Copyright is a practical right, not an inherent right. The only reasons humans get copyright at all is because it's useful for society to give it to them.
The onus should be on OpenAI to prove that it will benefit society overall if AIs are given copyright. We've already decided that many non-human processes/entities don't get copyright because there doesn't seem to be any reason to grant those entities copyright.
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The comparison to humans is interesting though, because teaching a human how to do something doesn't grant you copyright over their output. Asking a human to do something doesn't automatically mean you own what they create. The human actually doing the creation gets the copyright, and the teacher has no intrinsic intellectual property claim in that situation.
So if we really want to be one-to-one, teaching an AI how to do something wouldn't give you copyright over everything it produces. The AI would get copyright, because it's the thing doing the creation. And given that we don't currently grant AIs personhood, they can't own that output and it goes into the public domain.
But in a full comparison to humans, OpenAI is the teacher. OpenAI didn't create GPT's output, it only taught GPT how to produce that output.
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The followup here though is that OpenAI claims that it's OK to train on copyrighted material. So even if GPT's output was copyrightable, that still doesn't mean that they should be able to deny people the ability to train on it.
I mean, talk about one-sided arguments here: if we treat GPT output the same as human output, then is OpenAI's position that it can't train on human output? OpenAI has a TOS around this basically banning people from using the output in training, which... probably that shouldn't be enforceable either, but people who haven't agreed to that TOS should absolutely be able to train AI on any ChatGPT logs that they can get a hold of.
That is exactly what OpenAI did with copyrighted material to train GPT. It's not one-sided to expect the same rules to apply to them.