In his comment, Mohammed notes that the word appears in a paper, available here:
http://www.michaeltye.us/Access.html ,Tye, Michael and Brian McLaughlin (1998), "Is Content-Externalism Compatible with Privileged Access?" in "The Philosophical Review." This is a dense paper of academic philosophy studded with technical terms such as "externalism."
From context: "We see, then, that principle (RA), the introspective evidence thesis, the alternative thoughts thesis, and privileged access form an incompatible quadrad. It follows that no one can consistently hold all four theses.
e see, then, that principle (RA), the introspective evidence thesis, the alternative thoughts thesis, and privileged access form an incompatible quadrad. It follows that no one can consistently hold all four theses."
It seems clear from context ("no one can consistently hold all four theses" in an "incompatible quadrad") that it means a set of four of SOMETHING, and that quadrad must be one of three things: a) just a synonym for "tetrad" (and a bad one), or b) a word with a technical meaning in philosophy for a group of four SOMETHINGS, or c) the authors' own neologism. It isn't coming up when I try some Internet dictionaries of philosophy.
I don't like it as a word because it is mixing a Latin-derived root ("quad-") with a Greek-derived ending ("-ad"). I don't have any kind of classical education, but a classically-educated gentleman of the Victorian era would find this mixing of Greek and Latin disturbing. The "proper" sequence is monad, dyad, triad, tetrad, pentad; hexad; heptad; octad, ennead; and decade.