(Descartes addressed this in his proposition that it is our awareness, our consciousness that defines our being: "Cogito, ergo sum." This logic would imply that unless we are aware and conscious, we cease to be.) That's bad logic.
The statement,
"I don't think, therefore, I am not,"
cannot be proven true,
from the truthfulness of the statement,
"I think, therefore I am.The "I don't think"statement is merely the inverse of the "I think "statement."
Elementary logic: Inverse: The inverse is simply the conditional with ‘not’ added to it.
1.Statement: If p, then q
2. Inverse: If not p, then not q
A statement is not logically equivalent ... to its inverse.
If they can't get elementary logic right, it makes anything else they say suspect, suspect of an agenda at work.