## Could there ever be evidence for an infinite being?

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The God of Anselm is understood as "that than which nothing greater can be conceived." From this definition, God can be presumed to be omnipotent, omniscient, omnipresent, perfectly free, uncaused, eternal, morally perfect, etc. God is fashioned as an infinite being, i.e. one who's abilities have no non-logical limitations. This definition, however, leaves us in an awkward epistemological position, as it ostensibly renders all potential evidence for such a being inherently ambiguous.

To speak specifically, any miracle, feat, or theophany wrought by an infinite being could—in principle—have also been performed by a finite being. That is to say, there seems to be an ineradicable ambiguity in any manifestation of an infinite being's power, precisely for the reason that the very same action could have been performed by a being that was not infinite. How might we finite beings ever know, definitively, which being we are actually dealing with?

How could any being, even God, possibly demonstrate His omnipotence? Omniscience? Moral perfection? How could we ever tell the difference between God and a being that is merely “God-like”? It would appear that these infinite attributes are—by their very nature—incapable of actual demonstration, and are thus intrinsically unverifiable. I am at a loss to explain how apologists set out in earnest to adumbrate the case for an infinite God when unambiguous evidence for such a being appears to be in principle unattainable.

Consider an analogous situation: Imagine that you are sitting in a room with nothing in it apart from a chain which enters from one side of the room and exits through the other side. From your vantage point you cannot see the outside world, but you can see that the chain clearly does not begin or end within the confines of the room. We are then asked, “Is this chain infinite?” How can our answer be anything other than a guess? What evidence or argument could possibly be adduced that would settle the matter definitively? It would appear that we are in no position to know which type of object we're dealing with, and therefore cannot verify that the chain is in fact infinite, even if it actually is. This epistemic hurdle seems to parallel any and all attempts to marshal evidence for an infinite God based on human experience (no matter how ineffable). Even if we were to experience the unmistakable presence of a powerful, immaterial, and personal being, we seem nevertheless to be in no position to say whether or not this being is essentially infinite.

How can we have unambiguous evidence for an infinite being if we cannot even verify that the being is infinite? How do we know it's not all in our heads? Perhaps to professional philosophers this not as big a problem as it appears to a layman like myself, but every time I try to think of ways to empirically justify theism, I fail to progress beyond this notion that any evidence for an infinite being is simultaneously evidence for an finite being. Am I completely off-base here?

If an "infinite being" wanted you to believe - you couldn't stop believing even in the face of insurmountable contrary evidence. – christo183 – 2018-10-16T11:15:13.707

@christo183 I suspected that this might might follow from the definitions we are working with, thanks for the input. – Bryson S. – 2018-11-12T08:04:23.553

Did you clearly define "infinite being?" What makes you think you're not already one yourself? A million years from now the atoms in your body will be repurposed to some other use. You never die, you only become a different aspect of the universe. You are as infinite as the universe is. Since it's clear that you never die, but just become a different part of the universe, what makes you think you're not already an infinite being? Or a part of one? – user4894 – 2014-07-18T22:50:10.463

@user4894 For one example, I cannot change the past, ergo I am not an infinite being. There is no need to persist in a Wittgensteinian obsession with language. For our purposes infinite equals unbounded, limitless, or essentially perfect. – Bryson S. – 2014-07-18T22:53:07.900

1If you refuse to define what you mean, your question is meaningless. Where did this "change the past" rule come from? What is limitless? You are just making up words and imagining they have meaning to others. That's why in philosophy it is essential to define your terms. Else we aren't talking about anything. Oooh X isn't infinite because X can't cheat at solitaire. That's the kind of nonsense you fall into when you refuse to make a definition of your terms. What is "essentially perfect?" Is there an inessentially perfect? You're just making up buzzwords without meaning. – user4894 – 2014-07-18T23:23:32.277

@user4894 I am not aiming to stir discontent so I will consider the point taken. Let's take one step back. Can you discern the line between a being that is "very powerful" and one that is "all-powerful"? If you can descry that distinction, then we are on the right path. An infinite being is a being whose abilities have no non-logical limits. (There are other ways to define infinite, but this should suffice for our purposes) – Bryson S. – 2014-07-18T23:28:37.163

@user4894 I have emended the question to reflect our discussion up to this point. – Bryson S. – 2014-07-18T23:32:49.360

