Textbooks for 1 example.

You are telling me that all the books in books2 and books3 can be acquired and read by myself completely free of charge legally without piracy?

If humans can get these books for free legally, why are so many people paying so much to buy them for their college courses?

I thought it's well known that LLMs are being trained on pirated content.

Textbooks aren't somehow banned from libraries. You'll find lots of textbooks in public libraries, school libraries, and other libraries where they can be read without paying for the book.

Now if you are saying they obtained the book from illegal sources that is a valid argument. But the issue there is orthogonal feeding the contents of the books into an LLM. It is legal for me to view and photograph the Mona Lisa. If I break into he Louvre to view the Mona Lisa, the issue isn't that I viewed the artwork. The issue is that I broke into the museum.

Yes but then the issue isn't whether copyrighted works can be used as training data, but how you can obtain those works to use them as training data. I agree that you can't justify copyright infringement based on the fact you are using it as training data. But I do not agree with those that say using a legally borrowed book as training data violates copyright.

But if you have an example of some types of books that it is impossible to borrow from anywhere on the planet please share. Textbooks are readily available from libraries.

No, they aren't banned, but not being able to find one at a library is not a legal justification for me to go and torrent it. It shouldn't be for a corporation training an LLM either.

It's widely known that some of the big LLMs were trained on book datasets that were acquired via torrents. And that those datasets do contain at least some books that are not available anywhere freely via legal channels.