The three "legs" of the Church are Scripture (Written Tradition), Oral Tradition and the Magisterium (the Church's teaching).
This must be so if we are to be able to know with certainty that what we consider to be Scripture is really the Word of God. Why? At the time of our Lord's death there were no New Testament writings. Jesus left his Apostles with a Church and Oral Tradition. Some Oral Tradition was recorded by various writers. Several centuries after Christ's death this body of Written Tradition was codified as Scripture by Christ's Church. From history we can see that Oral Traditon and the Church preceded Written Tradition (Scripture), and if Written Tradition is inerrant, than so must be Oral Tradition and the Church.
The argument for the inerrancy of Sacred Scripture is a spiral argument.
Matthew 16:18-19 supports the doctrine that Peter is given the keys to the Church. It says nothing about the church being given the authority to determine what is and isn't the Word of God.
What authority would determine what is and isn't the Word of God? It would have to be a divine authority, wouldn't it? Would Jesus leave us a fallible authority to determine the canon of Scripture?
In fact, this is what R.C. Sproul believes. He believes that he has a fallible collection of infallible books.
But Jesus left us the Church, which He calls "the pillar and foundation of truth." Logically then, He tells us to take our disputes "to the Church." So that is where I look when I want to know what constitutes the canon of Scripture. See the link above.
"On the first level we argue to the reliability of the Bible insofar as it is history. From that we conclude that an infallible Church was founded."
This kind of leap in logic is what is so baffling to me. The Houghton Mifflin company has produced many historically reliable books as well. It does not follow that the Houghton Mifflin company is infallible in any way.
With regard to oral tradition and the New Testament; Jesus left His Apostles (NOT "various writers") with the responsibility of spreading His good news throughout the world after His death and resurrection. From that charge we now have the Gospels and the remaining books of the New Testament. Considering they are based on the good news of Christ's death and resurrection, it would require extreme clairvoyance for the Apostles to write the books of the New Testament before Christ's death. But they did manage to squeek them out before their own deaths. I'm not sure oral tradition plays that key a role in what is essentially an autobiographical account of their own witness of the life of Christ.
"Would Jesus leave us a fallible authority to determine the canon of Scripture?"
You are assuming Jesus is incapable of influencing the actions of man without using the Catholic church. The fallible authority is Jesus Christ himself. Through Him, nothing is impossible. Even without the Catholic church.
"He tells us to take our disputes "to the Church." "
But in this passage, "the Church" is not capitalized. Jesus is referring to the local "church" or the assembled community. Obviously, there was no single church body that resembled anything like today's Roman Catholic Church. This often repeated scripture is used out of context when it is used to imply the overall dominion of "the Church". That simply is not the case. But as you infer, we once again are falling into a spiral argument.
In the final analysis, I see how you put the pieces together, but I disagree with the picture you create. But I sincerely appreciate your thoughtful explanations of the issues we've been discussing. Since this debate has raged for over 500 years, the odds of it being resolved on FreeRepublic are just about zero. But discussing the issues, in a frank, open manner is incredibly constructive toward building understanding if not consensus. I think we can both agree that is a positive step toward greater unity.