In the philosophy of mind, the question of the relationship between the physical and mental is at issue. The mind-brain identity theory holds that the relation in question is in fact the identity relation and that the brain (and possibly other parts of the body, like the CNS) literally is the mind.

To a scientific outlook, this can look like a straightforward and obvious statement of fact. Given that minds are real (we hope this much is apparent, even to hard-line materialists) and that if we look with our scientific instruments we find only physical stuff, it is convenient and simple to identify the mind with the physical stuff that we find when we go looking for it scientifically.

But this view does not mesh straightforwardly with our commonsense notions and our normal linguistic practices, hence the identity theory has been the subject of much controversy. Nonetheless, it has been extremely influential, and most current discourse in analytic philosophy on the ontology of the mental has been shaped by its defence, development or opposition.

In the ancient world, Epicurus could be considered a kind of identity theorist, but in its modern formulation, the originators of the theory were Herbert Feigl1, J.J.C. Smart and U.T. Place.

Place took the view that phenomena such as after-images, though real, can't be accounted for in a dispositional (ie. behaviourist) analysis of the mental (which he favoured in the case of concepts like belief and intention.) Finding untenable the traditional dualist view of mental events as distinct from, though correlated with, physical events, he was led to postulate the identity of the former with the latter. His view was that this identification was a scientific theory, in the same way that the identification of lightning with the motion of electrical particles is not a necessary truth, but a contingent one that we establish empirically.

The theory was expanded by D.M. Armstrong in his influential book A Materialist Theory of Mind where it was elevated to a fully fledged ontology. Roughly, Armstrong's view is that all real properties are causally based; he called this the causal theory of properties or CTP for short.

Thus, if we want to say that 'mental properties' (like is seeing a red after-image, for example) are real, then unless we wish to invent some non-physical variety of causality, which Armstrong certainly did not want to do, we have to postulate some corresponding physical property of the brain, in virtue of which our claim to be seeing a red after-image can be thought true.

But, as was pointed out, we need to be clear whether we are identifying mental properties with physical ones or just individual mental events and states with physical ones.

A theory which supports the view that mental properties are real and identical with physical ones is called a type-type identity theory, as it asserts there are types of mental events which are identical with types of physical events.

The more hard-line token-token identity theory, by contrast, is one in which we assert the identity of particular, single, mental states and events with particular single physical ones, but deny that there are necessarily any real physical properties corresponding to the terms we use to classify the mental (terms such as after-image, for example.)

The type-type theories, then, are realist about our descriptions of the mental (or at least they allow realism about these) whereas the token-token theories are not: propositions about the mental can be seen, at best, as useful approximations to the true physical description, or as simply denoting arbitrary disjunctions of physical objects. This has obviously travelled some distance from the identity theory as originally conceived, which sought to preserve the potential truthfulness of statements about the mental, and the token-token theory has been criticised for simply restating epiphenomenalism - the theory that mental events are some strange metaphysical exudence of physical ones - in a hidden guise.

But if, adopting the type-type approach, we say an after-image is identical to a process in the brain, then since the after-image is green we would have to say that the brain-process is green, since identicals share all properties. This objection against the type-type theories is regarded by many as fatal.

Donald Davidson has put forward a theory known as anomalous monism in which, though only token-token identity holds between the mental and the physical, there are nonetheless real physical and mental properties, but with no type-type-like correlation between them.

My own view is that it's the materialist, or physicalist stance that's leading us into trouble here. I am not inclined to say that there are two of me here, a physical one and a mental one, but if we adopt Armstrong's CTP, together with his view (shared, I think, by most identity theorists) that 'causal' means 'investigable by physics', then it seems quite clear that descriptions that are acceptable in physics will not exhaustively describe our experience (see inverse spectrum argument.) So I am led to postulate a 'dual aspect' version of neutral monism, instead.

The most significant current objection to the identity theory, however, is widely thought to be Hilary Putnam's multiple realizability argument, which considers that it would be possible for many different physical states to implement a single mental state, and since the mental states are identical to each other and the physical ones not, the mental states can't be identical with the physical ones. This consideration has probably been influential for those who espouse computationalist theories of mind on the analogy that many different physical arrangements can realise identical computations.

1. see nomological dangler.