My training was in math so when people say "infinity" I expect a clear definition that I can work with. If you want to posit an infinite being, I need to know what properties it has so I can think about it. Perhaps I lack the imagination for theology. But isn't changing the past violating a logical limit? Not a non-logical limit. So maybe we should figure out if being able to change the past is a logical or non-logical limit. Also, Anselm is pretty old, yet you're asking a question relative to the present. Anselm's definition is just word play, to me. – user4894 – 2014-07-19T00:04:44.837

1@user4894 Cards on the table, I completely agree with you that the concept of an unsurpassably great being is nonsense. My ontological objections to theism are diverse and numerous. However, I was willing to elide them on the basis that if I only knew logic better perhaps it would make sense to me. However, this abiding problem of what I will call "Divine Demonstration" has prevented me from accepting it.

I agree that retro-causality may be a poor example as it is more contentious than instructive. But what about moral perfection? Could we tell the difference between a virtuous being and God? – Bryson S. – 2014-07-19T00:57:41.753

1By "virtuous" I mean exemplifying moral virtues to an incredible degree. Can we tell the difference between being incredibly virtuous and infinitely virtuous? Based on my limited understanding, I don't think we can. I am therefore surprised that anyone defends the claim that an infinite being exists given that we would not know infinity if it were staring us in the face. – Bryson S. – 2014-07-19T01:00:39.430

Then we are in agreement. I think all attempts to subject God to logical analysis are doomed to failure. Talk of infinite beings is meaningless. But, a lot of smart people have written a lot about infinite beings. So maybe I'm wrong. – user4894 – 2014-07-19T01:09:16.557

The objection you're raising is also Hume's objection. – virmaior – 2014-07-19T01:53:33.533

FWIW, after reading your question, I began thinking about the phrase arbitrarily advanced civilization as is sometimes used by physicists. – Alfred Centauri – 2014-07-19T02:06:06.537

@AlfredCentauri Care to expound on the connotations/context of that phrase? – Bryson S. – 2014-07-19T02:08:18.370

I won't expound but I will recommend that you look up the novel "Contact" by the late Carl Sagan and the back story behind the 'wormholes' featured in it (look up "Kip Thorne" too). As I understand it, an arbitrarily advanced civilization is limited only by the impossible which seems on par with the idea of a being "who's abilities have no non-logical limitations". – Alfred Centauri – 2014-07-19T02:21:08.997

The move from something of 'which nothing greater can be conceived' to omnipotence etc. is of dubious validity. From a contemporary perspective it extrapolates from what might be a defect in an individual's imagination to a rather substantial claim about the external world. On the other hand, from a scholastic perspective it appears to posit a god with a contingent property, namely being contingent on what we can imagine. Even 500 years ago, good form suggested claiming a priori knowledge of God and calling it a day. – ben rudgers – 2014-07-19T04:20:00.963

@benrudgers I suspect that Anselm's notion was likely deeper than simply what we can conceive, and is generalizable to what any being could in principle conceive. I stumbled with this question myself when I first heard of the concept, but I now think "an unsurpassably great being" may be a closer to what was being aimed for. So do you agree that there is nothing we can point to in the world and say "Look at that, see??? Ah, now we know that God exists and is infinite based on this observation."? – Bryson S. – 2014-07-19T15:33:55.613

'Any being' includes the posited god. Thus the posited god is limited because like us there is something it cannot conceive. Our choices are inductive reasoning, claiming a priori knowledge, or assuming the premise (and attempting to obfuscate our assumption by abusing language). Not a big deal philosophically. A bigger deal when evangelizing for theology. – ben rudgers – 2014-07-19T15:50:42.727

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Taking this as the core question:

How can we have unambiguous evidence for an infinite being if we cannot even verify that the being is infinite?

The short answer is: We cannot.

Assuming that we humans have finite powers of perception, it is impossible to distinguish a being that exactly fills our perception window from one that extends beyond it.

For example:

• Any being that knows everything that we are able to verify is indistinguishable from an omniscient being: Any claim made by such a powerful (but not omniscient) entity outside our power to verify said claim may or may not be truth - say, claims about the native inhabitants of the 2nd planet around alpha centauri.

• Any being that that can seem to be anywhere we are able to look is indistinguishable from an omnipresent being: Any place we can't look may be a place the powerful (but not omnipresent) being also isn't able to go - say, inside the planet's core or out in the Oort cloud.

