"If A, then A" doesn't always appear to work

"If A, then A" is not always so.

"No reasonable definition of reality could be expected to permit this," Einstein, Boris Podolsky and Nathan Rosen wrote in a paper in 1935.

Yet our "reality" does permit this, because we can see it. How does logic cope with this?

http://www.nytimes.com/2005/12/27/science/27eins.html?pagewanted=1&incamp=article_popular