How abstract is abstract art?

I'm going to be a bit of a devil's advocate here, because, as mentioned previously, I'm a psych major by trade. The subject matter I'm going to address is one that, in a way, is rather humorous to me; abstract art. I know some people derive a great deal of satisfaction from abstract art, but some of it just seems silly to me. I remember when me and my now-fiance first started dating I stumbled across an abstract painting that looked like someone had just gotten pissed off and thrown random splatters of paint across a canvas. But, for whatever reason, he seemed to enjoy it.

Here's where my psychoanalytic though-process comes in.

The mind, by definition, is an organization-initiating mechanism. It makes sense of things. So to create something with no definitive purpose or explanation, is that really true artistic ability, or careless lack of inspiration? Or, on a deeper level, perhaps a portrayal of subconscious processes, which then, would give it a meaning? And, if the piece does indeed mean something tangible to the artist, does that make it any less abstract? Or, would it make it less abstract if the viewer knew about the purpose behind the seemingly random strokes? Or is it simply up to interpretation?

Hmm...

Stewart (2012) states "regardless of the initial motivation for their work, both artists and designers constantly scan their surroundings in an omnivorous search for images and ideas. (. . .) The most improbable object or idea may inspire motivation." (pg. 114).

So, perhaps, abstract art is simply the unlikely interpretation of an improbable idea. At least, that's the best definition I can come up with.