Jeffrey Rahn, 51, was arrested Thursday after library staff at the Church Street location noticed the images on Rahn's terminal and called police.
His arrest exposes the library system's ongoing struggle between Internet access and Internet safety.
"We're all about access and improving people's lives," said Library Director Kent Oliver.
Oliver told Nashville's News 2 there are filters on all library computers to restrict certain information, especially for children. However, adults can bypass the filter with a simple request to library staff.
"As long as what they're looking at is valid and considered legal under Metro law and Tennessee law, we're going to allow them to look at it," he said.
The downtown library is a public facility with nearly a thousand computers. Privacy and access are important, and limiting those things could infringe on First Amendment rights, which guarantees access to information.
"When a public library decides its going to provide Internet access, it pretty much has to open the doors to any legal communications," said Ken Paulson, President and Chief Executive Officer of Vanderbilt University's First Amendment Center.
"Legal communications" can apply to material that many find questionable, including pornography.
"A lot of adult material, the playboys, the penthouses, the porn that people access in this country to a great degree on the Internet," Paulson said, "bottom line is that it is legally protected under the First Amendment, like it or not. And public libraries have an obligation to let patrons access it."
Paulson made special note of the difference between pornography and obscenity. Obscene materials, like child pornography, are illegal and not protected by the First Amendment.
Filters, like those at the public library, help keep most obscene materials hidden from public access, but they are not fool-proof.
"The type of material this person was looking at, they could've brought it in on a thumb drive. They could've been looking at their email and had a clip on it. That isn't something that anything is going to catch," Oliver said.
According to police, Rahn admitted to viewing child pornography videos on a library computer. Approximately ten additional illegal images were found on his cell phone.
Rahn is charged with sexual exploitation of a minor.