How can you discern between the natural and supernatural? Once a supernatural thing occurs within our physical world, it is no longer beyond the laws of the physical world and would therefore be part of the natural world.
And there goes all of the atheists’ grounds with which to dismiss supernatural claims.
Supernatural refers to that which is “above”, superior in some way, the natural. Of course “natural” is not precisely defined, so anyone can argue in any direction concerning what is or isn’t above it.
What is referred to as the “Divine Realm” is defined as the realm of concepts and perfect forms, such as a perfect circle. The physical universe, the natural universe, cannot ever form a truly perfect circle. Thus a perfect circle belong in that class of divine forms and “super-natural”.
More significantly is the fact that all strategies, principles, and laws are also merely concepts. Where is the “law of gravity”? Where is the law that says the inside of a box is smaller than the outside? Where is the strategy of Divide and Conquer? None of these things exist as physical or natural entities except in the sense of being represented at the time by a particular event. As something falls, we can say, “See. There is the law of gravity.” But we are not actually seeing any law. We only see the effects of a law. The law is just an idea or concept. All laws, principles,and strategies (like how to con your parents into buying you a car or how to win the lottery) are a part of the Divine/Supernatural realm.
How Science can discern the natural from the supernatural is pretty simple. If it is changing in any way and even the slightest bit, it is physical or natural. Supernatural or divine entities can never change in any way. They can be called by different names, but a perfect circle will forever be a perfect circle. They can fall out of favor or become useless to ones efforts, but they are still always merely what they are.