  The reflection principle is the statement that if a sentence is provable then
it is true. Reflection principles have been studied for first-order theories,
but they also play an important role in propositional proof complexity. In this
paper we will revisit some results about the reflection principles for
propositional proofs systems using a finer scale of reflection principles. We
will use the result that proving lower bounds on Resolution proofs is hard in
Resolution. This appeared first in the recent article of Atserias and M\"uller
as a key lemma and was generalized and simplified in some spin-off papers. We
will also survey some results about arithmetical theories and proof systems
associated with them. We will show a connection between a conjecture about
proof complexity of finite consistency statements and a statement about proof
systems associated with a theory.
