A mathematician's (or, at least, <i>this</i> mathematician's) instinctive response to a paper titled "Against set theory" is to think that it must be the work of a crank (not to disparage the work of reputable mathematicians exploring alternative foundations—but I think that most of them know that, to earn their ideas a receptive foundation, they had better focus at least on what they are for rather than what they are against), but it should probably be noted that this is against set theory from a <i>philosopher</i>'s point of view, not a <i>mathematician</i>'s. (With which I can't quibble, though neither can I agree; I am no philosopher, and the fact that mathematics <i>can</i> be used fruitfully in philosophy doesn't mean that it always <i>should</i>.) Indeed, at a skim, the complaint seems to be much more about the mathematisation of philosophy broadly speaking, rather than about the encroachment of set theory in particular.<p>(I also take issue with the claim on p. 3 that Cauchy was doing only unconscious set theory. It is true that he came before what we might call Cantor's formalisation of the subject, but I think he probably thought in something much closer to a modern "naïvely set theoretic" way about mathematics than almost all o his predecessors.)