• Any being that can appear to do anything you can ask of it is indistinguishable from an omnipotent being: An interesting case would be a being with absolute power only in the domain of mental manipulation, being able to convince you and any number of co-witnesses (by creating false memories, etc.) without actually doing anything.

For an analogy:

Imagine that your entire life is spent in a large box with a single window looking out. Outside this window, all you ever see is a uniform, but pleasant, shade of mauve. This uniform mauve seems to extend in all directions, at least as best as you can determine by moving about in your box and using any tools that you have to try and improve your view.

• Is the mauve infinite in time? Was it there before you (or historical records of the thought-experiment-historians) existed, will it continue after you exist? Is it there only when you're looking?

• Is the mauve infinite in space? Maybe you're inside a small mauve bubble, or maybe the mauve ends a short distance beyond what you're able to see?

• Is the mauve infinite in its powers of 'mauve-ness', or does it differ from 'true mauve' by some imperceptible degree? Does it change colour over timescales that your eyes/brain cannot detect/comprehend?

That said, as a species we've developed a pretty big perception-window that an infinite-being candidate would have to fill!

(And if one day we do encounter a being indistinguishable from an actually-infinite one we'll probably have to say 'Close enough. Now what?')

It's this "close enough" move that I am objecting to. Arguably, we could have said close enough at any point in history and been dead wrong about what we were witnessing. An exceptionally skilled illusionist could get the nod by the standards adumbrated in your answer. That said, I like where you are taking the question. – Bryson S. – 2014-07-25T18:34:47.900

@BrysonS. - Fair call on the final parenthetical. I was more focused on the 'Now what?' when I wrote it, since a sufficiently-powerful being along those lines would probably force a complete re-think of physics at the minimum. – Dave B – 2014-07-25T18:50:02.517

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There are logical arguments for proving the infinity of God. What you quoted from Anselm is, however, not an argument. The link you referenced does summarize his argument, but the validity and the actual implications of the argument are debatable.

Firstly Anselm’s argument is an indirect argument proven through reductio ad absurdum. Such arguments often don’t illuminate the essence of the subject under examination beyond the presumed definition. As in this case the argument doesn’t directly prove and elucidate the infinity of God, it only disproves his finiteness by arguing that finiteness indicates defect which contradicts the presumed definition, and as such God’s infinity follows. However the actual meaning and implications of infinity itself remains to be elucidated.

Also, Anselm’s argument suffers from a serious fundamental flaw. The problem is where Anselm confuses the concept of an infinite being with its actual external referent! Conceiving that which nothing greater than can be conceived, doesn’t imply the necessity of an actual infinite being in the outside world, because ‘infinite being’ when conceived in the mind (contrary to the external world) is just a concept and therefore limited and finite, whereas it is in reality that an infinite being is really infinite! This subtle and mind-boggling flaw was first pointed out by muslim philosophers.

Therefore Anselm’s argument fails to prove both existence and infinity of God. There are however valid arguments for both premises proposed by muslim philosophers following the Mulla Sadra’s school of Transcendent Philosophy which I refuse to explain here as they go off topic.

But assuming that an infinite God is indeed proven to exist we can deal with the rest of your question.

To speak specifically, any miracle, feat, or theophany wrought by an infinite being could—in principle—have also been performed by a finite being. That is to say, there seems to be an ineradicable ambiguity in any manifestation of an infinite being's power, precisely for the reason that the very same action could have been performed by a being that was not infinite. How might we finite humans ever know, definitively, which being we are actually dealing with?

The validity of the above statement (i.e. any manifestation of an infinite being can also belong to a finite being) can be questioned depending on one’s theory of God and His relationship to the creation. For example, if we take the theory of Unity of Existence (as advocated by Mulla Sadra), there’s in essence nothing in existence except God. That is, all that there is, all that is done trace back to the infinite God. God is the only actual actor and agent in existence. Creations are only His “beams and shades” who have no independent, separate existence of their own. So no act or perfection can be essentially attributed to the creation (i.e. finite beings).

But as for observable evidences of his infinity, one can just look at the infinite and endless expressions of life on Earth; the endless unique identities of individual instances of creation. The natural universe is considered by many metaphysicians to be infinite in size. That if proven could count as evidence of God’s infinity; in their own right, the endless number of stars and galaxies in the cosmos. Also consider the endless emergence of phenomena around you. The world is in constant motion and development and at each instant unique realities come into existence, endless settings, relations and combinations of things.

