  We discuss the hypothesis that the debate about the interpretation of the
orthodox formalism of quantum mechanics (QM) might have been misguided right
from the start by a biased metaphysical interpretation of the formalism and its
inner mathematical relations. In particular, we focus on the orthodox
interpretation of the congruence relation, '=', which relates equivalent
classes of different mathematical representations of a vector in Hilbert space,
in terms of metaphysical identity. We will argue that this seemingly "common
sense" interpretation, at the semantic level, has severe difficulties when
considering the syntactic level of the theory.
