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"Imagine if you tried applying the same logic to other slogans - it would be a nightmare! Take “one person, one vote”, a classic of 20th century movements for universal suffrage; would Siskind try to argue the slogan means everyone only gets a singular vote in their entire life?"

I don't think this is a very fair comparison. "One person, one vote" is true given the clear and never forgotten clause "per election", whereas "The purpose of a system is what it does" is not so easy amended into "[Let's] re-focus the dialogue about a system onto its actual outcomes", and people don't amend it that way unless explicitly told. Therefore, the natural reading of "one person [should have] one vote" is true, whereas the natural reading of POSIWID is false. I think this matters, and that we shouldn't solemnly fling around slogans that are going to be naturally read as something that's false. The difference between the natural reading and the meaning you gave is large enough here that I think Twitter randos are kind of relevant, since the ubiquitous misuse of the term demonstrates its misleading construction. (Also, I think POSIWID's power as a piece of conversation re-centering rhetoric comes from its natural, incorrect reading, which is even more problematic. We shouldn't be misleading people, even if it's useful in refocusing discourse.)

I also don't think the case for your definition is as strong as you imply. The original quote, “[There is] no point in claiming that the purpose of a system is to do what it constantly fails to do”, really doesn't sound like a slogan at all to me, and sounds a lot like a statement that's trying to be propositionally true, or at least approximately true. Wikipedia calls POSIWID a heuristic, which is a metric POSIWID does poorly in. "The purpose of the New York bus system is to crush ants and emit CO2" is just not useful as an approximation. The Wikipedia quote doesn't really contradict the interpretation of POSIWID as an approximately correct heuristic, and in general the article doesn't give me the impression that it's about a propositionally false slogan. (cf. https://en.wikipedia.org/wiki/One_man,_one_vote)

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