In the above statements, it is presumed that all supreme attributes of God find expression even in the most trivial of phenomena. An ant is as just inclusive of God's attributes as is Archangel Gabriel, however, an angel enjoys an extremely higher more intense degree of the Divine qualities.

1Two beings stand before you: one is infinite, one is not. How do you tell which is which? If you cannot, how do you even know that an infinite being exists without assuming it a priori? I am asking about evidence, not subjective impressions of the grandeur of the universe (which can be just as readily expressed in non-theistic terms). – Bryson S. – 2014-07-19T03:01:39.053

@BrysonS. So are you only recognizing purely observable raw evidences with not attempt at making logical inferences from the observable data? – infatuated – 2014-07-19T03:08:38.733

I am questioning our ultimate ability to reason accurately. If our fundamental axioms turn out to be false, then the most rigorous proof of a proposition would be rendered meaningless. I am looking for a more empirical approach. For example, the proposition "The surface of the Sun is 6000K" can be unambiguously verified with observations that produce publicly available, intersubjective data. Is there anything analogous for the God envisaged by Anselm? – Bryson S. – 2014-07-19T03:11:36.953

1Additionally, if we do not start from the assumption that God exists and is infinite, how could the vast beauty of Nature sway the skeptical observer? – Bryson S. – 2014-07-19T03:16:12.393

@BrysonS., philosophical arguments rely on principles of logic and abstract concepts. The observable empirical evidences can be however taken as a basis for explaining phenomena that are not directly observable but can be inferred from the observable data. For example from observation of beauty in nature, one is related to the concept of beauty independent of its sensual referent. And it is ultimately based on contemplating the observable that we can find our way to the invisible. – infatuated – 2014-07-19T03:20:32.217

For our purposes, I am perfectly happy to accept invisible entities. The burden of my question lies entirely in discerning the finite versus infinite nature of said entities. You seem to have not provided a basis for the assertion that the creator of Nature is infinite, only the assumption that Nature is infinitely beautiful. But how would we know Nature is infinite? Also, is all of Nature beautiful? Presumably it's all made by the same perfect deity, so it would make sense that all of it should strike us as beautiful. But some things in Nature are, without doubt, aesthetically rebarbative. – Bryson S. – 2014-07-19T03:34:02.333

@BrysonS. It is an extensive topic, various related questions have to be examined, and some may seem outright foreign to you at the first glance. But what I wrote in the last the last two paragraphs were only observable evidences. But as you said some of them may be debatable. As for your particular issue with the beauty argument, it depends on your perspective. The mystic theistic view is that if one considers all phenomena as part of the greater Divine scheme of things, or in other words, through a holistic perspective, he or she shall never find any ugliness or flaw in the creation. – infatuated – 2014-07-19T03:46:51.233

@BrysonS. Also note that infinity can be best demonstrated through logical reasoning and mystical introspection. Confirmation of transcendental truths take much mental exercise and training. – infatuated – 2014-07-19T03:53:40.723

2"one can just look at the infinite and endless expressions of life on Earth ..." -- But you are confusing "infinite" with "really really big." There are only finitely many atoms on earth and only finitely many possible combinations of atoms. There is in fact a finite amount of biological variation on earth. If you look at a large finite number and call it infinite, you will be led to faulty conclusions. – user4894 – 2014-07-20T17:51:54.113

@user4894, if universe is infinite (as metaphysicians hold) then there would definitely be infinite number of virtually everything. However, even if not, there are still infinite expressions of being which is a widely accepted fact. All individual forms of being (animate or inanimate, living or lifeless) are completely unique and identical. This necessarily entails infinite number of possible forms of being. – infatuated – 2014-07-20T21:26:12.507

1@infatuated Can you quote any scientific evidence that the world is infinite? "All individual forms of being (animate or inanimate, living or lifeless) are completely unique and identical." -- Only finitely many people have ever lived and will ever live on earth. Finitely many. I can only repeat myself to point out that a large finite number is not infinite. Of course in a lyrical sense we all have "infinite potential," but that's not a statement about anything that exists in the actual universe. It's imperative to make this distinction. – user4894 – 2014-07-20T21:45:30.880

@user4894 "Only finitely many people have ever lived and will ever live on Earth" This is wrong! There has always been being and will be! So there have been infinite number of all forms of being (living, non-living) and will be! – infatuated – 2014-07-20T21:51:49.910

