Given that in human terms, empirical == dominant consensus, you are merely using a different word for 'primacy' in this context. It makes no difference to the structure.

Because : consensus of what? of sheer numbers of human adherents? of other statistic? historical evidence? of widest agreement by those with higher education in that field? of those with the most money to afford advertising? other? a consensus of multiple consensus(es)?

The dynamic of myriad possible vectors through language to express a given 'truth' remains, whether we define truth as empirical or consensus.

This is well-trodden ground of the theory of knowledge. People not being explicit about their assumptions about the world lead to destructive myths like "empirical fact" that collapse with the slightest institutional distrust.