[1]
For experiments from the Lamme lab, see (Sligte et al. 2008, 2010, 2011; Vandenbroucke et al. 2011). This result has been replicated by other labs. See for example, (Freeman & Pelli 2007). My discussions of these experiments appear in (Block 2007a, 2007b, 2008). See also (Jacobson 2014) for a discussion of a different relationship between the dissociation between access and phenomenal consciousness and the dissociation between phenomenal character and representational content.
[2]
He references (Grush 2007) but the point is also made in other critiques (Kouider et al. 2007; Papineau 2007; Van Gulick 2007)
[3]
For the record, I used the generic/specific distinction in earlier papers (though not using that terminology including the one that these critics were replying to. For example, in discussing the Lamme experiment in the BBS paper to which all of these opponents were replying (Block 2007a), I said:
“This supports what the subjects say, and what William James said, about the phenomenology involved in this kind of case. What is both phenomenal and accessible is that there is a circle of rectangles. What is phenomenal but in a sense not accessible, is all the specific shapes of the rectangles.” (p. 488)
The phenomenology as of a circle of rectangles is generic phenomenology; the phenomenology as of the specific shapes is specific phenomenology. Further, in an earlier version of the argument based on the Sperling experiment in 1995 I also appealed to a version of the generic/specific distinction, although somewhat less explicitly (Block 1995, p. 244)
“Here is the description I think is right and that I need for my case: I am P- conscious of all (or almost all - I will omit this qualification) the letters at once, that is, jointly, and not just as blurry or vague letters, but as specific letters (or at least specific shapes), but I don't have access to all of them jointly, all at once. [italics added]”
[4]
If you want to get a brief taste of the kind of argument I have in mind, look at one of: (Block 2014a, 2014b). In one of the articles cited (Bronfman et al. 2014), evidence is provided of specific information about uncued rows in a Sperling-like experiment. What I especially like about this experiment is that the authors provide 3 different tests of the claim that the specific information in the uncued rows is conscious.
[5]

In (Block 2011), I said “…generic conscious representations of non-square rectangles that do not specify between horizontal and vertical orientations is difficult to accept.” Note that this is not a blanket denial of the possibility of solely generic phenomenology but rather a denial of one specific kind of solely generic phenomenology. Hilla Jacobson and Hilary Putnam relate this kind of point about imagery to a principle of “cohesiveness” of the various aspects of an image (Jacobson & Putnam forthcoming).

[6]
Of course uniqueness does not require solely generic or solely specific phenomenology. Any sole level will do.
[7]
By “owner of a heart” he must mean some sort of biological classification (on a par with chordate) since obviously any individual mouse could lose its heart (even briefly staying alive) and still be a mouse.
[8]
In his reply to me (2014), Burge is more skeptical than I am about the power of appeals to adaptation, arguing that adaptation needs to be combined with other methods.
[9]
Fink seems to acknowledge such points in footnotes 14 and 22 but somehow ignores them in explicating phenomenal precision.