricting and facilitating its movements).