socially mediated (i.e. affected by social factors when the effect is not justified by empirical facts).

Hmm, "justified" generally has a social component, so I doubt that this definition is useful.

there is no way to express the concept that Ptolomy intended when he said epicycles

So this WP page doesn't exist? ;)

My position, FWIW, is that all of science is socially mediated (as a consequence of being a human activity), mathematics no less than any other science. Whether a mathematical proposition will be assessed as true by mathematicians is a property ultimately based on physics - currently the physics of our brains.