Peels considers arguments for the unreliability of introspection based on: the sometimes large effect of reporting method (e.g., button press vs. verbal report) on the content of introspective judgments; cultural variation in whether dreams are seen as colored; the poor correlation between self-reported visual imagery and performance on cognitive tasks often thought to be facilitated by visual imagery (such as mental rotation or folding tasks); people's ignorance of their capacity for echolocation; and people's ignorance of the lack of detail and precision in the visual field. In each case, Peels presents the skeptic's argument in a couple of pages and then offers a couple of pages of objections.
For example, Peels offers three responses to my observation that self-reports of mental imagery tend not to correlate with behavioral performance on seemingly related cognitive tasks. First, he points out that since people don't have access to other people's imagery, terms like "vivid" might be interpreted quite differently between subjects -- and thus people might be accurate in their own idiolect even if not in an outwardly measurable way. Second, he suggests that the aspects of mental imagery being reported (such as vividness) might not be relevant to the cognitive tasks at hand (like mental rotation), in which case lack of correlation is to be expected. Third, he notes that some studies (a minority) do report positive correlations. While in my discussion of this topic, I have given reasons to be leery of psychological findings that fail to replicate -- such as experimenter bias, "file-drawer" effects, the existence of confounding or intervening variables, and participants' tendency to confirm perceived research hypotheses -- Peels argues that I have presented insufficient positive evidence that such factors are at work in these cases.
The imagery case is, I think, illustrative of the debate in two ways: First, a lot hinges on examination of the empirical details, such as the precise nature of the measures. And second, a lot hinges on judgments of plausibility about which reasonable people might differ. For example, looking at hundreds of studies of visual imagery self-report and cognitive performance, a literature with lots of null results and non-replications, does one think (as I do), "That looks pretty bad for the reality of an underlying effect" or does one think (as Peels seems to), "There probably is an effect in there somewhere that the null studies aren't effectively getting at". This sort of thing is a matter of judgment. (And no, I don't think the typical statistical meta-analysis will yield a straightforward answer that we should take at face value.)
One's sense of plausibility, in such matters, comes close to being something like one's general academic worldview -- about philosophy, about psychology, and about their interaction. Here, I find the introduction and conclusion of Peels' essay interesting.
In the introduction, Peels lists four reasons the question of the reliability of introspection is important:
(a.) Ordinary "common sense" tends to treat introspection as a reliable source of knowledge. To reject its reliability is to challenge common sense.
(b.) There's a philosophical tradition from Descartes to Chalmers of taking introspection (appropriately restricted) as infallible. To reject introspection's reliability means abandoning the infallibilist tradition.
(c.)There's a contrary "scientistic" tradition that emphasizes science as the only secure source of knowledge and regards introspection as non-scientific. To reject introspection's reliability plays into the hands of those who want to privilege the epistemic role of science.
(d.) There's a debate within science about how to treat introspective self-reports.
As these observations make clear, issues about introspection are inextricable from one's general sense of what philosophers and psychologists should be doing. I suspect that it is background differences between Peels and me on these sorts of questions that drive our different senses of plausibility in interpreting the empirical details.
I want to resist the infallibilist tradition in philosophy, and the philosophical tradition that emphasizes "common sense", and other philosophical and metaphilosophical positions that seek to insulate philosophical reasoning from science. This is fundamental to my worldview and my vision of the nature of philosophy. My views on introspection are of a piece with this general worldview -- supporting that worldview, I think, but also supported by it. Other considerations that support such a worldview are (I argue) the incoherence and cultural variability of "common sense" and philosophical fashion, and evolutionary, cultural, and psychological reasons to think that people would likely be much worse reasoners about philosophical issues than they are about mundane, practical affairs.
I would add to Peels' four considerations also a fifth consideration of a somewhat different sort: People usually want to be taken at their word when they say they're not angry, not racist, happy with their life choices. To express doubt is to deny people a certain sort of authority over the story of what is going on in their own minds. An introspection-friendly approach tends to cede people that sort of self-authority; an introspective-skeptical approach denies that self-authority. Again, there are big-picture worldview questions at stake, which both inform one's sense of how to interpret the psychological evidence and are in turn either supported or undercut by some of that same evidence.
Although Peels' essay focuses on the empirical details of a few cases, this larger context both informs and motivates all work on the epistemology of introspection. Are we basically right about ourselves, and is philosophy of mind safe from radical scientific critique? Or is self-knowledge fragile and the armchair a tempting cozy spot to doze away into ignorance?