Bradley Monton

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini and Weber [1986]) can only solve the problem of 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 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi 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 guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact.

We discuss the cable guy paradox, both as an object of interest in its own right and as something which can be used to illuminate certain issues in the theories of rational choice and belief. We argue that a crucial principle—The Avoid Certain Frustration (ACF) principle—which is used in stating the paradox is false, thus resolving the paradox. We also explain how the paradox gives us new insight into issues related to the Reflection principle. Our general thesis is that principles that base your current opinions on your current opinions about your future opinions need not make reference to the particular times in the future at which you believe you will have those opinions, but they do need to make reference to the particular degrees of belief you believe you will have in the future.