Now on to particular comments on the argument.
[P] could stand to be refined a bit, whether in correction to universalistic proponents or otherwise, in considering what it means to claim that it is unjust (necessarily or otherwise) for S to deserve something. The statement as it stands is a self-contradictory claim, unless desert is construed to have no correlative relationship to justice. The universalist is either making such a claim (of no correlative relationship between desert and justice), or is instead trying to claim that S does not after all deserve P on the grounds specified.
I myself would quickly shut down an attempt to disengage deservedness from justice; although I won’t go into details why here, my reasons involve the relationship of justice to trinitarian theology, a relationship I find and believe to be unique to such a theology. But even universalists who agree with some (many? most? I know not all…) non-universalists that ‘justice’ primarily involves infliction of punishment on doers of injustice (such that this is what is most important in talking about the justice of God being fulfilled), will have trouble I think disengaging deservedness from even that notion of justice.
The issue then is whether any (S)inner deserves (i.e. whether it is just for S to receive) infinite §unishment for finite sins, or whether any (S) does not deserve so (thus receiving it would be unjust)–keeping in mind problems with understanding “infinite”, but also thus in understanding “finite”!
If “infinite” and “finite” are understood to be “an unending sequence” and “a temporary sequence or instant” respectively, then the principle would be illustrated just as validly if “an unending sequence” is only longer than the sequence of S’s relevant action by any amount. The question then is whether any S can deserve a P that lasts any longer than the sin of S, however long it took to do that sin.
And of course we commonly agree that S can fairly deserve such punishment. We even typically agree that S can fairly deserve such punishments when the quality approximates to that of “an unending sequence”, even when strictly speaking the timeframes involved are equivalent or reversed! So for years of betraying his country (as a spy for example), a man may be punished with a life sentence in prison, regardless of whether his remaining life sequence in prison is longer or shorter than the timespan of his betrayal. Or for betraying his country, a man may be executed, even though the execution may easily take less time to complete than the betrayal did.
The universalist making this appeal will have to be prepared on the same principle to challenge any punishment lasting any time longer than the crime took to commit; and I do not see any universalist being prepared to do so.
As DC also says, the argument of proportionality would also seem to involve injustice being fulfilled if a righteous man is rewarded any time longer than the time spent doing that for which he is being rewarded; and again no universalist anywhere will be prepared to challenge that. The argument from a principle application of temporal proportionality fails, as rebutted by DC so far (along with extensions to the illustration as I supplied above.)
What if “infinite” is treated as an ontological qualifier? As DC has argued, I think rightly, there is a way of trying this which ends in mere category error (thus is useless for a universalistic argument against non-universalistic punishment in that regard as well).
But what if “infinite” is treated as an ontological qualifier in the sense that the punishment comes from The One Who Is Infinite? By topical parallel, the sin comes from the one who is finite.
So the question is now, in effect, whether S, as a finite entity, deserves to be punished by God for sinning. I am entirely prepared to challenge any universalist (or anyone else) who thinks S would not deserve to be punished by God for sinning; but in practice even ultra-universalists (who deny any post-mortem wrath of God) still agree that S deserves to be punished by God for sinning. They may think God only punishes sin in this life, and/or they may think God has pretermitted all punishment by punishing Jesus Christ (who or Who was innocent of sin) for our sins, but they still typically agree sinners (not to say non-sinners like the Son of God) deserve to be punished by God for those sinners’ sins.
So much for any variant of universalistic argument from this direction so far.
There are, however, several other things to consider, including (but not limited to) the question of whether a person must necessarily deserve unending punishment for a sin that has ended; and if so why that would be–an argument often made (in several ways) by non-universalists in favor of hopelessly final punishment (of various sorts), and to which the universalistic argument mentioned by DC is chiefly presented for sake of rebuttal. Whether the rebuttal attempt fails or not, is there something there worth rebutting after all? Perhaps one or more versions of the idea are indeed worth rebutting even if at least one version of that idea is not? Or are all such attempts from non-universalists worth rebuttal?
That, and other topics, would be well worth discussing, too (I mean in this thread, in reply to DC’s original post); but so far as he goes, I think DC shows well enough that the common rebuttal attempt represented in his (counter-)rebuttal fares poorly.