Your definition is a valid one, however, it is not the only valid one. The issue is that "living" is a term that has defied concise definition. It was easy before microscopes. A mouse is alive. A rock is not. But the more we learn about nature, the less confident we can be as we try to draw a line between living and nonliving. I suspect that there will always be a grey area that might perhaps be better left unspecified. In mathematics a double negative equals a positive, but in language that is often not the case. In French, for example, specifying a negative may require two negative terms. "Nothing that does not exist can be found by science" is NOT the same as "Everything that does exist can be found by science." Language does not obey the laws of mathematics.
Nothing that's non-existant can be found by science or any other method of discovery. Still a double negative?
It isn't even true in Mathematics, just some cases. -10 + -3 =/= positive. In fact, you can state both "Nothing that does not exist can be found by science" and ""Everything that does exist can be found by science." in strictly mathematical terms. They are not equivalent.