Searle too makes a simple appeal to our intuitions, just as Turing did in appealing to the power of indistinguishability (i.e., if you can't tell them apart, you can't affirm of one what you deny of the other): Searle notes that, as the implementation is irrelevant, there is no reason he himself should not implement the code. So we are to suppose that Searle himself is executing all the computations on the input symbols in the Chinese messages -- all the algorithms and symbol manipulations -- that successfully generate the output symbols of the pen-pal's replies (the ones that are indistinguishable from those of real life-long pen-pals to real life-long pen-pals).
Searle then simply points out to us that he would not be understanding the Chinese messages he was receiving and generating under these conditions (any more a student mindlessly going through the motions of executing some formal algorithm whose meaning he did not understand). Hence there is no reason to believe that the computer, implementing exactly the same code -- or indeed that anyimplementation of that code, merely in virtue of implementing that code -- would be understanding either.
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