A baffling argument from credentials has led me to think about theological arguments from authority in general. (That baffling argument can be found here, but the background and resolution are too tedious to revisit.)
Objection 2. Further, if [theology] is a matter of argument, the argument is either from authority or from reason. If it is from authority, it seems unbefitting its dignity, for the proof from authority is the weakest form of proof. But if it is from reason, this is unbefitting its end, because, according to Gregory (Hom. 26), "faith has no merit in those things of which human reason brings its own experience." Therefore sacred doctrine is not a matter of argument....
Reply to Objection 2. This doctrine is especially based upon arguments from authority, inasmuch as its principles are obtained by revelation: thus we ought to believe on the authority of those to whom the revelation has been made. Nor does this take away from the dignity of this doctrine, for although the argument from authority based on human reason is the weakest, yet the argument from authority based on divine revelation is the strongest.
An argument from authority based on human reason takes the form, "X is true because Y, having given it some thought, says X is true." Generally speaking, that's not a very strong argument, even if it suffices for a particular practical matter (as when X is "My keys are on the table downstairs" and Y is "my wife").
But an argument from authority based on divine revelation takes the form, "X is true because God says X is true," and you only have to read three verses into the Bible before you find that this argument confers absolute conviction (assuming you believe God says X is true).
Well and good. But in practice, Christian theology makes heavy use of arguments from authority based on human reason, a practice St. Thomas justifies thusly:
Hence sacred doctrine makes use also of the authority of philosophers in those questions in which they were able to know the truth by natural reason, as Paul quotes a saying of Aratus: "As some also of your own poets said: For we are also His offspring" (Acts 17:28). Nevertheless, sacred doctrine makes use of these authorities as extrinsic and probable arguments; but properly uses the authority of the canonical Scriptures as an incontrovertible proof, and the authority of the doctors of the Church as one that may properly be used, yet merely as probable. For our faith rests upon the revelation made to the apostles and prophets who wrote the canonical books, and not on the revelations (if any such there are) made to other doctors.
St. Thomas, then, identifies three authorities, each conferring a different level of conviction:
Church Fathers and Doctors
proper but merely probable
extrinsic and probable
Remember, these are cases of arguments from authority: Y says X, therefore X. Any particular authority can also offer an argument, which can then be considered on its own merits.