No. It is not a circular, but a spiral argumentation: from history to Christ, from Christ to the Church, from the Church to the inspiration of Scripture.
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First stage: historical reliability of the texts.
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Second stage: divinity and resurrection of Jesus – recognized from the available data, not already presupposed.
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Third stage: founding of a Church with teaching authority; this Church, authenticated by Christ, testifies to inspiration and canon.
Thus, the authority of the Church is not derived from the (already) inspired Bible, but from Christ; and then the Church authenticates the Bible.
Sources
Scripture (EÜ): John 16:13; Luke 10:16; Acts 15.
Fathers/Teachers: Augustine; Newman (necessity of a “perpetual interpreter”).