Shirky arhived his speech on his own blog: Ontologies are Overrated.
William Denton on Web4Lib recommends a provokative talk by Clay Shirky. Shirky contends that LC Classification and other "ontologies" (which he defines as "assertions about essnece and relations among a group of items") may have outlived their usefulness. In the case of LCC, he maintains that driving force has been arrangement of things (i.e., books on shelves) rather than authentic relations among ideas. Complains about inconsistencies in LCC, where "Balkan Penninsula" stands as a top geographic category alongside "Asia." (What does he mean by this? In the G1994 Atlases part of the schedule, the region is subsumed under Southeastern Europe; in GB457 "Physical geography" section, it's subsumed under Medeterranean Sea region; I checked other areas as well, and nowhere does it appear as a top term).
He also complains that LCC is flat, and that it doesn't accommodate polysemy (though he refers to it as polypheny): "it enforces cookie-cutter categorization that doesn't reflect the polyphony of its contents--there is a literature of creativity, for example, made up of books about art, science, engineering, and so on, and yet those books are not categorized (which is to say shelved) together". LCC does allow multiple classification, though, and in any case, it is complemented by the LC Subject Headings which can accomodate as many different conceptual relationships as people can think of.
Shirky delivered his remarks at the O'Reilly Emerging Technology Conference. The audio recording is archived at ITConversations