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PhilGoetz comments on Logical Rudeness - Less Wrong
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IIRC, John Searle uses a subtle form of this in his rebuttal to rebuttals to his Chinese Room argument. He separates the attacks into different cases; then he uses one set of assumptions and definitions to rebut one case; then switches (without pointing it out) to a different set of assumptions and definitions to rebut another case. Neither set of assumptions and definitions is sufficient to rebut both cases.
This can be valid if the assumptions are brought in by the rebuttals he's defending against, and those rebuttals make contradictory assumptions.
Do the sets of assumptions and definitions contradict each other, or can they all be seen as subsets of a single set of definitions and assumptions? If they contradict each other then pointing that out should be an effective argument in most of the contexts where Searle writes.
I'm referring to Searle's responses to the responses to his article that were originally published in Brain and Behavioral Sciences 3, 1980. I studied them 20 years ago, but it would take me a long time to go back and re-analyze it to answer your question.
I wondered what you meant by different sets. I think that this answers my question (they might have been consistent). Thanks.