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When I look a sign from far away, I can't make out the letters. However, when I look at a human from a similar distance, I can recognize the face. Clearly my facial recognition system has adaptions for working with nearsighted eyes. A lens that can see its own flaws. And this couldn't have evolved only in humans. Mice probably have similar adaptions.

[...]

What about this: we have mechanisms to make proteins based on DNA sequences, but do we have any mechanisms for telling weather we have the right DNA sequence? Yes we do. Nearly every organism has error-correcting processes right after replication (where errors are most likely to be created), and many ways to avoid getting viruses to fool them.

The DNA replication mechanism relies on proofreading each segment right after it has been appended to the new copy. If the newly added segment differs from the base, it would be corrected, before the process moves to the next segment. It's a hard-coded biological mechanism, occurring locally within a cell. [1]

What's uniquely human in this argument is the ability to apply a corrective mechanism on the logical - or epistemological - level. The mechanism itself must be grounded in physical processes happening within our bodies and extends to the realm of thoughts. Humans, through evolving culture, found out that there is an innate bias, and then realized that we can make better predictions about the world if we compensate for it. That's what (I think) Eliezer meant by applying second-order corrective error to the first-order thoughts. The models of our physiology and mental processes produce an estimation of that error - the more accurate the model, the better the estimation of the corrective error, and finally, the more objective view of reality. The corrective mechanisms on the cellular- or tissue- or organ-level are present across the whole animal kingdom. In fact, they are the basis of life, but they are not what this article is about.

Setting this distinction aside, do we actually have any evidence of thinking about thinking being a uniquely human ability? Without doing the heavy lifting of investigating the corpus of data, I'd imagine this ability lives on a spectrum with some of the other species showing at least a minimal degree of self-reflection. My intuition is that a second-order correction wouldn't be possible without linguistic and symbolic capabilities, and traces of these are also present in other animals - like dolphins. 

[1] - https://bio.libretexts.org/Bookshelves/Introductory_and_General_Biology/Map%3A_Raven_Biology_12th_Edition/14%3A_DNA-_The_Genetic_Material/14.06%3A_DNA_Repair