The Infinity from Nothing paradox and the Immovable Object meets the Irresistible Force

Abstract

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. 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. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force.

Unmoved movers: a very simple and novel form of indeterminism

“…Various kinds of supertasks have also been widely used as a modeling tool, even to deal with problems unrelated (or at least not directly) to infinity. One of the most recent representative proposals in this regard is Shackel (2018), where the author considers the age-old question of what happens when the immovable object meets the irresistible force. The supertask "in a Newtonian universe" that he proposes to represent it illustrates (supposedly) what he terms "the Nothing from infinity paradox" (infinite mass and energy disappear completely, leaving an empty space).…”

The Nothing from Infinity paradox versus Plenitudinous Indeterminism

“…The Nothing from Infinity paradox (in Shackel, 2018) uses a supertask in which the combination of two infinitudes of point particles, a stationary infinitude and a moving infinitude (called the Ms and Fs respectively), meet and disappear, thereby constituting an instance of infinite indeterminism. I gave a number of proofs of the disappearance, starting with a simple one assuming the meeting can be treated as a composition whose outcome must be same as the outcome of each of its composing elements without https://doi.org/10.1007/s13194-022-00463-z thereby committing a fallacy of composition.…”