Can physicists engage with postmodernism?

Alan Sokal, a Professor of Physics at New York University, became a "celebrity" back in 1996 when he succeeded in publishing a paper in the leading postmodern journal, Social Text, that was a parody of the gibberish that some academic postmodernists write about theoretical physics. Sokal's web site documents the "furore" that this generated.

Sokal's recent book, Beyond the Hoax: Science, Philosophy, and Culture received a rather negative review from Peter Saulson in Physics Today. I symphathise with the review.
The subsequent exchange of letters between Sokal and Saulson is worth reading. There is also a somewhat critical review by David Mermin in Nature.  It seems Sokal has got somewhat carried away and is unable to see that some of the arguments and issues are a little more complex and subtle than physicists are used too.