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

Abstract
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.
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DOI 10.1080/0269859031000160603
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References found in this work BETA
Peter J. Lewis (1997). Quantum Mechanics, Orthogonality, and Counting. British Journal for the Philosophy of Science 48 (3):313-328.
Angelo Bassi & GianCarlo Ghirardi (2001). Counting Marbles: Reply to Clifton and Monton. British Journal for the Philosophy of Science 52 (1):125-130.
Peter J. Lewis (2003). Counting Marbles: A Reply to Critics. British Journal for the Philosophy of Science 54 (1):165-170.

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Citations of this work BETA
Bradley Monton (2004). The Problem of Ontology for Spontaneous Collapse Theories. Studies in History and Philosophy of Science Part B 35 (3):407-421.
Peter J. Lewis (2005). Interpreting Spontaneous Collapse Theories. Studies in History and Philosophy of Science Part B 36 (1):165-180.
Bradley Monton (2004). The Problem of Ontology for Spontaneous Collapse Theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (3):407-421.
Peter J. Lewis (2005). Interpreting Spontaneous Collapse Theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):165-180.

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