  Constraints on cosmology from recent cosmic shear observations are becoming
increasingly sophisticated in their treatment of potential systematic effects.
Here we present cosmological constraints which include modelling of intrinsic
alignments. We demonstrate how the results are changed for three different
intrinsic alignment models, and for two different models of the cosmic shear
galaxy population. We find that intrinsic alignments can either reduce or
increase measurements of the fluctuation amplitude parameter sigma_8 depending
on these decisions, and depending on the cosmic shear survey properties. This
is due to the interplay between the two types of intrinsic alignment, II and
GI. It has been shown that future surveys must make a careful treatment of
intrinsic alignments to avoid significant biases, and that simultaneous
constraints from shear-shear and shear-position correlation functions can
mitigate the effects. For the first time we here combine constraints from
cosmic shear surveys (shear-shear correlations) with those from "GI" intrinsic
alignment data sets (shear-position correlations). We produce updated
constraints on cosmology marginalised over two free parameters in the halo
model for intrinsic alignments. We find that the additional freedom is well
compensated by the additional information, in that the constraints are very
similar indeed to those obtained when intrinsic alignments are ignored, both in
terms of best fit values and uncertainties.
