Aquinas being my patron saint and one of my all-time heroes, I am loathe to say this, but his response in [12] seems utterly nonsensical. Perhaps I’m just not understanding it properly. If you have a better grasp on it, could you perhaps expound upon it?
I typically give him the benefit of the doubt - always. It has always been my experience that he has to be read numerous times to “get” what he means. The citation from SCG is no exception.
I do think, though that [11] might be a key
[8] Now, these arguments, though not devoid of probability, lack absolute and necessary conclusiveness. Hence it is sufficient to deal with them quite briefly, lest the Catholic faith might appear to be founded on ineffectual reasonings, and not, as it is, on the most solid teaching of God. It would seem fitting, then, to state how these arguments are countered by the partisans of the doctrine of the world’s eternity.
[11] Nor is the third argument cogent. For, although the infinite does not exist actually and all at once, it can exist successively. **For, so considered, any infinite is finite. **Therefore, being finite, any single one of the preceding solar revolutions could be completed; but if, on the assumption of the world’s eternity, all of them are thought of as existing simultaneously, then there would be no question of a first one, am, therefore, of a passing through them, for, unless there we two extremes, no transition is possible.
I suspect what he is getting at, especially with the "any infinite is finite,’ is something akin to how the numerical “distance” between any two integers has an infinite capacity to hold fractional numbers within it.
Likewise, perhaps the infinitesimally small durations possible within measurable units of time means something like any “infinite” can be held between or within finites. Is he claiming that infinite time could be contained within a finite time when viewed from a different place in the sequence?
Didn’t Hawking argue that the Big Bang “initial” moment could wrap around an infinitely decreasing curvature of time - a series of smaller and smaller intervals such that no discernible “beginning” needed to exist? I think he modeled the “beginning” of time as an infinitely decreasing curve rather than a point. Not trying to be anachronistic, but Is that what Aquinas was up to here?
[12] The fourth argument is weak. For there is no reason why an addition should not be made to the infinite on that side of it which is finite. Now, from the supposition of the eternity of time it follows that time is infinite in relation to the prior but finite in relation to the posterior; for the present is the terminal point of the past.
On third reading, it sounds like he is claiming that time is not infinite in both directions but “finite” in an indeterminate sense (in relation to the posterior) going backward from the present (the terminal point), but infinite (in relation to the prior) going forward into the future.
On a previous second reading I originally thought he was concluding the opposite. That time could be observed as finite going forward from the present terminal point, but still have been infinite in the past. This doesn’t seem to answer the traversing infinite time dilemma, though.
Yet, if the idea from [11] is brought forward, perhaps what he is getting at is something like Hawking’s idea that time may “bend” from an infinitely small succession of intervals gradually getting more to what would be increasingly greater and more detectable (finite to observation) intervals at the level of human observation.
Think of the space time continuum as a “mesh” that is gradually expanding both in terms of spatial distance and temporal duration. If, going back from the present, the space-time continuum gets progressively smaller in both space and time, then it could go backwards infinitely, but since the “duration” gets progressively smaller going backward, the “beginning” while infinitely getting “shorter” in terms of time, would not be a detectable beginning, but, relatively speaking, the infinite would be traversed in a virtual instant. Makes sense?
So when Aquinas talks about why “an addition should not be made” does he mean the kind of “progressive” change that would entail the prior time would be regressively smaller going backwards from the terminal point (present) because “addition” would occur going forward on the apparent “finite side?”
The more I think about it, the more I think it is the only reading that makes sense.
