Um, he doesn't. He is talking about Searle's argument, but he is not refuting it. Explicitly he says:
"Where
others invoked complexity considerations to argue with Searle about the metaphysical question,
I’m invoking them to argue with Penrose about the practical question."
Aaronson is not arguing with Searle at all, he is using Searle's argument as an example of other peoples faulty thinking about complexity. Aaronson understands (which is why he doesn't elucidate Searle's argument) that Searle is talking about meaning, and Aaronson is criticizing other peoples critics of Searle that are based in computation for failing to understand complexity:
"I find this response to Searle extremely interesting—since if correct, it suggests
that the distinction between polynomial and exponential complexity has metaphysical significance.
According to this response, an exponential-sized lookup table that passed the Turing Test would
not be sentient (or conscious, intelligent, self-aware, etc.), but a polynomially-bounded program
with exactly the same input/output behavior would be sentient."
More to the point, Aaronson doesn't address the meaning (or as he says, the metaphysical) questions at all. He is interested in the complexity problem of producing a machine that passes the Turing Test, and how philosophers don't seem to grok that very practical problem. Searle recognizes the practical problem for what it is (lookup tables can be Turing complete) and talks about meaning and asks us to consider where the meaning of things are, and shows that meaning does not exist in the functions or the data the functions process. So that even if a machine passes the Turing Test, it fools the observer. The machine still would not be "intelligent"; it would not be conscious.
"Where others invoked complexity considerations to argue with Searle about the metaphysical question, I’m invoking them to argue with Penrose about the practical question."
Aaronson is not arguing with Searle at all, he is using Searle's argument as an example of other peoples faulty thinking about complexity. Aaronson understands (which is why he doesn't elucidate Searle's argument) that Searle is talking about meaning, and Aaronson is criticizing other peoples critics of Searle that are based in computation for failing to understand complexity:
"I find this response to Searle extremely interesting—since if correct, it suggests that the distinction between polynomial and exponential complexity has metaphysical significance. According to this response, an exponential-sized lookup table that passed the Turing Test would not be sentient (or conscious, intelligent, self-aware, etc.), but a polynomially-bounded program with exactly the same input/output behavior would be sentient."
More to the point, Aaronson doesn't address the meaning (or as he says, the metaphysical) questions at all. He is interested in the complexity problem of producing a machine that passes the Turing Test, and how philosophers don't seem to grok that very practical problem. Searle recognizes the practical problem for what it is (lookup tables can be Turing complete) and talks about meaning and asks us to consider where the meaning of things are, and shows that meaning does not exist in the functions or the data the functions process. So that even if a machine passes the Turing Test, it fools the observer. The machine still would not be "intelligent"; it would not be conscious.