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gwern comments on Tidbit: “Semantic over-achievers” - Less Wrong Discussion
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You don't necessarily add restrictions to a language to stop it from being Turing-Complete, you can just not give it the necessary axioms or whatever. I mean, in a regular language, there's no rule saying 'you can use all these regexps and atoms unless you're using them like this, because that would be Turing-complete'.
For a human example, look at the reports about the Piraha language. It's not that they ban recursion out of superstitious dread of the infinite or something - it's apparently that they simply don't understand it/use it.
You should be extremely careful when citing Piraha for anything, because it's highly controversial and the evidence is scant either way. For example, Everett found a phoneme in their sound system on his second or third trip that hadn't been there on the previous ones - apparently the tribe doesn't use that sound when talking to outsiders, because the other local tribes think it sounds silly. This isn't to say that they're hiding recursion from outsiders, only that there hasn't been enough fieldwork done with them to say anything with a high degree of certainty.
True enough. But on the strength of what we currently know about the Piraha, would you agree that they don't have rules which specifically ban or suppress or mention recursion in order not to use it? (That is, if the reports about the Piraha turn out to be true, would Normal_Anomaly’s argument be correct if we extend it to the Piraha language, that removing recursion/Turing-completeness "requires extra, arbitrary restrictions"?)
Yes, absolutely. I don't even need to go past English to find structures that we don't use for no apparent reason (ie. the structure will get marked as 'odd' but not flat-out wrong by native speakers, and the meaning will be completely intelligible), so it's plausible to me that a culture might just not like recursion in their language for no apparent reason.
That's very interesting. I thought that all human languages were "Turing-Complete" because otherwise they wouldn't be able to do everything they were used for.
Humans don't compute unbounded loops in their spoken languages. :)