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> TM+Halting oracle > TM

Why is this a failure of the Church-Turing thesis? The Church-Turing thesis says, "Anything that can be computed in our reality (i.e. by a human, ignoring resource constraints) can be computed by a TM." TM+Halting oracle doesn't satisfy the hypothesis.

It's not a failure of Church-Turing. The whole point of my comment is that you can easy construct more powerful models that are "unreasonable" because they don't exist in our universe. It's the same for programming language models.

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