@user4894 As for scientific evidence I think it must be common knowledge. At least for humans it is proven that there are no single two of identical human beings no matter how closely similar they are. Genetics has proven that! But philosophy alone can prove that even without recurse to any empirical proof. – infatuated – 2014-07-20T21:54:49.100

1@infatuated: But as for observable evidences of his infinity, one can just look at the infinite and endless expressions of life on Earth --- Except that this isn't an infinite number, it's just a very, very, mind-bogglingly, hugely, colossally gargantuan one. I could be wrong, but I think that's what the questioner was getting at - how do you tell the 'big' from the 'actually infinite'? – Dave B – 2014-07-23T14:47:15.763

@DaveB Well, it is not really the actual infinite number of existing/exited phenomena that is being argued here, but the ceaseless emergence of unique phenomena that indicates a creator who is constantly generating unique expressions. That is, the universe is offering infinite possibilities for being. Yet, if the infinity of the actual existing/exited phenomena should be argued, it can be proven if eternity of the natural world is proven; that the universe came into existence since an infinite time in the past. – infatuated – 2014-07-23T20:00:29.450

1@infatuated: Taking 'eternity of the natural world' to mean the Earth, we already know it's not eternal: We know that the Earth is finite in time. Though that timeline dwarfs the sum entirety of all human existence ever, we know that the Earth formed roughly 4.5 billion years (or Ga - giga-annum) ago, that the first cells arose roughly 3.5 Ga ago, that multi-cellular life arose roughly 1 Ga ago. We know that the Sun will eventually become a red giant (and shatter any illusions of infinity at the other end), sometime between 1 and 5 Ga into the future. (But I think we drift off-topic now?) :) – Dave B – 2014-07-23T20:27:29.753

Also, having commented without expanding the comment thread, I see that @user4894 did a great job raising these very same points. – Dave B – 2014-07-23T20:34:27.133

@DaveB, by natural world I meant the whole universe not just Earth! The argument was: if the universe is eternal then infinity of forms of being follows because of uniqueness of all individual forms of being and they include living and non-living forms, such as planets, stars, plants, animals, human beings etc every instance of which is unique and non-duplicable. – infatuated – 2014-07-23T20:59:51.983

1@infatuated There are about 10^87 atoms in the universe. If the universe is indeed finite, there are only finitely many possible configurations of these 10^87 atoms. And there is currently no physical theory that accounts for the universe being infinite. – user4894 – 2014-07-24T00:12:30.680

@user4894, you fail to get the crux of the matter. Whether or not there are finite or infinite number of atoms, whether or not time or universe are infinite, each new phenomena is exceptionally unique. You fail to see that even a single atom is a new phenomenon just a moment later! – infatuated – 2014-07-24T00:37:19.543

2@infatuated: But if the universe is finite in time the number of states the universe will experience will again be mind-blowingly, computer-breakingly huge... but still, strictly speaking, a finite number. That, I think, is what the questioner was trying to get at: how do we differentiate between the mind-blowing and the actually infinite? So far as I know, we can't. – Dave B – 2014-07-24T18:04:58.503

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A god demonstrating his omnipotence would mean to make something which makes us convinced of his omnipotence. The simplest way to do that would be to manipulate our mind in a way that we believe in his omnipotence. An omnipotent god can almost certainly do that.

The only way an omnipotent god might not be able to do so (noticed by virmaior in the comments) is if there was a logical inconsistency, that is, if creating such a believe would inevitably destroy the ability to believe it. However evidence shows that we are able to believe all sorts of things, even against all evidence, and thus one can conclude that obviously our mind is able to hold believes independent of evidence. Indeed, many people even alrady hold the believe that there exists an omnipotent being, so that believe is not impossible. It is very unlikely that all people's minds being in such a state would be logically impossible if some people's mind being in that state isn't. If it is not logically impossible, an omnipotent god of course can put our minds in such a state.

