Can God do the impossible?

A vast majority of sects within Abrahamic religions, believe in a supernatural being who has created this World(usually from nothing) and also that this deity or god, can absolutely do anything. In other words, Abrahamic religions believe there is a supernatural being named “God” which is omnipotence.

This, however, raises the omnipotence paradox:

Can God create a stone which he cannot lift it?

The proposed resolution

To discuss this paradox from logical point of view, I rewrite it here as a reference. We have a statement:

God can create a stone which he cannot lift it.

People often assume that the abovewritten statement can be either True or False. And both cases lead to paradox. I would say perhaps the problem is with the boolean and binary valued logic which we use. As we can see in Computer Science and Mathematics, the logic needn’t to be always binary. And paradox exists because we use a binary logic. Now if we use a Ternary logic which is a superset of binary logic but with a third value of “Unknown” or “Undecidable”, we could resolve the paradox. The above statement would have a third truth value which then solves the paradox.

Such these paradoxes don’t only happen with relation to supernatural beings. For instance see Liar’s paradox.

Motivation

The main motivation of adopting a Ternary logic is overcoming limits of the binary one we use. For instance, imagine a decision problem in Computer Science:

A program on a universtal turing machine is given an input and it should output either true or false.

The problem’s that a program on a universal turing machine can never solve an undedidable problem. So it cannot output true nor false.

The similarity of both these problems is limit of of our binary system. So if we add a third value of “unknown” or “undecidable”, the problem is then solved.

Also as something related, see Gödel’s incompleteness theorems.