  We discuss the presence of ghostly instabilities for metric-affine theories
constructed with higher order curvature terms. We mainly focus on theories
containing only the Ricci tensor and show the crucial role played by the
projective symmetry. The pathological modes arise from the absence of a pure
kinetic term for the projective mode and the non-minimal coupling of a 2-form
field contained in the connection, and which can be related to the
antisymmetric part of the metric in non-symmetric gravity theories. The
couplings to matter are considered at length and cannot be used to render the
theories stable. We discuss different procedures to avoid the ghosts by adding
additional constraints. We finally argue how these pathologies are expected to
be present in general metric-affine theories unless much care is taken in their
construction.
