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You have not supplied a reason for why we should have copyright. To say "Copyright exists because it gives the right to copy" or "Copyright exists to monopolize copying things." is begging the question.

I did not say this to my best understanding of English. You asked why there is copyright, I told you why. Because book press companies cried for monopoly to their rulers. That is why. It came into exstence and no one abolished it.    

Then I disected the article you linked.

And then I said, I agree in principle that something like a copyright should exist. If you wanna know why I think this, it is because we are a society and have concepts like ownership and rules around it.   I also mentioned examples where this copyright thing has gone too far and  is misused.

So the question would be, if whatever rule of ownership of an idea or orginal work should cover  the right to refuse to have this  thing be used to influence other things. The thing in question being an algorithm learning from it. Because an outright copy would already be covered by existing copyright.

I could argue that including this right of refusal would represent an extension of copyright to also be a patent of the idea behind the original work. So no one else could learn enough of the idea of the work to make a similar work or a work based on similar principles. 

So my current opinion is, that no permission would be needed, as it could not be given. Legally speaking. Just as a person would not need a permission to learn from  that other work and get inspiration.  But that person would also get strife for creating plagiarisms. So basically, I put more weight on the usage  and less weight on the creation of those AI tools.

I am also of the opinion that it is shortsighted to put emphasis on the creation of the tools. Especially big companies would have no problems to aquire training material by other means and do AI anyways, but it now would not include the collective influence of all those people that opted out.