How can God be infinite if actual infinites cannot exist?

--It can be discussed that non-being, true nothingness cannot be a causal source. Were there ever utter nothing, such would therefore forever obtain. There would be no world.But, manifestly, there is a world.-- 100 percent correct. tribune7

Headlined: https://uncommondescent.com/philosophy/god-as-a-necessary-maximally-great-endless-being-vs-the-challenge-to-an-actual-infinity/ kairosfocus

Folks, I think several themes are worth highlighting. It can be discussed that non-being, true nothingness cannot be a causal source. Were there ever utter nothing, such would therefore forever obtain. There would be no world.But, manifestly, there is a world. So, we must ponder the logic of being, at least in a nutshell. Candidates to being may be such that core characteristics central to identity stand in mutual contradiction such as those of a square circle. Such are impossible of being. And, we see principles of distinct identity necessarily embedded from the outset, especially that truths must be all so together so X and Y where Y = ~ X is not a possible state of affairs. If something could exist in a possible world were it actualised as a state of affairs, it is a possible being. Of these, some Z can be in at least one possible world Wi, but not in another "neighbouring" one, Wj -- contingent beings. The difference Wi - Wj will contain some unmet on-off enabling circumstance for Z . . . a necessary causal condition or factor for Z, say C. If Z is a fire, it requires heat, fuel, oxidiser and an uninterfered-with combustion chain reaction (cf. how Halon extinguishers work). By contrast, we can see a being N that has no dependence on any such C, which will be in any and all possible worlds. That is, N is a necessary being and will be part of the common framework for any world W to exist. For example, distinct identity (A vs ~A) entails that two-ness ans so also the endless set of naturals, must exist. And, without necessary causal factors C, such has no beginning or end. Given that a world exists, at least one being N must be necessary. (Theists, classically hold that things like numbers are eternally contemplated by God, for instance.) Any given case Ni is eternal, causeless, framework for any possible world, enabling and structuring it in some way. Notice, eternality not infinity, has been asserted, on the strength that for some W to be, some N must be as key to its framework. We readily see this for two-ness etc. Such is strange to our ears, maybe, but that is a fault of our education not the logic. Now too, our world is one of finite stage causal succession as we can see from succession of generations. But it is dubious for such to have existed to the infinitely -- endlessly -- remote past, as to succeed from some stage s_k to s_k+1, s_k+2 etc is equivalent to a counting succession 0,1,2 . . . which succeeds without limit but in an instance will be such that some later s_p to s_p+1, s_p+2 etc can again be matched 1:1 with 0,1,2 . . . thus showing that a transfinite span, credibly, cannot be traversed in finite-stage successive, cumulative steps. Thus if we are at a now, no S_k is transfinitely remote, even beyond say a big bang at 13.8 BYA. Our world W_a is credibly not some Ni, and has a beginning. It has a cause, a capable, sufficient one. Where, we exist therein as responsibly and rationally free, morally governed creatures. This constrains the N_a that is at the world-root. For, post Hume et al, only at that level can the IS-OUGHT gap be soundly bridged. And we all know that after centuries of debate, only one serious candidate stands -- just put up a viable alternative if you think you can. Good luck with that: ______ (Predictably, a fail.) This is: the inherently good creator God, a necessary and maximally great being; worthy of loyalty and of the reasonable, responsible service of doing the good in accord with our evident nature. But, what about, God is infinite? I suggest, this first means that God is not externally limited or weakened so that he can be defeated or utterly frustrated in his purposes. Which, is among other things a way of saying that God is not evil, that being the privation, frustration or perversion of good capabilities out of their proper end. God is also eternal and indestructible, as he has no dependence on external, on/off enabling causal factors. Thus, his being is without beginning or end, endless. This, being a characteristic of necessary being, which is required once a world is. So, I think we need to reflect on what sense is meant when it is suggested that an actual infinity is impossible of being, and what are its strengths and limitations. For sure, an endless past of finite stage causal succession seems impossible and a physical, materially based infinite quantity is also dubious. But, the transfinite set of natural numbers and beyond the surreals great and small all seem necessary -- framework to any world. Which in turn suggests mind capable of such a contemplation. And more. KF kairosfocus

Out of all of these conjectured ideas about God, how might we go about finding and discarding errors they contain? critical rationalist

