The Fair Use doctrine covers reprints of articles for scholarly and educational purposes. Copyright infringement is not even on the radar. It's an absolute total nonissue.
You are thinking of the "progress of science and useful arts" clause of the US constitution.
But review the outcome of the decision
L.A. Times v the Free Republic.
Jon does assume liability, including the risk and potential expense of a lawsuit.
That said, most of what I have read that you have posted is highly unlikely to draw the ire of a disgruntled copyright owner - at least not to the point of litigation. I've made similar postings myself. But in the unlikely event of a cease and desist order being served to the owners of this site, or a law suit being brought against this site, the responsibility and cost of defense would fall to Jon. At that point, it will no longer be a non-issue.
There is a clear way for us to avoid this - simply secure for the site the written permission of the copyright holder to post it.