Is Castle supernatural?

To my knowledge there is no objective answer on this unless the show runners commented on it in which case I don’t know.

But I’d love to hear y’all’s opinions. On episodes like the alternate universe in S7 and the time travel one in S6. And any other example I can’t think of. Either one of those could be supernatural, it could’ve actually been Mayan artifact that actually transported him to another universe. Or the guy could’ve actually been a time traveler.

Or they could be just been strange cases that appeared that way but had a completely logical explanation. Castle hit his head and dreamed the other universe or the time traveler could just be mentally ill.

Personally I say it’s supernatural because I’d rather it be and there’s nothing to my knowledge that disproves it. The time traveler being right about their future is also a great reasons. But what do y’all think?