These books have been mentioned on the list before, but I'm recommending
them again because a lot of new members have joined since we last talked
about them. To motivate you to read these books, I've given some questions
that each book helps answer or provide the necessary background knowledge
to discuss. I'd say that the first book in this list should be required
reading for all members of this list, while the other two are more
optional. If anyone else has more book recommendations, please feel
free to add to this list.

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_An Introduction to Kolmogorov Complexity and Its Applications_, Ming Li
and Paul Vitanyi
(What is "measure", "prior", "universal distribution"? How can we explain
why laws of physics exist and why we don't see random deviations from the
laws of physics?)
_Theory of Recursive Functions and Effective Computability_, Hartley
Rogers
(What does "computable" mean? What do we know about uncomputable
mathematical structures? Should we assume that we're in a computable
universe?)
_The Foundations of Causal Decision Theory_, James Joyce
(What justifies using numbers between 0 and 1 to represent degrees of
belief and using probability theory to constrain/manipulate those numbers
(i.e. probabilities)? Is the use of probabilities still appropriate if all
possible universes exist, and if so how should it work? How should we make
decisions if all possible universes exist?)