I assume that no interesting controversy exists over whether there is an epistemic sense of “seems”. I question whether there additionally exists a phenomenal sense of “seems”. I question whether there are phenomenal appearances in addition to epistemic appearances.
To get a handle on what the alleged distinction is supposed to be, it helps to consider the following picture. Smith and Jones are two little men in two little opaque boxes. Mediating between the interiors and exteriors of their boxes is a camera that feeds into a computer capable of reliably detecting the presence of dogs near the boxes. Smith’s dog-detecting device has a video readout that displays Smith the printed word “dog”. Jones’ dog-detecting device has a speaker that says “dog” aloud upon dog detection. Both Smith and Jones, via the use of their dog detectors, come to judge that a dog is just beyond the walls of their boxes. Smith and Jones are alike, then, with respect to the ways things epistemically seem to them: insofar as they judge that dogs are present, it epistemically seems to them that dogs are present. However, in spite of these similarities between Smith and Jones, there are notable differences. In particular, there are differences in the evidence they rely on as the bases of their dog-detecting judgments. Smith’s evidence concerns what’s happening on the video display whereas Jones evidence concerns what’s happening with the audio speaker.
Is the above picture a good model for distinct kinds of appearance? Suppose we do something to transform the differences between Smith’s and Jones’ box interiors into a difference between the insides of Smith’s and Jones’ heads. Suppose we kick them out of the boxes and have only their own senses mediate between them and dogs. Smith is deaf but sighted and Jones’ is blind but has his hearing intact. Smith and Jones come to both believe that there is a dog present, but one does so by seeing the dog and the other does so by hearing the distinctive bark. Are the differences that arise in spite of their similarity in judgment worth calling a distinct kind of appearance? Are the ways dogs appear to Smith and Jones epistemically identical but phenomenally distinct? I think not.
If there is indeed a distinction to be made sense of, we need to be able to make sense of two different kinds of cases: one in which phenomenal appearances remain constant while epistemic appearances change and one in which epistemic appearances remain constant while phenomenal appearances change. Neither of the versions of the story about Smith and Jones involve the requisite changes. Whatever changes would be required to change Smith into Jones would change various beliefs Jones had, beliefs like whether he was looking at a monitor versus listening to a speaker
In the first version of the story, Smith and Jones differ with respect to their evidence, e.g. screen vs. speaker. In the second story, there is also a difference with respect to evidence. But it is a big mistake to think that in either story the evidence is something in the heads of Smith and Jones. In the second story, the different evidence is the difference between light reflected and sound emitted. These different kind of events trigger in Smith and Jones certain beliefs which in turn give rise to inferences, the conclusions of which are the common belief that a dog is present.