  We present a method to measure the growth of structure and the background
geometry of the Universe -- with no a priori assumption about the underlying
cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear
data we simultaneously reconstruct the lensing amplitude, the linear intrinsic
alignment amplitude, the redshift evolving matter power spectrum, P(k,z), and
the co-moving distance, r(z). We find that lensing predominately constrains a
single global power spectrum amplitude and several co-moving distance bins. Our
approach can localise precise scales and redshifts where Lambda-Cold Dark
Matter (LCDM) fails -- if any. We find that below z = 0.4, the measured
co-moving distance r (z) is higher than that expected from the Planck LCDM
cosmology by ~1.5 sigma, while at higher redshifts, our reconstruction is fully
consistent. To validate our reconstruction, we compare LCDM parameter
constraints from the standard cosmic shear likelihood analysis to those found
by fitting to the non-parametric information and we find good agreement.
