A great post by Sean Cubitt, in which he argues that isolating medium specificity for arts is misguided and that it's particularly misguided in an age in which digital technology is blurring previous distinctions - in his words, "the divisions between film, video and digital media arts make no sense and weaken all three." In arguing this, he gives a claim that normatively is like Noel Carroll's attack on the "specificity thesis" but with a McLuhan-esque twist: the nodes of mediation become if not the essence then the most important aspect of artistic expression.
It's a thesis I find though-provoking, but let me propose another way at the question by posing it less about specificity of medium per se than about the specificity of aesthetic forms. Take prose literature in either its short-story or novel forms. In the 18th century the novel emerged as a literary form that imposes expectations for writer and guides aesthetic experience for reader. On one hand, mediation (the printing press and print capitalism) had everything to with its emergence (and magazine publishing for the later short story format). On the other hand, it's a remarkably stable aesthetic form that's largely independent of media and technology changes. Sure, there have been some important changes: writers can use word processing to write (maybe this has an aesthetic impact); readers can use digital copies in ways they could not a book (searching for instance); and arguably technology and newer media have contributed to a decline in literary culture. But the aesthetic experience of a novel is still comparable whether I experience it in book form, off a Kindle, or even as a book-on-tape. Cognitively, these are quite different experiences and mediations, but we (I'm generalizing: most consumers) tend to bracket the delivery to get to the symbolic matter and the aesthetic experience.
Cinema's a little trickier, but you see something similar. Here, digital culture is more overwhelmingly shaping cinema in a digital age - and I don't mean to minimize this - but there's a way in which the "cinematic" is an aesthetic form that gets activated in theatrical experience, in television spectatorship, and in internet video in different ways. The expressive track-in shot, for instance, codes a certain emotional and proto-narrative effect regardless of whether it is projected in a cinema or broadcast on television. And if film and media scholars are exploring the ways DVDs have changed film culture, film spectatorship, and even the films themselves, we tend not to place much, if any, distinction on an analysis based on a cinematic projection and a video viewing of the film.
I don't argue that there's some ontological quality to the novelesque or the cinematic. Rather, I'm more influenced by Bourdieu's tendency to look to more-or-less formalized aesthetic cultures. In other words, one does not have to be an idealist philosopher to see that certain ideals are accepted, even enforced, more than others. These forms change over time, but social institutions (education, arts organizations, art markets) can keep aesthetic forms around and formalized for quite some time, even with internal gestures of modernization.
Finally, I would stress that our understanding of medium specificity depends in part on what we're trying to specify. Above I tend to privilege the symbolic and narrative dimensions of the art, in part because I think that's what a large number of art consumers in Western societies tend to do: we take the half-tone reproduction of a Caravaggio painting and try to abstract the aesthetic meaning of that painting, even if we might wish to experience it firsthand. But clearly, the conditions of experiencing an art work are not meaningless; it's just that useful branches of the study of art by necessity abstract them away.