Copernican reasoning involves considering ourselves, in the absence of other information, to be randomly selected members of a reference class. Consider the reference class intelligent observers. If there are extraterrestrial intelligences (ETIs), taking ourselves to be randomly selected intelligent observers leads to the conclusion that it is likely the Earth has a larger population size than the typical planet inhabited by intelligent life, for the same reason that a randomly selected human is likely to come from a more populous country. (...) The astrophysicist Fergus Simpson contends that this reasoning supports the claims that the typical planet inhabited by ETIs is smaller than Earth (radius about 5,000km; cf. Earth's radius = 6,371km) and that the typical ETI is significantly larger than us about 314kg, the size of an adult male grizzly bear). Simpson's applications of Copernican reasoning are novel and exciting. They should be of interest to philosophers concerned with Richard Gott's delta t argument, the N=1 problem in astrobiology, limited principles of indifference, and probabilistic epistemology in general. While we agree with Simpson about the qualitative direction of his conclusions, we take issue with his presentation of precise quantitative results because his methods (1) display bias, (2) ignore other variables contributing to population size, (3) commit an equivocation, and (4) conceal their dependence on arbitrary assumptions. (shrink)

Gott (Nature 363:315–319, 1993) considers the problem of obtaining a probabilistic prediction for the duration of a process, given the observation that the process is currently underway and began a time t ago. He uses a temporal Copernican principle according to which the observation time can be treated as a random variable with uniform probability density. A simple rule follows: with a 95% probability.