If Scripture is not the source by which all truth claims must be measured, what is?
Scripture and Tradition. The true "rule of faith"—as expressed in the Bible itself—is Scripture plus apostolic tradition, as manifested in the living teaching authority of the Catholic Church, to which were entrusted the oral teachings of Jesus and the apostles, along with the authority to interpret Scripture correctly.
This oral teaching was accepted by Christians, just as they accepted the written teaching that came to them later. Jesus told his disciples: "He who hears you hears me, and he who rejects you rejects me" (Luke 10:16). The Church, in the persons of the apostles, was given the authority to teach by Christ; the Church would be his representative. He commissioned them, saying, "Go therefore and make disciples of all nations" (Matt. 28:19).
And how was this to be done? By preaching, by oral instruction: "So faith comes from what is heard, and what is heard comes by the preaching of Christ" (Rom. 10:17). The Church would always be the living teacher. It is a mistake to limit "Christ’s word" to the written word only or to suggest that all his teachings were reduced to writing. The Bible nowhere supports either notion.
Further, it is clear that the oral teaching of Christ would last until the end of time. "’But the word of the Lord abides for ever.’ That word is the good news which was preached to you" (1 Pet. 1:25). Note that the word has been "preached"—that is, communicated orally. This would endure.
If Scripture is not the source by which all truth claims must be measured, what is?
For Methodists, it’s the Weslayan Quadilateral; Scripture, tradition, reason, and experience.