This is getting circular and silly. Perhaps I can put an end to it.
First off, art vs. design. Without going to much deeper, I think they are not mutually exclusive. A working definition I think could be that art is expressive (ie. the artist is communicating to the viewer an emotion, message, etc.) while design is impressive (ie. provides a function for the user). That being said, certainly art can be design and design can be art. At it's most basic, you could say that most art is also design in the way that art is also about providing the function of a an emotional experience. This function is fully valid in design as it is a basic function on the Maslow's hierarchy of needs and really no different than the primary function of a teddy bear or the secondary function of a car, or other expressive designed object.
Now then, in photography, there are obviously different kinds I think we need to separate. There is photography as documentation (ie. snap a pic of something with your iPhone) in which the photo itself is just a particular media (ie. 500 years ago you'd draw it or paint it), and photography as an endeavor unto itself, which includes commercial photography, artistic photography, etc. The photo is the end result regardless of if it is part of a larger whole (ie. ad campaign, put in a frame, photoshopped, etc.).
Design is a process of making things ("things" used as a shorthand as obviously you can also design UI, UX, non-tangibles) that have a particular intended function. In the process of doing so, various tools are used such as pencils, paper, CAD, whatever. The design is then manifested or manufactured where additional inputs such as tooling, engineering, etc. are involved. At the end, the design is also part of a larger whole, such as a brand, a package, a marketing strategy, distribution, etc.
Thus, I propose that -
1. photography (not snapshots) is purposeful and the intent of the photographer = intent of a designer
2. in photography anemotion or visual message is the function of the photograph = function of a designed object
3. photography being a part of something more is no different than design being part of a larger process or system.
Therefore photography, if all above is qualified, is = design.