The Internet tells me that the idiom “question everything, especially rumors [sic]” can be traced back to ‘The Proverbs of Alfred‘ (mid-twelfth century), which are ascribed to King Alfred the Great (c.848-899). Clearly, the concept has been around for a while.
The System of Doctor Tarr and Professor Fether is a short story by Edgar Allen Poe, published in the November 1845 issue of Graham’s Magazine (Vol XXVIII, No. 5, pp 193-200). It contains the sentence “Believe nothing you hear, and only one half that you see.” While being attributed to Poe, it’s now commonly misquoted as “believe only half of what you see and none of what you hear.” Ironic.
When applied to itself, the quote becomes an ouroboros; a snake eating its own tail. Reading is (usually) a process of sight: so, since one sees the words, which ‘half’ of them should be believed? And if someone were to speak those same words (or if one should listen to them within one’s own head) then they become sound — are being heard… and so none of it should be believed. It’s a perfect phlyarologism: it disappears up its own backside.