  We discuss the question of whether or not a general Weyl structure is a
suitable mathematical model of space-time. This is an issue that has been in
debate since Weyl formulated his unified field theory for the first time. We do
not present the discussion from the point of view of a particular unification
theory, but instead from a more general standpoint, in which the viability of
such a structure as a model of space-time is investigated. Our starting point
is the well known axiomatic approach to space-time given by Elhers, Pirani and
Schild (EPS). In this framework, we carry out an exhaustive analysis of what is
required for a consistent definition for proper time and show that such a
definition leads to the prediction of the so-called "second clock effect". We
take the view that if, based on experience, we were to reject space-time models
predicting this effect, this could be incorporated as the last axiom in the EPS
approach. Finally, we provide a proof that, in this case, we are led to a Weyl
integrable space-time (WIST) as the most general structure that would be
suitable to model space-time.
