When I taste a glass of wine, there is a sense in which the phenomenal character of the taste of the wine is for me, rather than for you. This for-me-ness can be construed as the relation between some phenomenal character and the subject of consciousness. Moreover, the “me” in for-me-ness refers to the subject of consciousness, whatever it turns out to be. Several philosophers argue that for-me-ness is constitutive of the phenomenological structure of consciousness, i.e., to explain the phenomenological structure of consciousness, one must at least appeal to for-me-ness.
Among those who defend the above position, one prominent group of philosophers defends Higher-Order Thought (HOT) theories of consciousness, including David Rosenthal and Peter Carruthers who employ different notions of HOT to explain for-me-ness. Arguably, both of them commit to the claim that for-me-ness realizes the interpretation function when it comes to constituting the phenomenological structure of consciousness in contrast to the speaker's proposal—Perspectival-Reflexive Representationalism.
*adapted from the abstract written by K.Yan, which you could find the original content provided in the reading material below.