The problem is an illusion created once we start dividing the world up into concept words, and then keep trying to refine our conceptual boxes without realising that the words are abstractions, not indicative of essences. There is no mind-body, there is no i-you, there is only the world and I am the whole of my world; no more, no less.
So, when John Searle poses the question "How can subjectivity be a real part of the world?", the answer is that it is not: The world and subjectivity are the same thing.
It may appear a trivial point, but it makes no alteration to an object whether we measure it in Metres or Feet. This is why disagreeing over what we define as 'self', 'mind', or 'belief' is completely irrelevant. It has no bearing on anything, it is like arguing over which ruler we should use. We can refine the word 'self' so that it equates to the neurological brain structure, or so that it is a type of behaviour...but all this does is gives us a definition of the word. It does not mean that 'I' will continue to exist if I am simulated in a computer. Because, there is no 'self'...this is just a word we use to artificially glue together the sensations, thoughts, behaviours, attitudes, relationships, memories and physical body that seem to fit together under one umbrella.
In this way, we can see the crucial logic-gap in Richard Gregory's reply to Searles. In arguing for Artificial Intelligence, he claims that we should allow enough flexibility in the word 'belief' such that we are not automatically disallowing a mechanical structure, a thermostat, from having such things. It's a fair point. We can broaden the word belief so that it includes thermostat states (eg it being 'too cold in here'). But that does not magically make the thermostat state the same thing as a human belief (or vice versa). It merely means we've stretched the word beyond what we normally mean by it. The same problem is apparent in Norbert Wiener's cybernetic theory: We can reach a level of abstraction where machines and humans are functionally equivalent, and thus analogous. But, there is an obvious level of specificity where they are quite fundamentally different. The mere fact that we can find one way of describing two things so that they are the same, does not mean they are the same in every way. But many, especially in the field of artifical intelligence, seem to miss this.
But I digress. If we accept the postmodern line of thought, promulgated by various thinkers from many different fields, that there is no essential 'object', no separable objectivities correlating to our words which hold their determined natures 'out there' (this thought has been called many different things...the best of which I think is social constructionism). If we accept this, then the way we measure and define is of the utmost importance. For in this way, it is the kind of ruler we use which creates the properties we perceive. Thus, the language we use determines our world. This is not to say that it affects or alters objectivity, for 'the world', my world, is a synonym for subjectivity. The world we live in is formed via language, for it is our thinking-ruler...it is through our language that we measure the world and thereby determine it to be constituted of feet or metres.
For this reason we should be supremely careful about the language we use.
One of the major problems comes when we begin to define self apart from life. For those who identify self with mental processes, they remove the self from the world and place it solely within the brain. No longer is the self constituted by the life it lives - that is, by living, and by making itself in the world - it is now a byproduct. And (in this view) the world exists without selfhood, this is the problem: we have separated self from world by using these definitions.
And, I think, it is language that has done this. By creating the illusion of a shared, non-subjective reality, we slowly have come to think that it is more important than the subjective. Perhaps we could never have done what we do as a species without this subjugation of the inner, of the personal worlds. Civilisation depends on language, and language's imputation of objectivity. Interestingly, it was precisely language that so mystified Plato (and Socrates): it created the illusion that there were abstract, ineffable forms behind the word-concepts we use. Language abstracts from reality, and then we attempt to argue that language defines a 'higher' reality than the material one we experience.
Further, the question of whether the mind is physical or non-physical is demonstrably false: there is no such tidy entity as 'the mind': it is just a category we use (and so, for clarity, are 'mental events', 'thoughts', 'qualia' etc). Like 'love'. The category is useful and it works, but we do not seek either a physical or non-physical entity called 'love'. We recognise it is just a useful word and everyone knows what we mean when we use it. The same with the word 'mind'...but we are tempted, led astray, into thinking that the individual world, subjectivity, equals the mind, in distinction from the body which houses the brain. Nonsense! Utter nonsense. There is just the world. No physical. No mind. Just world, just life.