Is this a circular argument: "The Bible is inspired because the Church says so; the Church is infallible because the Bible says so"?

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.

  1. First stage: historical reliability of the texts.

  2. Second stage: divinity and resurrection of Jesus – recognized from the available data, not already presupposed.

  3. 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”).