Property dualism: at least some mental properties are fundamental, i.e. not identical to any non-mental properties, like neurochemical or functional properties. Typically, property dualists contend, against materialists, that what philosophers call a phenomenal state, i.e. the undergoing of an experience with a distinctive qualitative character, is not identical to any neurochemical (or functional) state. For example, an experience of pain is not identical to the undergoing of C-fibre stimulation, even if C-fibre stimulation always occurs when we experience pain, and vice versa. Hence, the phenomenal property of being in a state of pain is not identical to the neurochemical property of being in a state of C-fibre stimulation, or any other neurochemical (or functional) property. As we have seen, property dualists generally argue that there is an unbridgeable explanatory gap between neurochemical and phenomenal facts. That is, we lack an explanation as to how it is that phenomenal states 'just are' neurochemical states. If two things X and Y are numerically identical, then it is logically impossible for one to exist without the other. Thus, we may say that a logically necessary connection holds between X and Y, such that the existence of X logically entails that of Y, and vice versa. The dualist complaint is that there is no explanation as to why such a connection should hold between, say, the state of experiencing pain and the state of undergoing C-fibre stimulation. For many dualists, this is strong reason to reject the thesis that the state of experiencing pain 'just is' the state of undergoing C-fibre stimulation, as well as all identifications of phenomenal states with neurological ones.
We can reconstruct the argument as follows:
(1) There is no explanation as to how phenomenal states are identical to neurochemical states.
(2) If there is no explanation as to how phenomenal states are identical to neurochemical states, phenomenal states are not identical to neurochemical states.
(3) Therefore, phenomenal states are not identical to neurochemical states.
Notice that the argument's begins with the statement of an explanatory gap (premise (1) ) and ends with the statement of an ontological gap (conclusion (3) ). That is, the argument, through premise (2), infers a claim about the manner in which things exist, from a claim about a lack of explanation.
As some materialist critics of the argument have shown, e.g. Papineau 1998, one can try to block this inference by putting pressure on premise (2). One can accept the argument's first premise, but deny that the ontological gap follows from the explanatory gap, by arguing that the demand for an explanation is unreasonable. If two things X and Y are identical, it makes sense to ask how we know that they are identical, but it seems odd to ask why they are identical. For example, if you tell me that Bruce Wayne is Batman, I may ask you how you know this, but you'd be surprised if I asked you, 'But why is Bruce Wayne Batman?' You might interpret my question along the lines of 'Why did Bruce Wayne become a masked vigilante?', but you'd be very puzzled if I replied with 'No, I mean why is the person Bruce Wayne the same person as the person Batman?'. This is like asking, 'why am I the same person as myself?'. Things just are what they are, and, on the face of it, it makes little sense to ask why this is so. Thus, it could be argued, the absence of an explanation for the identity of, say, the experience of pain and C-fibre stimulation is nothing to be worried about, and, against premise (2), certainly shouldn't lead us to deny that they are identical.
I think this objection rests on an ambiguity in the request for an 'explanation'. If I ask you to explain to me why my phone has disappeared, I am asking you to give me the cause of my phone's disappearance, i.e. the prior event or fact that brought about its disappearance. If on the other hand I ask you to explain Spinoza's theory that God is the only substance, I am asking you to make the theory intelligible to me.
The way I see it, the 'explanatory gap' problem is not that we know of no prior cause of the identity between the experience of pain and C-fibre stimulation, but rather that such an identification is unintelligible. If things X and Y are identical, their identity, while not 'caused', is nevertheless made true by some other fact. The identity of Batman and Bruce Wayne is made true by the fact that they are the product of the same particular fertilization event, i.e. involving the same sperm and egg. The fact that my Dad's car today is the same as the car that existed three years ago is made true by the fact that there is some special kind of causal continuity between the two. Given such facts, the non-identity of X and Y is inconceivable: for example, given that Batman and Bruce Wayne are the product of the same particular fertilisation event, it is impossible to conceive of their non-identity. Arguably, it is part of the very concept of identity that identity-claims be made true by some other fact in this way. And therein lies the problem for the identification of the experience of pain with C-fibre stimulation: materialists cannot give us any fact by which the relevant identity-claim is made true. This is why thought experiments about, say, the conceivability of C-fibre stimulation existing without the experience of pain, or vice versa, are so prominent in the case for dualism. If the experience of pain and C-fibre stimulation were identical, there would be some fact given which it would be impossible to conceive of one without the other. But, we know of no such fact, and we can't even conceive of a fact that would do the job. This last point allows us to deal with a common rejoinder to dualist arguments. It used to be thought that the Morning Star and the Evening Star were two different stars, though we now know that they are in fact the same planet, Venus. But before this discovery, people presumably would have been able to conceive of the Morning Star existing without the Evening Star, or vice versa (or, at any rate, it would have seemed to them that they could conceive of this). Hence, we are told, the conceivability of pain without C-fibre stimulation, or vice versa (or the appearance of this conceivability), is no good reason to disbelieve that they are the same thing. But there is a key difference between the two cases: if I was born before the discovery of the identity of the Morning Star with the Evening Star, I wouldn't know how they are identical, but, after a bit of thinking, I would know how they could be identical. That is, I could imagine that they are the result of the same particular planet-formation event, and understand that this would entail that they are the same thing, though perceived from different perspectives. Indeed, I would understand that, if it were the case that they were the result of the same particular planet-formation event, the existence of one without the other would be inconceivable. In contrast, in the case of pain and C-fibre stimulation, I can't even see what sort of fact would make true the statement of their identity, and hence do not understand how they could be identical. I can think of no possible neurochemical (or other) state of affairs such that, if it obtained, the existence of C-fibre stimulation without the experience of pain would be inconceivable. It is in this sense, I think, that the (alleged) identity of phenomenal states and neurochemical states lacks an explanation: it is unintelligible, because we cannot see how they could be identical. And if that's right, then it seems to me that, insofar as a metaphysical system ought to minimize unintelligible claims, this is strong reason to reject the identification of phenomenal states with neurochemical states. This, in my view, is how the explanatory gap leads us to an ontological gap.