Four strategies for dealing with the counting anomaly in spontaneous collapse theories of quantum mechanics

A few years ago, I argued that according to spontaneous collapse theories of quantum mechanics, arithmetic applies to macroscopic objects only as an approximation. Several authors have written articles defending spontaneous collapse theories against this charge, including Bassi and Ghirardi, Clifton and Monton, and now Frigg. The arguments of these authors are all different and all ingenious, but in the end I think that none of them succeeds, for reasons I elaborate here. I suggest a fourth line of response, based on an analogy with epistemic paradoxes, which I think is the best way to defend spontaneous collapse theories, and which leaves my main thesis intact.