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In LW jargon I'd phrase it as: "It's a system one thing, not a system two thing." I think this is what most people do mean when they use "it's an art, not a science." When something is considered an art and not a science it's something that can't be done well by "just" following a set of instructions. Keep in mind that the popular view on science (when it's positive) is seen as strictly adhering to the scientific method (form hypothesis-->test hypothesis-->adjust hypothesis) and that this is something that anyone can do. The difficulty of each individual step is ignored or seen as something that can be learned without much trouble. The pop-culture view on art is "mysterious process."
And you're probably right that you can distill (some) parts of art into "rules" about good art. I recently heard a radio interview with a professional photographer and he could explain why each photo was good or bad by adhering to a set of simple principles and he could explain those principles. I do think, however, that part of what makes him a great photographer is that those simple principles have become part of his system one thinking.
I think that's a great way to phrase it!
I'm a bit skeptical that this is true. I sense that the majority of people don't actually believe that art is reducible.