The cosmological conclusions of weak lensing surveys are very sensitive to the assumed redshift distributions of sources placed in different tomographic bins. In reality, these distributions are not known quantities, so from a Bayesian perspective they should be treated as random objects, constrained by data. For photometric redshifts, the data are fluxes in a number of bands. In this talk, we look at the influence of this redshift uncertainty from a principled Bayesian perspective, and show how, in the case of the KiDS-Viking 450 cosmic shear survey, this approach changes the tension that exists between the results and Planck-derived parameters, indicating either a stronger case for new physics, or a weakening of the tension.