Nick Bostrom wrote:
A proper calculation using Bayes' theorem is missing in the article. The
conclusion is false.
E.g. let's assume that (2) and (3) are false. So, we know with almost 100%
certainty that we are not living in a simulation, and we know with almost
100% certainty that a posthuman civilization is going to run significant
number of simulations of their evolutionary history.
Concluding that (1) must be true is thus precisely the Doomsday argument
which is false because of improper Bayesian reasoning:
No, this is different from the Doomsday argument. DA relies on the premiss
that subjectively distinguishable observer-moments are in the same reference
class. The Simulation argument presupposes only the much weaker assumption:
that subjectively indistinguishable observer-moments are in the same
reference class. (For an explanation of this terminology and the ideas
behind it, I refer you to my forthcoming book Anthropic Bias: Observation
Selection Effects in Science and Philosophy, Routledge, New York, April
2002. I have made five sample chapters (as many as the publisher would
permit) available at http://www.anthropic-principle.com/book/.´´
Why not make the book available for free for all membrers of this list?
Anyway, although the effect may be different from the usual doomday
argument, it is completely analogous. The analog of the self indicating
assumption would be to assume that the prior probability for the cases is
proportional to the number of simulations that will be run by posthuman
civilizations (plus one). In the above case this will nullify any evidence
that seems to prove that we are not alive in a computer simulation, and will
steer us away from early doom.