I am finally getting around to working on a paper on higher-order thought theory and introspection. I started thinking about this back in 2015 and presented an early version of it at the CUNY Cognitive Science Speaker Series (draft of paper here…sadly it is at Academia.edu which I do not use anymore). That was just a month before my son was born and I don’t think I had it quite nailed down. I put it one the back burner and then got caught up doing all kinds of other things.
But I’m back on it now, and am working with Adriana Renero. I am excited about this project because I don’t think that this aspect of the theory has been given enough attention. The basic idea that I had was that the traditional model of introspection offered by higher-order theorists -that one has a conscious higher-order state- needed to be supplemented. It seems to me that when one has an ordinary conscious experience of blue one is representing the first-order state as presenting a property of the physical world and when one introspects one represents the first-order state as presenting a property of one’s mind. In ordinary conscious experience it seems to me like I am being presented with objects which have colors, or make sounds, etc but when I introspect I seem to be presented with properties of my own experience. Thus conscious experience and introspection of this sort both rely on second-order thoughts that represent the relevant first-order states. Both of these second-order thoughts deploy a concept of the relevant mental quality: one concept attributes it to the physical object and the other attributes it to one’s own experience.
Rosenthal seems to agree with this, for example saying
When one sees a red tomato consciously but unreflectively, one conceptualizes the quality one is aware of as a property of the tomato. So that is how one is conscious of that quality. One thinks of the quality differently when one’s attention has shifted from the tomato to one’s experience of it. One then reconceptualizes the quality one is aware of as a property of the experience: one then becomes conscious of that quality as the qualitative aspect of an experience in virtue of which that experience represents a red tomato
Consciousness and Mind page 121
However, the way he fleshes out this distinction is in terms of *conscious* thoughts. So, when one is conceptualizing the mental quality as a property of the tomato, on his view, this amounts to one having, in addition to the higher-order state which renders one conscious, conscious thoughts abut the tomato. When one ‘reconceptualizes’ it as a property of experience, one’s higher-order state is itself conscious. Thus the difference for him is one of what one’s conscious thoughts are representing. But this doesn’t seem to me to do the trick.
The reason for this is that it seems to me that this would still be the case even if I had no conscious thoughts about the object I am perceiving. Suppose I am consciously perceiving a blue box and yet I am not consciously thinking about the blue box. In such a case it still seems to me that my conscious experience presents the blueness of the box as a property of the box itself. To bring this out even more we can consider the case of an animal that does not have any conscious thoughts, ay a squirrel. Our squirrel may nonetheless have conscious experiences and it seems to me strange to think that the squirrel’s experience does not present the blueness of the box as a property of the box.
Another issue here is that the relevant higher-order thought is the same throughout on Rosenthal’s account. So it must conceptualize the blueness of the box as a property of my experience the entire time. So why think that I ‘reconceptualize’ it when I have a conscious higher-order thought?
The same seems true for the case of introspection. If I am introspecting my experience of the box then it seems to me that the blueness is a property of the experience even if I am not having any conscious thoughts about the mental blue quality. I am not denying that I ever consciously think about my experience, only that this is required for introspection.
So what, on my view, is the content of these higher-order states? My current thinking is that in the case of typical conscious experience one has a higher-order thought with the content ‘I am seeing blue’ and when one introspects one has a higher-order state with the content ‘I am in a blue* state’ or ‘I am experiencing mental blue’. Of course to see blue is just to be in a blue* state and these two intentional contents are different ways of saying the same thing but they still seem to me to result in different experiences.
I am still thinking through this and any feedback would be appreciated!
Richard Brown 
The passage you quote, Richard, takes a couple of shortcuts, which in context seemed to be OK, but from a full theoretical point of view is not. Let me explain.
I see something red and round. So I’m in a qualitative state with the mental quality red and round. On my view (my quality-space theory) that mental quality isn’t conscious on its own. (Let’s not argue about the term, ‘mental quality’.) And since I see something red and round, I also conceptualize the stimulus as something red and round.
When I then become aware of this seeing, on my view by having a HOT that I’m seeing something red and round, I then become aware of seeing a red, round, stimulus property. Before having this HOT, I was conceptualizing the stimulus as something red and round, and so aware of some physical perceptible stimulus as having the properties of being red and round. But I wasn’t consciously aware of any of that. Now with my HOT, I’m consciously aware of all that–and so I’m consciously conceptualizing something as having the perceptible properties of being red and round.
I’m also aware of the mental qualities of red and round–but not yet consciously aware of them. So although I have also conceptualized myself as being in a state with those mental qualities, I have not yet consciously conceptualized myself in that way.
Now I introspect, which on my view is having my awareness of the seeing become a case of conscious awareness of the seeing–by having a third-order thought that I have a second-order thought that I’m seeing something red and round. Now I’m consciously aware of the mental qualities of red and round that my qualitative state exhibits, and so I’m also consciously conceptualizing myself as being in a state with those mental qualities.
So when I’m in a nonintrospectively conscious state of seeing something red and round, I *consciously* conceptualize the the qualitative property that figures in that seeing as a property of the stimulus. When I’m in an introspectively conscious state of seeing something red and round, I *consciously* conceptualize the the qualitative property that figures in that seeing in two ways–as a property of the stimulus (by way of the second-order thought) and as a property of a qualitative state of mine (by way of the third-order thought).
So the passage you quote from my “Introspection and Self-Interpretation” in Consciousness and Mind is taking a shortcut, partly by not saying that I’m talking about *conscious* conceptualizing and partly by not mentioning that the conceptualization of the qualitative property as a property of the stimulus doesn’t go away when I introspect.
Why the shortcuts? Well, the context (Boghossian-Velleman) is talking about *conscious* conceptualization. So I followed suit. And introspection involves not only the occurrence of a third-order thought, on my view, but a shift of attention from what the second-order thought is about (the seeing of the statement) to what the third-order thought is about (being in a conscious visual state of a particular sort). So the *attentive* conscious conceptualizing is on the mental quality, and no longer on the stimulus property.
I very much appreciate your in effect challenging me on these matters. I hope that the foregoing at least helps clarify what my view is.