I think to treat the differend that shows up in the rather trivial-seeming exchange of digs between Chomsky and Zizek as a mere infantile “spat” is already to come down on one side of the quarrel (Chomsky’s side) and one side of the division (the analytic side). Zizek’s whole intellectual style incorporates finding the far-reaching philosophical and political issues in the anodyne details of ordinary and mediatic life. This is a very important component of the Continental approach.
There is something more substantive at stake in the Chomsky/Zizek differend, and that is a difference in cognitive styles between Continental and Analytic modes of thinking. I am no great fan of Zizek’s and I have criticised him in several places on this blog.
I criticise Zizek for example here: https://terenceblake.wordpress.com/2011/11/27/avatar-zizek-vs-the-post-jungian-vision/. But note that I criticise him for being insufficiently faithful to his typological method, separating out one typological series (the Oedipal one) as the key to all the other series. I also think that analogical or typological reasoning can be quite potent, but it is not infallible, and needs to be checked against the facts. I discuss a particular example of typological reasoning that fails here: https://terenceblake.wordpress.com/2012/05/17/harmans-table-talk-2-on-analogical-typology/
I am not concerned who won the “match”, nor even about the particular persons involved, but about the styles of thinking. Chomsky and Zizek are only incidentally concerned with the facts. Chomsky cannot stand Continental style theory and doesn’t seem to have read much of it (he is to that extent non-empirical), and Zizek relies so much on theory that he doesn’t bother to get his facts straight.
Both are in fact doing badly what each of their philosophical epistemes requires, and thus they reveal even more clearly the presence of such incommensurable frameworks in what they say. I think the discussion of the Khmer Rouge example is a red herring (forgive the pun!). Zizek is not vey good at analytic argument and tends to proceed typologically (or by “gestalts”). Chomsky, while arguing well analytically, presupposes that such typological reasoning is irrational and its conclusions are either erroneous or without interesting content.
One can see in the in general pretty mindless declarations of support on both sides that the public is not really very interested in the arguments either, but rather in confirmation of their opinions (this is normal and obvious) but also, I would argue, in confirmation of their way of thinking.
Analytic philosophy tends to frame certain deepseated disagreements reductively as mere “spats”. One reason for this attitude lies in the status accorded to “incommensurability”. In analytic philosophy the very existence of incommensurable theories (here we already have a limitation to the semantic domain) is admitted, if at all, only as a conclusion to a long and difficult debate.
However, in Continental philosophy the existence of incommensurabilities is very often the commonly recognised starting point for thinkers such as Lyotard, Deleuze, Derrida, Foucault, and Badiou. It is far easier from a Continental perspective to see in such disputes more than just personal attacks and quibbling, but as indicative of fundamentally different images of thought.
Chomsky admits to looking at these thinkers’ theories and at seeing nothing there. He does not ascend to the meta-level to see if there are systematic presuppositions causing a form of cognitive blindness, he simply infers that there is nothing to see.
Perhaps it all goes back to Hegel’s PHENOMENOLOGY. The dialectical way of thought lets one see ideas as gaining their content and their sense from being inscribed in different figures of consciousness (or phenomenological worlds, or understandings of being). The specific rules of transition from one figure to another that Hegel proposes may or may not be accepted, but the post-Hegelian mode of (dialectical) thought makes abundant use of such typological perceptions and arguments.