It actually depends on how omnipotence plays out with respect to laws of logic. It's possible that omnipotence has limits such as not being able to coerce belief without undermining the capacity to believe. Moreover, the implications that God can do so and God does do so are different such that the mere absence of doing so does not imply that God cannot do so nor that God does not exist. – virmaior – 2014-07-19T14:26:55.230

"Moreover, the implications that God can do so and God does do so are different such that the mere absence of doing so does not imply that God cannot do so nor that God does not exist." — That was not the question. The question was if it is possible that an omnipotent god demonstrates his omnipotence, not if it is inevitable, or even just if it would be a wise move for an omnipotent god to do so. Your argument about logical possibility is sound, but I'd say evidence speaks against it: People manage to believe all sorts of nonsense even against evidence, so obviously there are states … – celtschk – 2014-07-19T14:34:01.867

… of minds which correspond to believes independent of evidence, and an omnipotent god of course could put our mind into such a state. – celtschk – 2014-07-19T14:35:01.827

Fair enough! +1 to you. – virmaior – 2014-07-19T14:36:48.963

I've now added some text about the "logical loophole" to the answer. Thank you for the +1. – celtschk – 2014-07-19T14:43:37.317

@celtschk The question remains, are we in an epistemic position to tell whether the universe we inhabit is overseen by an infinite and omniscient deity as opposed to a finite one? A hypothetical about what an omnipotent being could do seems to tell us next to nothing about the world we actually live in. I care less about what an omnipotent being could do if it existed, and more about whether one actually exists in any meaningful sense of the word. – Bryson S. – 2014-07-20T18:58:36.673

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Why or how the Infinite became the finite is an impossible question as it is self-contradictory. We can see this from another side when we seek to know how the Absolute has become the relative. Supposing we knew the answer, would the Absolute remain the Absolute? It would have become relative. What is meant by knowledge in our common sense idea? It is only something that has become limited by our mind, that we know, and when it is beyond our mind, it is not knowledge. Now if the Absolute becomes limited by the mind, It is no more Absolute; It has become finite. Everything limited by the mind becomes finite. Therefore, to know the Absolute is again a contradiction in terms. That is why the question has never been answered, because if it were answered, there would no more be an Absolute. A God known is no more God; He has become finite like one of us. He cannot be known. He is always the Unknowable One.

But does that not entail that we cannot, even in principle, have evidence for such a being? And if so, how would we know whether or not such a being even existed? Could we ever know? – Bryson S. – 2014-07-25T18:30:59.387

If there is a God, He is in our own hearts. Have you ever seen Him? It is an actual perception. Only the man who has actually perceived God has religion. Those who have perceived Him have perceived Him in a more intense sense then you see this external world. You will know the Truth because you have become the Truth. But it is done with great difficulty. Saints of different religions have realized Him through the power of introspection, he who has seen Him has seen the Reality, beyond being and non-being. He cannot be 'known' but He can be perceived. – Swami Vishwananda – 2014-07-26T14:35:33.537

The question remains, what evidence do you have that this being is in fact infinite, as opposed being merely extremely powerful? – Bryson S. – 2014-07-26T14:58:37.873

There is no proof or evidence in the sensual world. All proofs given in the sensual world are limited by time, space and causation and are therefore limited... All proofs in the sensual world are limited by the limits of language. Everything in the sensual world is limited. To those who have perceived the Reality, it is self-evident; no proof is required. – Swami Vishwananda – 2014-07-27T02:35:32.470

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There are two possible answers to the main question:

1) No, there can't ever be evidence for an infinite being,

2) There is evidence, but since human beings are incapable of "perceiving" it, it is the same as if there is no evidence.

In regards to the question, would we be capable of distinguishing between something performed by an infinite being or a "not so infinite" being? The answer would also be no, as long as the "not so infinite" being performance is also beyond our perception. If both performances are beyond our perception, we would not be able to tell which being did what?

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Yes, pending a slight change to the question. (see A → B, below)

I suggest we utilize Solomonoff induction (LW's narrative intro for those who don't know some basic theory of computation) in order to examine the issue. I will need one other tool: the concept of a non-recursively enumerable set of axioms. I claim that there are two kinds of infinite being:

1. infinite in number
2. infinite in description

Many people seem to think in terms of #1, but I want to argue that this is not a helpful way to think. Instead, I say we should think of an infinite being as not being describable by a [finite] computer program. That is, no longer how many lines of code you right in your simulator of the infinite being, you'll always be in error. You could get closer and closer to describing that infinite being, but you'd never 'finish', except as t → ∞ (which may be what John 17:3 claims).

Solomonoff induction plays on the idea of simplicity, which is notoriously hard to define. We may, however, be able to use Kolmogorov complexity, as argued in The Computational Theory of the Laws of Nature (I suggest reading the section "God's Problem" and "God's language"). When we want to explain a sequence of observations, per Ockham's razor, we want to pick the simplest explanation. That would be the algorithm with lowest Kolmogorov complexity. So, I can rephrase the question:

Could a sequence of observations ever be best-explainable via a type-2 infinite being, where "best-explainable" means having lower Kolmogorov complexity than any description?

