I'm no heavyweight here nor am I a talented debater, so you have to be nice to me!
I don't really intend to fight this one out; I've got a lot of other things I'm studying and dealing with right now. But I notice that there isn't much 'chatter' from my fellow Sola Scripturaists here. Not that they need my help here, but at least this might keep you entertained in the meantime...
How to prove the canon of Scripture using Scripture. I admit I don't have a complete argument here... at least not yet. In case you were wondering, no I am not smart enough to come up with all of this on my own. I remember some of this from New Testament 101 in college... I wish could remember all of what my professor used to prove what belonged to Scripture and what did not. I will dig around and perhaps I will find my notes. Either way I doubt it would leave anyone "quaking in their boots." But here goes...
Luke 26Did not the Christ[a] have to suffer these things and then enter his glory?" 27And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself.
Okay here we have Jesus explaining what was prophesied about Him in the Old Testament Scriptures. Ordinarily this would just be one of many references to Scripture, but we do see a glimpse of what Jesus was thinking about when He was thinking about Scripture. He began with Moses... I'm sure someone can bring up the point that Luke does not specifically mention Genesis, Exodus, Leviticus, Numbers, or Deuteronomy by name. Fair enough. But I think we can probably assume Jesus is talking about the Books of Moses here. The Prophets are mentioned as well, thought not by name. However the list of books he was referring to here is (for the most part) pretty obvious.
I was always taught that there were roughly three divisions of the Old Testament: the Law, the Prophets, and the Writings. I also remember being taught that prior to the destruction of Jerusalem this three-fold division was thought of as a two-fold division of the Law and Prophets. So you could argue from this standpoint that Luke is establishing the general collection of the Law and the general collection of the Prophets as Scripture. You can make of that what you like. I think the many quotes from the Law and Prophets (including the books often grouped as the Writings) prove at least that those books are thought of as canonical. Overall I think that the Old Testament is accepted as a Scripture. Don't even ask me about how the DC fits into all of that, I don't know that much.
As for the some books in the New Testament...
2 Peter15Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. 16He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.
The subject here are the letters of Paul. Admittedly they are not named, but it seems to be that they are well known enough to Peter's audience. Anyways, these letters are compared to "the other Scriptures." I can't help but think that phrase places the letters of Paul in the category of Scripture.
Perhaps if the letters of Paul could be called Scripture then the letters of Peter could as well, therefore making 1 and 2 Peter canonical. If that is true then perhaps the writings of the other Apostles could be thought of as Scripture as well in John, 1 John, 2 John, 3 John, and Revelation... even Matthew. But this would be making a real stretch to try and prove that from this verse I think. Even I can admit that.
Of course in that case I do have a problem here: both of the books of the Bible I quote from to prove the canonicity of the OT and Letters of Paul... I can't prove that they are canonical themselves! Leave it to me to shoot down my own proof.
Maybe someone more skilled than me can flesh out what I've started. Peace out!