If you have a ton of ideas and they're all, for the most part, general, vague, novel, and abstract, practice prototyping. Make it really dirty, don't over-think it, and keep a closed-mind while in the beginning stages of a project; IOW, don't pre-optimize your project by recursively worrying about other edge cases, write for a single case and get something on the screen.
Given your background, I'd scratch all these "big picture" or "overly ambitious" ideas and return to a domain you're more confident in, pick something (axiom, rule, theorem, etc.) specific, and see if you can express or simulate an example of the "thing" in action.
Given your background, I'd scratch all these "big picture" or "overly ambitious" ideas and return to a domain you're more confident in, pick something (axiom, rule, theorem, etc.) specific, and see if you can express or simulate an example of the "thing" in action.