Now, you would be perfectly well within your rights to argue that actual infinities are absurd. The Mathematician David Hilbert intended his “paradox of the Great Hotel” to demonstrate this, and similar paradoxes have been raised by mathematicians and philosophers for centuries. I actually agree, in a qualified sense, with this position; I think it is absurd to posit an actually infinite set of causes, for instance. However, I am not an A-theorist about the nature of time (mostly because I see that as incompatible with the doctrine of God’s omniscience and simplicity), and I do not believe that there are chronons (that is to say, objective fundamental indivisible finite units of time). I do believe that God is atemporally eternal, that the events to which we refer as ‘future’ are actually infinite in number, and that they are, each of them, actual. I do not believe that heaven involves an objective present, a ‘now’, and that the flow of time tends towards infinity merely as a limit (i.e., a potential infinite rather than an actual infinite). For, in that case, God would (I think) have to be both omniscient and constantly changing his mind, for as facts would objectively go from being future-tense true to present-tense true, and present-tense true to past-tense true, God would have to be keeping track of that rollover of propositional truths. I find that unconscionable because it seems incompatible with God’s immutability and divine simplicity. So, instead, all the events in heaven are actual, and there are infinitely many of them, so I do accept that there can be an actually infinite number of events. I think you should too, if you’re a Catholic, unless you find a way out of the troubles I just briefly outlined.
You cannot measure infinity, because it is literally “without end.” If you measure something, then you have reached its end, otherwise you wouldn’t be able to measure it.
Set theory gives us the mathematical technology required to measure transfinite quantities and talk meaningfully about transfinite arithmetic. This is in part what Cantor did for mathematics and set theory; it is why he is to set-theory what Einstein is to physics.
I think part of the trouble comes from trying to quantify something which is not quantifiable. We can provide subjective interpretations of the severity of our pain, but we cannot actually compare that pain with someone else’s. One person’s ten might be another person’s two.
This is a great point. To it I can only say that even if we have no way to measure the difference in subjective experiences of pain with any meaningful precision, we all know that some pain is more intense than other pain. We can proceed, therefore, to talk analogously about finite measures of pain even if such measures are strictly inscrutable to us (especially when considering the
poena damni.
No matter what, we know that the souls in Hell will experience “perfect suffering,” just as each soul in Heaven will experience “perfect happiness.” This suffering will be the full amount of suffering their soul is capable of experiencing.
This is not quite so. Consider, for instance, the following from the sixth session of the Council of Florence, (July 6, 1439):
“Also, the souls of those who have incurred no stain of sin whatsoever after baptism, as well as souls who after incurring the stain of sin have been cleansed whether in their bodies or outside their bodies, as was stated above, are straightaway received into heaven and clearly behold the triune God as he is, yet one person more perfectly than another according to the difference of their merits. But the souls of those who depart this life in actual mortal sin, or in original sin alone, go down straightaway to hell to be punished, but with unequal pains.”
So, the council literally affirms
poenis disparibus, even in hell, not to mention that one person more or less perfectly than another beholds the triune God according to the difference of their merits.
I am a little insulted that you don’t think we’re giving your question due consideration. Just because you don’t like our responses doesn’t mean we’re being lazy in considering your proposition.
Mea culpa, this is doubtless due to my impatience. I appreciate the sincerity and the effort (and the intelligence, and the charity) of the responses. However, I was honestly hoping to be impressed; I was hoping that a fellow Catholic on here might be able to come up with some obscure canon (or something) which I’ve missed, something which might undermine the view I’m proposing. On the upside, if I can find no principled opposition even after having sincerely sought it, that raises the likelihood that there just is no principled Catholic case to be made against the view.
Since so much of this relies upon a technical understanding of infinities and set theory (which is becoming increasingly obvious to me now), perhaps I can be permitted to direct those of you interested to this really great video:
youtube.com/watch?v=SrU9YDoXE88
Maybe it’ll help us all to better frame the our inquisitions (so to speak).