Is cosmology just a plausibility argument?

I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never do; this recommends abandoning realism. Despite this, we can adopt a scientifically correct pragmatism and understand aspects of the cosmological model with enormous confidence. I illustrate these points with discussion of one certainty--expansion--and two current controversies--the existence of large extra dimensions and the possibility that the matter distribution forms a fractal on large scales. I argue that the existence of large extra dimensions is certainly plausible, but a fractal universe is untenable.