In the debate concerning the final fate of the unrepentant, the argument is frequently made that a finite number of sins warrants infinite punishment because the sins are against God, who is infinite. The level of punishment deserved, it is argued, is based not on the sin but rather on who is sinned against. Since God is perfectly holy (usually described as “infinitely holy”) and is infinite and eternal, any sin against God warrants infinite and eternal punishment.
For the sake of ease, I will refer to this as the “infinity argument” here.
Consider the words of Jonathan Edwards:
But God is a being infinitely lovely, because he hath infinite excellency and beauty. To have infinite excellency and beauty, is the same thing as to have infinite loveliness. He is a being of infinite greatness, majesty, and glory; and therefore he is infinitely honourable. He is infinitely exalted above the greatest potentates of the earth, and highest angels in heaven; and therefore he is infinitely more honourable than they. His authority over us is infinite; and the ground of his right to our obedience is infinitely strong; for he is infinitely worthy to be obeyed himself, and we have an absolute, universal, and infinite dependence upon him.
So that sin against God, being a violation of infinite obligations, must be a crime infinitely heinous, and so deserving of infinite punishment. ((Jonathan Edwards, “The Justice of God in the Damnation of Sinners,” reproduced at Christian Classics Ethereal Library, n.d., http://www.biblebb.com/files/edwards/je-justice.htm (accessed on March 20, 2016).))