by left fin do you mean his pectoral fin (the little ones he flaps and uses to move around?) does it look like it's continuing to deteriorate?
I've heard of fish biting their tails, but i'm also concerned about fin rot. How often do you change his water? If his water conditions aren't optimal, fin rot is a possibility and you'd need to treat that, depending on its severity. If it's not too bad, clean water and aquarium salts. If it's getting bad, you may need to try a med like jungle fungus clear. how big is the tank? Other fish in it?