I claim that this, however, is not quite the right question. It asks us to explain what already is. What if we wish, instead, to predict the next observation? This is a subtle shift, from:

A. What best explains a given sequence of observations?
↓
B. Where does a given sequence of observations most likely point?

If I am allowed to tweak your question from A → B, then we can talk about two different options for B:

I. The next observation will be like previous, and require no increase in Kolmogorov complexity.
II. The next observation will be different, and require an increase in Kolmogorov complexity.

If we run into enough II-type observations, I claim we are justified in inferring that our universe is infinite in description, via induction, despite the problem of induction. Furthermore, via Fitch's Paradox, the potential for infinite knowledge requires an extant omniscient being. So either everything that is knowable is already known, which would lock us into an epistemically finite universe, or there is an extant omniscient being, which means that being is infinite.

Would such an omniscient being "know" how to create new information? If so then it would create something previously unknown to it (which should be impossible), If not then there is something is presently does not know, namely how to create new information. Is the concept not self-contradictory? – Bryson S. – 2014-07-19T03:07:37.827

@BrysonS., What requires an omniscient being to create new information? I'm a bit worried that this is going to rabbit-trail down a discussion of how divine attributes can intermingle, which seems like it is too far afield. That really ought to get its own question, linked from here, don't you think? – labreuer – 2014-07-19T03:53:58.057

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Don't you see that what you described in your naive and fascinated way is already answer to your question? Your mental search and failure to find Is already a manifestation of something bigger than you.

That fascinating and magnificent thing/things going ON in your head while you write to us, do you see them as infinite and powerful manifestations of Gods?

Your imagination. You will not call it infinite?

Don't you see that finite is just another side of infinite? (think continuity)

tHink more

You pointed out some great examples. But I was wondering why you described them as signs of 'Gods'? Can there be more than one infinite God? – infatuated – 2014-07-20T14:54:45.477

1I am perfectly happy to accept Nature as bigger than myself. So, what's your point? The topic at issue is how to verify that something is infinite as opposed to finite. I don't see how your commentary contributes to that discussion. – Bryson S. – 2014-07-20T15:44:58.080

@BrysonS. To that discussion i said that everything is infinite. Do you see it? – Asphir Dom – 2014-07-20T20:31:22.703

1@Asphir Dom A definition that includes everything is utterly useless, precisely because it applies equally to all of existence. If I said to you that my car is "WkjbTf," my favorite color is "WkjbTf," my mind is a framework within "WkjbTf," and in fact the entire universe is "WkjbTf," you would be right to say that I should stop talking nonsense because the term "WkjbTf" is unintelligible. That which refers to everything refers to nothing. What difference does replacing "WkjbTf" with "infinite" make? None that I can see... – Bryson S. – 2014-07-20T21:00:06.640

@BrysonS. Nice ideas and flow. I am glad you accepted nature as something bigger. "That which refers to everything refers to nothing". You don't see how this quote of you is clue to the idea you seek? God is everything and thus his manifestation can only by infinitesimally small - the thing you called nothing. You are just not seeing it. Alas it is always in front of you. You want to calculate it, right now. If you seek definitions you need to understand first that you will have very hard time to define all aspects of infinity using logic. – Asphir Dom – 2014-07-21T02:09:30.940

1@AsphirDom First off, do you accept that there is a possible world in which the idea of an infinite God exists but the deity itself does not? If you do not accept this possibility, then we might as well stop our discussion here. If you do think that such a world is possible, how can we tell whether or not we are living it? – Bryson S. – 2014-07-21T02:17:37.160

@infatuated I used word Gods to stress that God is not lonely inside himself. – Asphir Dom – 2014-07-21T02:18:26.727

@BrysonS. Just a moment ago you said statements about everything make no sense and now you are trying to make statement about everything (speaking of possible worlds)? You have a wrong ground about finite. We are not finite. That is the whole point. We do not understand infinity and finity themselves. That is why we should not be too fast in our judgements. Finite and infinite are one thing, they are glued together by the idea of continuity (see Math. Analysis). That is why your question is a paradox leading to clarity about these two seemingly different conceptions. – Asphir Dom – 2014-07-21T02:26:46.240