First order logic, set theory and God

[Belacqua]

-and to that we can add...if the car disappears when some part burns up...which it doesn't...then a man would disappear when he lost a leg.....which, again, just a friendly psa, we don't.  

I pointed out a little earlier today that there is a difference between essential parts and accidental parts. 

For something like a T-shirt it's easy to see the difference. To be a T-shirt, the thing has to be made of something flexible and have holes for the head and arms. Those are the essential parts; if it lacks those, it's not a T-shirt. (A T-shirt-like-thing with no holes isn't a T-shirt, it's a sack.) The accidental parts are the color, the band logo, the inside label. Those things can change and it's still a T-shirt. 

It's a little less clear when we're dealing with people. No one would argue that a man missing a leg is no longer a man, and the OP doesn't demand that. I think that a man missing all his internal organs is no longer a man, though. A partial corpse is not a person. This could be argued, but since the OP includes function as a part of the system, I'd say that the ability to be alive is an essential part of a person. Lacking that, it's a corpse.

The essential parts of the person are essentially, not temporally, prior to the person.