BY that case then, yes, it can exist. Just 'cos you can't logically explain something, doesn't mean that there isn't a logical explanation... So until we reach a level of knowledge and understanding allowing us to explain what we at this time call 'supernatural' then we have to have it as an unknown.
For example, would colours not exist if we didn't understand how we percieve colour, how it is the product of radiation and absoprtion etc etc?
My point is that even though CURRENT logic might suggest supernatural things are impossible, it could very well be that the principles that logic is based on are flawed.
Take the edge of the universe as another example. Logic would suggest that there must be one, but what's beyond the edge? If the answer is that the universe is folded in on itself, then logic stumbles on the principle of all things having a definable edge... So although my logic is correct, it's foundation is flawed.
The same applies with the logic and supernatural. Just becuase we assume there are boundaries and unbreakable laws of physics and maths it doesn;t mean we are actually right... we just haven't tested the theory fully. If we had, we'd be able to explain the supernatural perhaps... and then it wouldn't be 'super'natural anymore....
Sometimes I soooooo wish I hadn't given up the Absinthe....