The moment you can build a science on a negative argument; you have open the floodgates for all kinds of entities.<quoted text>
Not at all sure why you would think that. I can think of several 'negative arguments' that are very important in science. For example, that the different types of perpetual motion machines are impossible. That violation of any number of conservation laws is impossible. That global decrease of entropy is impossible.
If you open the floodgates of valid negative arguments; you'll be up to your neck in mythical creatures by tomorrow. Good luck!