I received the following question:
I frequently don't understand the meaning of "infinitely X". For example, is "infinitely good" even meaningful?This question is a pretty fun one, and it is one that is fairly nuanced in its own way.
The simple answer
To be completely straight, the answer to this question, in the context meant, is "probably not." We should be cautious, though, with an answer like that because infinity can be understood to have a few different meanings, and in one of those meanings, "sort of" is nearer the mark for an honest reply. Particularly, I think we all have a general and qualitative sense of what is meant by "infinite goodness," and that is the state of being unsurpassable in its good quality. Metaphorically, then, it definitely has some meaning, but whether this phrase literally means anything or not is less clear.
If we understand infinity to be taken as an actual infinity, meaning an infinitely large quantity that is somehow manifest, I would suspect that the answer is "probably not." We don't know for sure if our universe is infinite in scope, thus admitting infinities in the physical, and all meanings of actual infinities would have to count abstractions if it isn't. Even so, X, say "goodness," could be an abstraction, but since something like goodness seems to be necessarily rooted in physical experiences of sentient entities, it's unlikely that something could be "infinitely good."
Before getting on to other possible meanings of infinity, though, the idea of infinite goodness needs some elaboration. Goodness, plainly, is a difficult thing to measure, and since "infinite goodness," as it immediately seems to us, implies a quantity of goodness, some kind of metric is needed to give meaning to this turn of phrase. Of course, much can be hidden in this complexity, as is often the case, and so it is easy to pass off phrases like "infinite goodness" without an easy rebuttal.
Even if we suppose that we can measure goodness in some salient way, though, what would be meant by (actual) infinite goodness. By definition, in this context, infinite means that if we were to take some part away from this collection (of goodness), it would not be diminished (in goodness). Inversely, if we were to add something to this measure of goodness, say another act that could be deemed good, we would not actually increase the total goodness present. This, I think, presents an odd state of affairs, and where theology comes into it, it leaves open a door to nonsense.
To wit, on the claim that God is infinitely good, if measured by that which he has come to make be good in this world, if some act of goodness were to be undone or left undone at God's responsibility, God's goodness would not be diminished. On the other hand, if God were to do more good than we currently see, it would not increase his goodness at all. This would seem to justify a great deal of utter moral atrocity while leaving God perfectly good. Of course, to caring, feeling beings like ourselves, it would also render God's goodness perfectly hollow and meaningless, divorced from anything we can identify with the word "good." This strikes me, then, as rendering the notion of the "infinite goodness of God" as an empty concept, mere words said to convey some non-literal meaning.
Getting more complex
"Infinitely" can mean more than the literally infinite idea captured in actual infinity, though. It could apply to potential infinities as well. A potential infinity is, in essence, the unlimited capacity for more. Like with numbers, no matter what number we're thinking about, we can think of larger numbers than that. In this case, "(potentially) infinitely good" would mean that however good we conceive of something like God being, he possesses the capacity to be more good--and not just in a way where we are approaching some maximum limit of goodness that cannot actually be reached (a supremum of goodness just outside the set of possible states of goodness). In this case, we should see as reasonable and possible as large an increase in goodness as anyone might imagine.
On the surface, this seems pretty reasonable, if a little outlandish. I do not think it is, though, because it brings us back to the question of what defines "goodness." If defined in terms of the experiences of sentient beings, it strikes me as a definition that requires a universe able to spawn and hold an unending number of such beings. Maybe that's the case, but then tying that notion of goodness back to a single entity like God gets pretty strange, particularly since any positive amount of goodness (and thus far from maximum possible goodness for any) spread out over (potentially) infinitely many sentient beings would render an "infinitely good" God that still left a lot to be desired.
More importantly, then, it raises the question of what infinite goodness would mean for God. Would such an infinitely good God be beholden to create a maximal amount of good for each being, a large amount, a little, or goodness that just barely tips the balance toward net-good? I think most of us recoil at the notion that "infinitely good" can be used to describe a God that so orders the universe such that every sentient life suffers exactly enough to just barely break even on the good versus not-good spectrum of total life experience. Indeed, many of us reject the idea of a God that allows whatever suffering in real life to be made up for with infinite reward in some promised afterlife.
Getting even more complex
There's another possible meaning for this phrase, "infinite goodness." Take, for example, the notion that God and everything God allegedly has done maximizes goodness in the universe. Technically, this isn't "infinite" goodness necessarily, but the question was about whether or not this phrase has any meaning, this being one of them--proposed, for instance, by Kurt Gödel's ontological argument (see Dot, Dot, Dot) for the existence of God. Could "infinitely good" here actually mean "maximally good," with people using a faulty means of communicating this ideal? Evangelical Christian apologist William Lane Craig seems to think so.
Well, consider what it would mean for God if it were the case. Such a God would have to have so-ordered the universe so that a single additional or different act of any kind on his part would necessarily make it worse off. This commits us, then, to a remote God that is not in any way involved in our affairs unless via the particularly sick way in which he has ordered the world to where we must ask (or beg) for his intervention in order for him to give it to us but in which he has predetermined it to be so all along.
We could step back one step and go to the claim that God's "infinite goodness" really means a "potential maximum goodness," which hopefully starts feeling very gerrymandered in the usual theological way. By this I mean that God has ordered the universe so that if we all use our free wills (NB: It begs the question to assume we have these, but that's a different topic for a different discussion) the way he hopes we will, making no errors, then maximal goodness will be achieved. This may be theologically, and perhaps even philosophically, defensible, but what a hamper God is in, and what an opportunity pastors have to blame people for the troubles they and others face in life.
This, of course, is the kind of "infinitely good" God many people believe in: one that made things so that they would be maximally good if people would just stop screwing everything up. There's a reason those without belief reject this idea as repugnant: it is repugnant.
Of course, we could go on and on and on with excuses for why God's "infinitely good" nature doesn't mean what "infinitely good" means, and we could probably find scripture or the writings of early theologians to back up every word of it, but what a disingenuous waste of time that would be.
Other properties that aren't goodness
To be complete, we should wonder about other properties, like knowledge or power, often said of God to be infinite. By the given definition of the (actual) infinite, I think it divorces them from reality, God with them. This, of course, is a major theme within Dot, Dot, Dot.
Another point to make, though, is that even if God is potentially infinitely able or knowledgeable, this seems to commit God to having an actually infinite set of abilities or knowledge. I provide what I think is a very compelling argument for this claim near the end of Dot, Dot, Dot, and so interested readers can find it there. Since that actualizes infinity in God, we're back to the situation in the previous paragraph: God is divorced not from the universe but from reality itself. This isn't a cute theological hack either, I'm claiming with it that such a God is imaginary, existing only via the minds of people.