How does the Westminster Confession address the paradox of the Bible canon? Chapter I, Article IV of the Westminster Confession (1647) reads:

The authority of the Holy Scripture, for which it ought to be believed, and obeyed, dependeth not upon the testimony of any man, or Church; but wholly upon God (who is truth itself) the author thereof: and therefore it is to be received, because it is the Word of God.

This is very similar to Article I in the Chicago Statement on Biblical Inerrancy (1978):

WE AFFIRM  that the Holy Scriptures are to be received as the authoritative Word of God.
WE DENY  that the Scriptures receive their authority from the Church, tradition, or any other human source.

But nowhere does Scripture define its own composition.
Would not some extra-Biblical source or sources have to be credited here as a relevant &quot;testimony of man or Church&quot; upon which the authority of Scripture itself must somehow depend?  Such sources would include Church Fathers, Church councils, consensus within one's denomination or branch, trust in the Bible publisher(s), or, at the very least, personal belief or intuition.
Is this a valid point? Has it ever been addressed by those who hold to the Westminster Confession?  If so, how is it addressed?
Yes, the Westminster Confession of Faith answers this apparent, but not real, circularity as follows. In Chapter 1 Paragraph 5, we read:


  We may be moved and induced by the testimony of the Church to an high and reverent esteem of the Holy Scripture. And the heavenliness of the matter, the efficacy of the doctrine, the majesty of the style, the consent of all the parts, the scope of the whole (which is, to give all glory to God), the full discovery it makes of the only way of man's salvation, the many other incomparable excellencies, and the entire perfection thereof, are arguments whereby it does abundantly evidence itself to be the Word of God: yet notwithstanding, our full persuasion and assurance of the infallible truth and divine authority thereof, is from the inward work of the Holy Spirit bearing witness by and with the Word in our hearts.


The last clause (starting with "yet notwithstanding, our full persuasion...") is the key. The Holy Spirit convinces the believer that the Bible is true. This is the epistemology of the Christian. It is not circular, because it has an infinite reference point starting with God. God has to reveal himself before anyone knows anything about him.

Incidentally, the Bible actually does talk about itself, particularly in Luke 24, 2 Timothy 3:16-17, and 2 Peter 3:16. If you mean that the Bible does not define its own Table of Contents exhaustively, I would agree with you. The early church recognized the canon, it did not define the canon. This is consistent with John 10:27. There is a good lecture series by Richard Gaffin on how the canon originated.