I agree with Thomas Nagel, John Searle, and others that conscious experiences are irreducible to physical states. I have endorsed the idea that felt pain, phenomenal pain, pain as experienced or lived through (er-lebt), the pain that hurts, has a subjective mode of existence, a "first-person ontology" in Searle's phrase. If this is right, then phenomenally conscious states cannot be reduced to physical states with their objective mode of existence and third-person ontology. As a consequence, an exclusively third-person approach to mind is bound to leave something out. But there is an objection to irreducibility that needs to be considered, an objection that exploits Frege's distinction between sense and reference.
The basic idea is that linguistic and epistemic access to one and the same item can be had in different ways, and that duality of linguistic and/or epistemic access need not be taken to argue ontological duality in that to which one gains access. Reference to one and the same item can be routed through different senses or modes of presentation (Frege's Darstellungsweisen). Different terms, with different senses, can be used to target one and the same referent. 'Morning Star' and 'Evening Star,' though differing in sense, can be used to refer to the same celestial body, the planet Venus.
Why not say something similar about the physical state I am in when I feel pain? Why not say that there are two ways of accessing the same physical state? The one mode of access is via neuroscience, the other is 'from the inside' via the pain's qualitative feel to the one who endures it. If so, there are not two states or events one physical and the other mental differing in mode of existence; there is exactly one state or event, and it is physical. Dualism is avoided. The upshot is that, contra Nagel, the third-person physicalistic approach to the mind does not leave anything out. One may go on to tax Nagel, Searle, and Co. with illictly inferring a difference in mode of existence from a difference in mode of linguistic/epistemic access. Something like this objection is made by Christopher Peacocke in his review of Nagel's The View from Nowhere (Philosophical Review, January 1989.)
It's a nice try, a very nice try. And it is exactly what one would expect from someone who takes an objectifying third-person view. What's more, it would be in keeping with Occam's Razor if mind could be seamlessly integrated into nature. Unfortunately, the pain I am in is not a mode of presentation, or means of epistemic access, to the underlying brain state. Thus the Fregean analogy collapses. The sense of 'morning star' mediates my reference to Venus; but my pain quale, even if it is caused by the brain state, does not mediate my reference to it.
Let me see if I can make this clear. The suggestion is that the same physical reality appears, or can appear, in two different ways, a third-person way and a first-person way, and that this first-person way of access is no evidence of a first-person way of being. One problem is the one I just alluded to: there is no clear sense in which a pain quale is an appearance of a brain state. The former may be caused by the latter. But that is not to say that the pain quale is of the brain state. The felt pain does not present the brain state to me. It does not present anything (distinct from itself) to me. After all, the felt pain is a non-intentional state. No doubt it has a certain content, but not an intentional or representational content. One can describe it without describing what it is of, for the simple reason that there is nothing it is of. An intentional state, however, cannot be described without describing what it is of.
The Fregean sense/reference analogy therefore breaks down. The basic idea was that one and same reality can appear in different ways, and that the numerical difference of these ways is consistent with a unitary mode of existence of the reality. A felt pain, however, is not an appearance of a reality, but an appearance that is a reality. The appearing of a felt pain is its being, and its being is its appearing. And because this is so, the felt pain is a distinct reality from the brain state. Not only is it a distinct reality, it is a distinct reality with a distinct, irreducibly subjective, mode of existence.
Nagelus vindicatus est. There is something essentially incomplete about a third-person approach to reality. It leaves something out, and what it leaves out is precisely that which makes life worth living. For as Wilfrid Sellars once said to Daniel Dennett over a fine bottle of Chambertin, "But Dan, qualia are what make life worth living!" (Consciousness Explained, p. 383) In vino veritas.