  A librationist set theory \pounds ${}$ is developed. It descends from
semantics for truth, initiated by by Kripke, Herzberger, Gupta and others. #
extends the system \pounds, of Librationist closures of the paradoxes in Logic
and Logical Philosophy 21(4), 323-361, 2012. The focus is upon the paradoxes in
theories of sets. A central result is that the extension
#$\mathscr{HR}(\mathbf{D})$, of #, accounts for $\mathbf{NBG}$ set theory, with
the global Axiom of Choice and Tarski's Axiom. Moreover, # also succeeds with
defining an impredicative manifestation set $\mathbf{W}$, $\mathit{die \
Welt}$, so that #$\mathscr{H}(\mathbf{W})$ accounts for Quine's $\mathbf{NF}$.
Nevertheless, the points of view developed support the view that the
truth-paradoxes and the set-paradoxes have common origins, so that the
librationist resolutions of the set theoretic paradoxes at the same time are
resolutions of the truth theoretic paradoxes. Both the librationist resolutions
of the set theoretic paradoxes and the truth theoretic paradoxes have
non-trivial implications: librationist set theories have the consequence that
there are no absolutely uncountable sets, and librationist truth theories allow
the use of syntactical modalities in ways which circumvent well known
limitations, first pointed out by Montague in 1963. So librationism has a truth
predicate which is useful for more precise discourse, and # retains the
ideology of the author's 2012 article, that the set theoretic universe is
countable. But the set within which $\mathbf{NBG}$ is interpreted "believes"
that there are sets which are uncountable. The situation is analyzed much as by
Skolem, though it is not suggested that the notion of $\mathit{set}$ is
imprecise: for the bijection from the set of finite von Neumann ordinals to the
full universe is not a member of a classical set theory.
