---
pubDate: 2021-08-26
title: A Proof That God Cannot Create a Rock So Heavy He Cannot Lift It
tags:
  - philosophy
abstract: A proof that God cannot create a rock He cannot lift.
table_of_contents: false
---

_Note_. These proofs use the
_[law of the excluded middle](https://ncatlab.org/nlab/show/excluded+middle)_
(and _double-negation elimination_, which is equivalent to the law of the
excluded middle)
[[nCatLab: Classical Logic](https://ncatlab.org/nlab/show/classical+logic)].

**Theorem**. God cannot create contradictions.

_Proof_. By the law of the excluded middle, either God can create contradictions
or He cannot.

- First, suppose that God can create contradictions. It is a contradiction for a
  contradiction (i.e. an impossibility) to be possible, so by the
  [principle of explosion](https://en.wikipedia.org/wiki/Principle_of_explosion)
  it follows that God cannot create contradictions.
- Second, suppose that God cannot create contradictions. Then the result follows
  immediately.

Since the result holds in both cases, the result holds.

**Corollary**. God cannot create a rock He cannot lift.

_Proof_. Suppose for the sake of contradiction that God _can_ create a rock He
cannot lift. God is omnipotent (by definition), which implies that He is able to
lift any rock. It is contradictory for there to be a rock that God cannot lift
while God has the ability to lift any rock. So the supposition introduced a
contradiction, and by the previous theorem God cannot create contradictions,
hence the supposition must be false. The result follows by double-negation
elimination.

**Corollary**. God cannot keep all of His promises while also breaking one of
his promises.

_Proof_. Suppose for the sake of contradiction that God _can_ keep all of His
promises while also breaking one of his promises. This is a contradiction, and
by the previous theorem God cannot create contradictions, hence the supposition
must be false. The result follows by double-negation elimination.

**Remark**. The corrolaries also follow fairly directly from the principle of
explosion, since they both have the form "suppose a contradiction, then derive
the result." They are presented as corollaries for the sake of demonstrating
specific instances of applying the derivation of the theorem.