Boyfriend and exes

My boyfriend who has had a history of flirting with women on social media has been engaging quite a bit with his exes via social media. The same boyfriend who claims that he doesn't believe that exes can be friends. I recently found out that he attends a a great deal of one of his exes art shows and sometimes she comes over for him to do a bit of graphic design work for her business (they are both visual artists). I confront him about this and he does not deny the action but explains that though he is still attracted to her and is "totally in awe of her and her artistic ability" it's strictly business. He claims of he hung out with her socially they would probably begun to like each other again so he doesn't place himself in those situations. He likes her but her certainly doesn't want to be with her is how he explains it. He says there are things he looks back and appreciates about their relationship but he wouldn't want her back. How am I suppose to take this?