[FOM] Proof "from the book"  Aatu Koskensilta aatu.koskensilta
at xortec.fi Wed Sep 1 05:49:23 EDT 2004  Jeffrey Ketland wrote:
>The notion of "reflective consequence" has been analysed by
Feferman. Using >the Kripke-Feferman truth axioms, Feferman
defines a theory Ref(S) which he >calls the "reflective closure"
of S. This is meant to contain the sentences >one "ought to
accept", when one initially accepts a mathematical theory S. >In
a sense, Ref(S) is the result of iterating the construction from
S to >Tr(S). Feferman doesn't advocate iterating Ref(S), but I
do not see why.  The problem here seems to be that if you
advocate iterating Ref(S),  you're committing yourself to
theories of truth which are substantial and might not follow
from what one is implicitly committing oneself when accepting S.
This might be  illustrated by the fact that Ref(Ref(S)) will in
general be stronger than what you get by  autonomously iterating
reflection, so accepting iterating S |-> Ref(S) leads you beyond
the  constructive w