Well, I don't think our brains work by applying "logic" when we think about Gödel's theorem (or anything else). We evolved to do pattern matching, so each of u

Well, I don't think our brains work by applying "logic" when we think about Gödel's theorem (or anything else). We evolved to do pattern matching, so each of us spends decades to learn more and more sophisticated pattern matching techniques, starting from mom and dad's faces to counting things to multiplication tables to, finally, understanding Gödel's theorem (for some people). In light of this, we can reinterpret "However, a human can look and see that the Gödel sentence is true" as: When you take the best pattern matching machine nature has produced, train it with distilled essentials of centuries of mathematical geniuses, and present it with the Gödel sentence, the pattern matcher strongly signals "This looks true!" When viewed this way, it looks less like an inherently human-specific achievement, but more like exactly how ML algorithms work. The only difference is that ML cannot quite pull it off, so far.