The procrastination paradox is isomorphic to well-founded recursion. In the reasoning, the fourth step, “whether or not I press the button, the next agent or an agent after that will press the button” is an invalid proof-step; it’s shown that there is an inductive steps ending at the conclusion, but not that that chain has a base case.
This can only happen when the relation between an agent and its successor is not well-founded. If there is any well-founded relation between agents and their successors—either because they’re in a finite universe, or because the first agent picked a well-founded relation and build that in—then the button will eventually get pushed.
The procrastination paradox is isomorphic to well-founded recursion. In the reasoning, the fourth step, “whether or not I press the button, the next agent or an agent after that will press the button” is an invalid proof-step; it’s shown that there is an inductive steps ending at the conclusion, but not that that chain has a base case.
This can only happen when the relation between an agent and its successor is not well-founded. If there is any well-founded relation between agents and their successors—either because they’re in a finite universe, or because the first agent picked a well-founded relation and build that in—then the button will eventually get pushed.