The problem with arguments like this is that they are based on an assumption that the human mind has the ability to address them. We have this belief that we are all powerful -- or can be. Once we realize that we are not we find a peace and pleasure in dealing with the myriad and amazing things in front of us that we can. We further find pleasure in being awed and amazed and even entertained by the force outside us that is greater than us. If you know Jesus you know the important thing and everything else you learn is just gravy. tribune7

Sebestyen @6 Analogies by their very nature are flawed. But with this one you hit a home run! Excellent! ayearningforpublius

But all means, knock yourself out :) mike1962

Doesn't Hilbert space calculus lead to infinite number of dimensions? If God had an infinite number of dimensions, what would that mean in our 3 or 4 dimensional perception? J-Mac

How can God be infinite if actual infinites cannot exist?

I don't think neither finite nor infinite are terms that can be applied to God since both of them are measures of time and it doesn't make sense to assume God is governed or even just influenced by time. He created it together with the whole universe and is therefore completely outside of this realm. Consider the following: Someone is capable to create a computer game featuring a digital world with its own laws (theoretically completely different compared to ours) and self-conscious entities like us (but also perhaps very different). What would be the relationship between the programmer, the world and the "inhabitants"? 1. The world and it's inhabitants are completely dependent on the programmer who could start and stop the progress of the world at any time, reverse it, fast forward and also change the course of events at will. Wiping the hard drive would mean the end of this world. 2. The programmer on the other hand is completely independent of the game world and its inhabitants, not bound or influenced by those laws. 3. Any interaction with the inhabitants could only be established and maintained by the programmer in any way he/she deems fit (except for bugs, perhaps) and could only take place within the game world (unless the programmer could "extract" inhabitants and put them into another world or into something else entirely, e. g. a robot that's physically living in the programmer's world. Sebestyen Sebestyen

An infinite number of CDs or an infinitely long nose may indeed be absurd. However, the existence of various actual infinities does not strike me as absurd. Mathematical semantics is a hobby of mine, and infinities keep showing up all over in the kinds of reasoning involved: e.g., in showing certainty of convergence in a probabilistic language, but in an unbounded number of steps. I heard that Godel was a mathematical realist who believed in the actual existence of the real number line and other infinite objects, as I do. I find arguments such as the articles' excessively thin soup for my taste. HJJJr

How can God be infinite if actual infinites cannot exist?

If you cannot get something from nothing then, even if this particular universe had a beginning, something must have preceded it. And if you can't get something from nothing then that 'something' must have always existed - in other words, an infinity. Seversky

Reality is reality. How can you put a boundary on such a comprehensive conceptual truth? It just seems that, somehow, there is infinitely(!) more, at least, to that particular conceptual truth than its concept and the concepts it comprises - you can't say 'constitutes', because that puts a limit on it - even potentially - if we are not already in territory that is too abstruse for pedantically-analytical conjecture. I always thought Christ's words, 'I am the Way, the Truth and the Life', were extraordinarily baffling, but Christians and Jews know that the utimate reality (God), is personal, indeed, for Christians, at least, ultrapersonal. Strangely enough, considering he was a Jesuit priest, somewhat recondite theologian and paleontologist, Teilhard de Chardin, remarked that the more he had studied his field, the more it became apparent to him that the ultimate truth was personal. Strange, since it is axiomatic of the Christian faith, to put it mildly, but, then, he would surely have been adverting to the 'scientific' (cough) (cough) consensus of the zeitgeist he had to live with/study under. Mike said it, above, in fewer words! Axel

The Ultimate Reality is beyond all these questions. Human brains are never going to figure it out. mike1962

For example, if I had an actually infinite number of CDs all with an infinite number of songs on them, if you listened to only one CD, you would hear the same number of songs as you would if you had listened to every CD in my collection.

I have two responses to this: 1) The number of songs on all the CDs is the same as the number of songs on just one of the CDs, so there is no absurdity in equating the two. 2) Since this is all supposed to take place in the real world, we should observe that it's impossible to actually listen to all the songs on even a single one of these CDs. At every point in the future, one would have only listened to a finite number of songs, so this thought experiment is predicated on an impossibilty. (I'm assuming that we are supposed to begin listening to the CDs at some point in time.) daveS