Storr's flippant dismissal of Art.sy's taxonomy as "reductive" isn't even wrong – it's completely irrelevant. It's the same thing as complaining that Pandora's music genome is reductive. Obviously it's reductive. Applying a systematic taxonomy to music or art – or living creatures or languages or anything at all – clearly cannot capture the nuance and fullness of detail of the actual items to which the taxonomy applies (except my best friend's taxonomy of black metal, which I'm pretty sure has a subsubcategory for every song ever). But such systems aren't intended to do that. It's akin to complaining about the Library of Congress classification system because each book's classification doesn't fully specify its content. That's not the point of the system. It's a navigational and organizational aide, not a complete encoding.
A real critique would address the site's success as a navigational and organizational aide. I suspect that Storr uses texts full of reproductions of art in his classes. Does he also complain that they are "reductive" because they are imperfect reproductions of the original artworks? I doubt it. I bet he does, however, select the texts that serve the purpose of helping students of art understand the intellectual and artistic landscape better than others. It's completely absurd to complain that a textbook fails to reproduce the experience of seeing an artwork in person. Of course it doesn't. It is, however, helpful to discuss how a text does and doesn't succeed in providing an understanding of the space of art which it covers.
While I like your comment I do wonder whether it may rest on a misunderstanding of the work 'reductive'. I believe it is being used in the philosophy of science sense wherein reality can be understood in terms of the workings of components. It stands in contrast with holism, for example Quine's semantic holism.
A real critique would address the site's success as a navigational and organizational aide. I suspect that Storr uses texts full of reproductions of art in his classes. Does he also complain that they are "reductive" because they are imperfect reproductions of the original artworks? I doubt it. I bet he does, however, select the texts that serve the purpose of helping students of art understand the intellectual and artistic landscape better than others. It's completely absurd to complain that a textbook fails to reproduce the experience of seeing an artwork in person. Of course it doesn't. It is, however, helpful to discuss how a text does and doesn't succeed in providing an understanding of the space of art which it covers.