In this paper, "Sensations and Brain Processes" (1962, but this view dates back to mid-fifties), Smart lays out the identity thesis and then defends it against a number of objections that had been raised in the literature of the time.

What is going on when I say that it looks to me like there is a yellowy-orange patch of light on the wall? Although Smart finds Wittgenstein's answer appealling, that one is not making a report, but is instead expressing a temptation to make a report that there is such a patch of colour, he does have reason for thinking that one is actually reporting something. What one is reporting, however, is not that one is experiencing an irreducibly mental event. This is the thesis he wishes to defend. Why? Because science has been progressing so much that it seems likely that one day it will be able to completely explain the mind in purely physical terms. He cannot believe that mental events, like having sensations, are outside of the physical realm. Not a very scientific view. If mental events were outside of the physical realm, then they would be "nomological danglers", they would not be explained by the laws we use to explain everything else. Smart believes that there are no philosophical arguments that compel us to be dualists.

The Wittgensteinian/behaviourist view about sensation statements is that sensations are nothing over and above behavioural facts about the person. So to say that there seems to be a patch of colour on the wall is just a piece of behaviour that means that one might be disposed to say that there actually is a patch of colour on the wall. It is not a report, but it is the exercise of a disposition.

Smart, though, believes that when one makes such a statement, or when one states that one is in pain, one is making a genuine report, but just not a report about something non-physical. Because he believes that mental processes just are types of physical processes, and that pain is something physical, then when one says that he is in pain, what one is reporting is a physical process. Smart reduces mental phenomena to physical phenomena, so he is a reductive physicalist. However, he rejects Ryle's kind of reduction - he says that it doesn't follow from his reductive physicalism that all mind-talk can be translated into brain-talk. Talk about sensations means something different than talk about brain processes, but it doesn't follow that sensations cannot be brain processes.

Consider Frege's distinction between sense and reference. The example Frege uses (as does Smart, which suggests he had Frege in mind) is that of Hesperus and Phosphorus, or the Morning Star and the Evening Star. The two names refer to the same thing - the planet Venus as it turns out, but they don't mean the same thing, they don't have the same sense. If they did, then it wouldn't have been a discovery that MS = ES. If the names were synonymous, we would know a priori, but that is not the case. So having different senses doesn't ensure having different reference.

Smart's theory is that there is a strict but contingent identity between mental processes and brain processes. By strict identity, he means that the two processes are not simply spatially and temporally continuous with one another (like personhood), but that they are one and the same thing at the same time.

Objection 1
We don't need to know anything about our brain processes, or even that the brain has anything to do with thought, to make claims about our sensations. So sensations couldn't be brain processes.
Reply: uses the example of lightning = an electrical discharge. Lightning is publicly observable, so therefore is the electrical discharge - these are just two different way of describing the same thing. Two senses, one reference. You can know that you are witnessing a flash of lightning and not know you are witnessing an electrical discharge. Same for sensations and brain processes.

Objection 2
It is only a contingent fact (if fact) that when we are having a certain sensation, we are having a certain brain process. This is just a correlation, which may be proven to be wrong. So when we report a sensation, we are not reporting a brain process.
Reply: all this objection proves is that talk of sensations/afterimages does not mean the same as talk about brain processes. That doesn't prove they are two different things. Just because it is a contingent fact that sensation s = brain process b, it doesn't follow that they are not identical. If sense = reference, then this would be a problem, because if they had the same reference, then they would mean the same, but we don't have to accept this theory.

Kripke in Naming and Necessity claims that all identiy is necessary, that there cannot be contingent identity. A thing is necessarily identical to itself, so if is contingent that sensation s is brain process b, they can't be strictly identical. If they are strictly identical, then they are necessarily so. Why would Smart insist that the identity is contingent?

Objection 3
This is the one Shaffer takes up. 1 & 2 don't prove that sensations are something over and above brain processes, but they do prove that one experiences sensations and brain processes differently, and so there must be some properties of sensations that are irreducibly mental. This is the position of property dualists. There must be something distinctive about the sensation, there must be some different way of picking it out, just like the MS is picked out in the mornining and the ES is picked out in the evening. One appears in the morning and the other doesn't and so when we make an identity claim, we are actually saying something non-trivial. Sensations then must have some phenomenal property that the brain processes lack in order to pin down the identification of something as a mental process.
Reply: The topic-neutrality of sensation statements. When someone says it seems to them that there is a yellowy-orange patch of colour on the wall, then he is saying that there is something going on in him that is similar to what goes on in him when he is looking a a yellowy-orange patch of colour in good light etc. But he is not saying how they are similar, but just that they are similar. We will talk about this reply in more detail when discussing Shaffer.

Objection 4
The after-image in not in physical space, whereas the brain process is. So they can't be identical.
Reply: Smart is not claiming that the after-image is identical with a brain process, but rather that the experience of having an after image is identical.

Objection 5
Brain processes can be fast or slow, can form shapes in the brain etc. but we can't talk about sensations in this way. This is an appeal to Leibniz' Law of the Indiscernability of Identicals.
Reply:  They don't have the same meaning and they don't have the same logic, but that doesn't mean they can't be the same thing. Some day it might make sense to talk of sensory experiences in the same way we talk about brain processes.

Objection 6
Sensations are private, brain processes are public. Only I have privileged access to my sensations, whereas other people can observe my brain processes. This is an epistemological objection: there are different ways of knowing sensations from brain processes, so how could they be the same?
Reply: Again, the logic of sensation reports is different from the logic of brain reports. At this point in science, it is true that we each have privileged access to our own experiences, but once we know more that may change.

Objection 7
I could be made of stone (i.e., not have a brain) but still have sensations.
Reply: Again, all this objection show is that "experience" and "brain process" do not mean the same thing, but it doesn't show that they don't have the same reference. Otherwise, this objection just begs the question against materialism - it doesn't prove materialism is false.

Objection 8
Wittgenstein's "beetle in the box" objection. We all have a beetle in the box (e.g., pain), but we only ever see inside our own boxes - private access. What I mean by "beetle" could be very different than what you mean. How could we possibly tell whether or not we all have the same thing inside our "boxes"? Any rule of language must have public criteria for its correct application.
Reply: topic neutrality again. "To say that something looks green to me is simply to say that my experience is like the experience I get when I see something that really is green." I am not saying how they are alike - my description is neutral as to whether it is a mental or physical similarity. Shaffer argues that this can't be so.
 

Is the identity thesis an empirical or a priori claim? If the question is whether sensations are brain processes, or liver processes, or heart processes, then, Smart says, it is an empirical question. But if the question is whether some form of materialism is correct or whether epiphenomenalism (mental processes are just by-products of or in addition to physical ones and play no causal role - they are causally inefficacious), then is is not an empirical issue. There could be no evidence to decide between the two, but epiphenomenalism is not a scientific position and Occam's razor (fewer assumptions, better explanation) would insist we choose materialism.