Summations Only

In what way could science be MORE agnostic than it already is.Science currently makes absolutely no statements or predictions about religion or the supernatural beings that religions present.Science, in fact, completely ignores the supernatural because... it's supernatural.The only time there is a conflict is when someone's religion tells them something which is factually incorrect.Science doesn't care WHICH religion is wrong, it doesn't care about the implications of the incorrect statement.Science just backs reality. Every time, all the time.

In Plato's cave, the subject can only see the shadows on the wall. They can not evaluate what they are seeing. They can't "turn around" or "cast their own shadow" or "look at their own body".In other words, they do not experiment. They do not try and disprove what they are seeing.Science ignores the supernatural because the supernatural does not exist. If it existed, it wouldn't be "super"natural, it would just be "natural".When you try and include the supernatural into explanations about what is happening or how it is happening, you quickly realize that the supernatural is worthless.Examples: The wind blows because...
A) Different air pressures in different areas are trying to equalize.
B) Zeus wants it to
C) Ghosts want it to
D) Baby Jesus wants it to
E) Thor wants it to
F) An invisible dragon wants it to
G) Bigfoot wants it to
....
ZZ) An UNKNOWN magical creature or being wants it toThat list is LITERALLY endless and only A offers us anything we can test and later use to explain other things.If you allow for A supernatural explanation, then you must allow for ALL supernatural explanations which means that no question can be answered ever.Worthless.

It's a contradiction of terms that is causing the confusion.If something is "supernatural" it doesn't exist, therefore science can not "investigate" it.Science can run all sorts of experiments designed to not detect something which doesn't exist, but that's not really science.If I hold up a pencil and claim it's a bleepbloop detector, then wave it around and proclaim that no bleepbloop was detected, did I do an "investigation"?

Nope."they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. "The can only observe and even then, only from one angle.No experiments whatsoever. They can't even observe themselves to determine if they are shadows.If you want to use a literary reference, I suggest you at least familiarize yourself with it first.

I prefer to say it's an antonym of "natural".Natural meaning existing within reality.
"Super"natural existing outside of reality.It's possible that someone THINKS that something is supernatural but later it is revealed that it isn'tExample: Lightning.However, when the thing which is being considered is a lifeform which predates reality, it's pretty safe to assume that the thing which exists outside of reality is not a part of the set "reality".

Right, IF it exists. If the thing is supernatural, then it doesn't actually exist and therefore can not be studied

Dictionary.com for one.supernatural  
adjective
1.
of, pertaining to, or being above or beyond what is natural; unexplainable by natural law or phenomena; abnormal. Of course, but that thing wouldn't actually exist.For example, it's possible that my pet invisible dragon who farts unicorn is supernatural.He just isn't _real_. You are contradicting yourself.If a being exactly matching Thor "actually exists" then he is not supernatural by definition because... he _actually exists_.