Losing your marbles in wavefunction collapse theories

Peter Lewis ([1997]) has recently argued that the wavefunction collapse the ory of GRW (Ghirardi, Rimini and Weber [1986]) can only solve the problem o f wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 i s in the box and marble 2 is in the box and so on through marble n, then al l n marbles are in the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) h ave replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cann ot persist, according to the GRW theory, for more than a split second ([199 9], p. 709). On the contrary, we argue that Lewis's argument survives Ghira rdi and Bassi's criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarant ees that the principle can never be empirically falsified, leaving the appl icability of arithmetical reasoning to both micro- and macroscopic objects intact.