Atheism is, in a broad sense, the rejection of belief in the existence of deities. If you don't rule out the existence of a god/ supreme being/ tooth fairy, then you are an, at the very least, agnostic.
In religious belief, a deity is a supernatural being, who may be thought of as holy, divine, or sacred. Some religions have one supreme deity, others have multiple deities of various ranks. Most atheists, myself included, do not believe in anything supernatural, AKA ghosts, superman etc.
Ghosts if they existed would not be supernatural merely very extrordinary [Superman is a fictitious character and shouldn't be believed in anyway but in the comic he is not portrayed as supernatural] Supernatural is a null concept anyway; by my definition anything that physically exists exists in nature
In my mind 'supernatural' would be something that cant be explained by the sciences or rather, breaks the laws of nature. so something undiscovered would not be, though if it could go back in time, use telepathy etc, I'd go for supernatural
I think your definition is extremely narrow. Just because someone lacks the belief that god/s exist does not mean they also have to believe that god/s can't exist. It is like if my friend says he knows what next week's lotto numbers are . Now i can perfectly well disbelieve that he has any clue as to what next weeks lotto numbers actually are without necessarily believing that it is impossible for the numbers he has picked to come up.
This is the same logic that prompts people to qualify their position when no qualification is necessary in the real world. (e.g. "There is probably no God.") Your logic cannot be faulted. It can, however, be ignored as easily as you can ignore someone claiming to be able to predict next week lotto numbers.
So being intellectually honest should be easily ignored?
When your concept of "honesty" bears no relation to reality, yes, it absolutely CAN be ignored. Whether it SHOULD be ignored is entirely up to the individual. From my perspective, I'll go ahead and live in the real world, thanks. I'll leave all possibility of God, any day now, parting the clouds, lifting the veil of His secrecy, and proving once and for all that He DOES exist. Hey, could happen, right?
It's not my definition, it's THE definition.
"with superior abilities even of one who caused the Earth to come into being "
You are not an atheist of any kind. A "being" capable of creating the earth would certainly constitute a supernatural being or "God". If you're not willing to rule out such a being (or at least present SOME evidence for its existence) you don't qualify. Study up and try again later.
Why would that be a certainty? What if a form of soft solipsism is true and the being who ends up having created our perceived universe is just a lowly programmer of a highly advanced and intelligent alien species which also came about by evolution from natural means? Would the word god actually best describe such a lowly programmer? Which is why i think he asks how do we actually define the word god?