  Paul Bernays and David Hilbert carefully avoided overspecification of
Hilbert's epsilon-operator and axiomatized only what was relevant for their
proof-theoretic investigations. Semantically, this left the epsilon-operator
underspecified. In the meanwhile, there have been several suggestions for
semantics of the epsilon as a choice operator. After reviewing the literature
on semantics of Hilbert's epsilon operator, we propose a new semantics with the
following features: We avoid overspecification (such as right-uniqueness), but
admit indefinite choice, committed choice, and classical logics. Moreover, our
semantics for the epsilon supports proof search optimally and is natural in the
sense that it does not only mirror some cases of referential interpretation of
indefinite articles in natural language, but may also contribute to philosophy
of language. Finally, we ask the question whether our epsilon within our
free-variable framework can serve as a paradigm useful in the specification and
computation of semantics of discourses in natural language.
