  The theories of pre-quantum physics are standardly seen as representing
physical systems and their properties. Quantum mechanics in its standard form
is a more problematic case: here, interpretational problems have led to doubts
about the tenability of realist views. Thus, QBists and Quantum Pragmatists
maintain that quantum mechanics should not be thought of as representing
physical systems, but rather as an agent-centered tool for updating beliefs
about such systems. It is part and parcel of such views that different agents
may have different beliefs and may assign different quantum states. What
results is a collection of agent-centered perspectives rather than a unique
representation of the physical world.
  In this paper we argue that the problems identified by QBism and Quantum
Pragmatism do not necessitate abandoning the ideal of representing the physical
world. We can avail ourselves of the same puzzle-solving strategies as employed
by QBists and pragmatists by adopting a \emph{perspectival quantum realism}.
According to this perspectivalism (close to the relational interpretation of
quantum mechanics) objects may possess different, but equally objective
properties with respect to different physically defined perspectives. We
discuss two options for such a perspectivalism, a local and a nonlocal one, and
apply them to Wigner's friend and EPR scenarios. Finally, we connect quantum
perspectivalism to the recently proposed philosophical position of
\emph{fragmentalism}.
