The breathtaking category mistake in this sentiment is not only disturbing from an abstract point of view, it is cause for deep concern for the future of human inquiry, if we continue to naively demand that all knowledge of the world be communicated in one form or another of bayesian/cartesian modeling, under a watered-down, diluted Popperian epistemological regime (exemplified in the OP's blog title, "Less Wrong".)
I have to take issue with one aspect of your response, though. I lay the blame for this trend, unsurprisingly, at the feet of Descartes himself. The article's sentiment towards Aristotle and Plato and indeed all previous philosophy is first expressed, with nearly the same dismissive arrogance (albeit couched much more subtly for political reasons) in Descartes' Discourse on Method. The Discourse is in fact a much more eloquent (naturally) and far-reaching version of the exact same argument in the OP. It is Descartes' naive dualism and reductionism, as well as his not-so-subtle dismissal of medieval and ancient philosophy, for precisely the same reasons found in this article, that laid the groundwork for the current large anti-intellectual, naively reductionistic trend.
Kudos on the Alexander citation -- I think if you dig deeply into his philosophical and metaphysical roots, you'll find a similar suspicion of naive Cartesian dualism, and a rejection of the simplistic mechanistic metaphors that animate it.
I believe it is in fact this rejection, coupled with a return to more confidence in formal realities, closer to the specific philosophical bent of works like Aristotle's Poetics, that is the basis Alexander's entire project. Note that Alexander has received more attention in many ways outside of his discipline (such as in the software community), for precisely his criticism of the radicalized Cartesian/modernist tendencies in contemporary architecture.