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

Nicholas Shackel

doi:10.1007/s13194-017-0192-2

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.

Highlights

Since Zeno, supertasks, tasks that involve infinite actions or interactions, have had an important role as objects of philosophical contemplation
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 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

Summary

Introduction

Since Zeno, supertasks, tasks that involve infinite actions or interactions, have had an important role as objects of philosophical contemplation. Some people reject altogether the application of classical Newtonian mechanics to infinite systems Even if they are admitted, one may raise questions about the initial conditions that are posited for these supertasks, such as how they could ever come about, or whether their possibility doesn’t depend on some mysterious creation by a god. Previous supertasks in Newtonian universes have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism They have usually offered only a single argument to their paradoxical conclusions, making them vulnerable to single rebuttals. The fact that a version of it can be given a formal model shows the easy dismissal may be too quick

The Nothing from Infinity paradox

What happens when the Ms and Fs meet

The Infinity from Nothing paradox

The paradox of the Immovable Object meeting the Irresistible Force

Conclusion