The river that swallows all rivers
More recently we have supertasks such as Benardete’s Paradox of the Gods,
A man decides to walk one mile from A to B. A god waits in readiness to throw up a wall blocking the man’s further advance when the man has travelled ½ a mile. A second god (unknown to the first) waits in readiness to throw up a wall of his own blocking the man’s further advance when the man has travelled ¼ mile. A third god … etc. ad infinitum. (Benardete 1964, pp. 259-60)
Since for any place after A, a wall would have stopped him reaching it, the traveller cannot move from A. The gods have kept him still without ever raising a wall. Yet how could they cause him to stay still without causally interacting with him? Only a wall can stop him and no wall is ever raised, since for each wall he must reach it for it to be raised but he would have been stopped at an earlier wall. So he can move from A.
[…]
In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. […]
{ European Journal for Philosophy of Science | Continue reading }
photo { Alex Prager, Crowd #2 (Emma), 2012 }
