Intentionality and the Inner
The mind is directed outward onto something other than itself. This intentional object might be a particular or a universal, mental or physical, existent or non-existent. It is not identical to the mental state that takes it as object. Moreover, the outer object is essential to the mental state that is directed towards it, constitutive of that state. The object can generally be apprehended and known by others—say, a color or shape or object in space. It is not in itself private or hidden. The mind is characterized by outer objects: “externalism” is true. But the mind is also said to be “inner”: not a public thing, but a private and unobservable thing. An experience of color, say, is something inner—invisible, unlike color itself. These two properties of the mind seem to be in tension, as if one of them has to go: for how can what is constituted by something outer also be essentially inner? How can one and the same thing be both private and public—both “in here” and “out there”? How can the mind be internal and external at the same time?
But there is no irresoluble contradiction here; though there is rhetorical dissonance, which perhaps accounts for the lack of emphasis on the inner nature of mind from philosophers impressed with Brentano’s thesis. We just need to distinguish object from act: the act is inner and the object is outer. An inner mental act has an outer non-mental object. Another person can be in the dark about one’s inner states even though they have public objects, since it may not be determinable which object the mental state concerns. I can fail to know what color you are experiencing even though I am acquainted with all the colors: I don’t know which color is the intentional object of your inner experience–it might be red or it might be green (as in an inverted spectrum case). Perhaps I can’t know your inner state, though I am perfectly familiar with the objects that define it, viz. colors. The mind is both inner and outer, with no contradiction between these two properties. Externalism does not imply third-person knowledge, still less that the mental is not inner.
Indeed, it would seem that being inner is a necessary condition for also being outer, since the mind is necessarily inner—so it cannot be directed outwards without itself being something inner. Intentionality requires innerness. There can be no such thing as an outer mental state that has an outer object. A perceptual experience could not be an outer thing as a matter of metaphysical necessity; so an experience of color cannot be public—though colors are. Expressions of the mind can be public (behavior) but not states of mind themselves. It is not clear exactly why this is so: why should (mental) intentionality be possible only for states that are inner? There seems to be no explanatory or conceptual link here: why does directedness to the outer depend on what is directed being inner? Why do we apprehend the public world from a place of privacy? But it appears to be so, since there are no counterexamples. The converse is not so obvious: not all inner states have intentional objects—such as bodily sensations like pain (though this has been disputed). So being inner does not entail having an outer object. But having an outer object does entail being inner: no intentionality without innerness. 
In so far as acceptance of intentionality leads to reluctance to acknowledge the innerness of mind, the reluctance is misplaced: the mind can be both inherently inner and also necessarily directed outwards. Note that this notion of innerness is not the same as the notion of the internal–what lies spatially within the skin or head. That notion is neither necessary nor sufficient for innerness. The mind cannot be both internal and external in thissense of “internal”: but it can be both inner and outer in the sense intended above. That indeed is definitive of the mind: the mind is that which is inner and yet directed outwards—inner act, outer object. 
 I am speaking of mental intentionality here, not linguistic intentionality (reference): the latter is public, unlike the former. I hold (with many others) that linguistic intentionality is dependent on mental intentionality, i.e. outer signs depend on inner mental states. Thus my claim is that all original intentionality is inner.