Consul wrote: ↑March 9th, 2022, 12:29 pmHere is an excerpt from an essay of mine, written years ago, on the arguments for the existence of God, concerning the problems with applying infinite attributes to "beings." You might find it interesting.
Of course, if the idea of an actual infinity is incoherent, then the idea of an infinitely extended body is incoherent too.
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Claim #1 (first version): God is a "being" which exists in neither time nor space, or alternatively (second version), He exists in all times and places simultaneously.
With regard to the first version (no location), the question to ask is, What is the difference between a "being" which does not exist at any time or place and a being which does not exist at all? How can we tell the difference? The reader is invited to pause here and attempt to answer that question before proceeding . . . . After every location in the universe has been examined and nothing is found which we can agree is God, what do we believe we are saying when we continue to claim that He exists?
In our ordinary understanding of the term, to say that a thing exists is to say that if we look in a certain place (and time) we will find the thing. The time and place need not be specified, and may not even be known: often a claim that something exists is made in order to launch a search -- "Thar's gold in them hills!" It is this implication --- that the thing might be found -- which gives the verb, "to exist," any purpose in the language. Those who would disagree that this implication follows from a claim of existence are invited to explain what communication function "to exist" would serve otherwise -- what good would the term be in such a case? What use would it have? What information would anyone convey by asserting it of something?
"To be" is to be someplace, somewhen. If propositions of the form "X exists" carry any information at all, it is the information, "There is a time t and a place s such that at t and s one can find X." To say that something does not exist is to say that there is no intersection of t and s such that X can be found there; all possible combinations of t and s are empty of X. Thus (on our ordinary interpretation), to assert that something "exists outside space and time" is to assert a contradiction.
It is important to realize that none of this has the slightest thing to with what the universe is like. It has only to do with how effectively we can communicate with one another about the universe. To claim that "X exists outside of space and time" is to abolish the distinction intended when we say that something either exists or does not exist; someone who makes this claim has said that this distinction is of no value. Instead of things which exist and things which do not, we have things which exist in space and time and things which exist outside them; if God "exists outside of space and time," why not assert that demons, unicorns, fairies and poltergeists exist outside space and time? Why not argue that in this realm outside space and time, electrons, stars, and worlds exist also, populated by gorgons and dragons? Or even by cowboys and Indians? Or by Rhett Butler and Scarlet O'Hara? Instead of saying that Santa Claus does not exist, why not say he exists outside of spacetime?
Saying that God (or anything else) exists "outside space and time" is to propose a new construal of the verb "to exist." As we suggested above, we do not reject such proposals out of hand. But we are entitled to a certain conservatism: before we accept such proposals we should demand some showing of how our ability to describe the world to one another is improved by the proposed conceptual shift. And it is difficult to see what advantages for comprehension the strategy here proposed confers. A Santa that "exists outside space and time" leaves no more gifts than a non-existent Santa; a non-spatio-temporal unicorn is no easier to ride than an unreal one. How, in fact, do we tell the two apart? On the other hand, there would seem to be a major disadvantage: we have just created, willy-nilly, a new universe utterly bizarre and totally inaccessible. And how does that facilitate our understanding of the world?
We stress that it is a logical point we are making here, not an ontological one. We are not trying to say what does and what does not exist or where things exist. Nonetheless, someone may say "It does not seem impossible to me that something might exist outside space and time. Surely the universe is bigger than our imaginations.” But this critic assumes that “spacetime" is itself a place; that it is something one can either be inside or outside of, and that (for all we know) things can be outside as well as in. He assumes that the proposition "God exists outside spacetime" is of the same form as "Ginkgoes are known to exist outside China." But this assumption is mistaken: "spacetime" is not itself a place and time; it is intended to refer to all the places and times that there are. Saying that something exists "outside space and time" is not to say it exists somewhere else, because there is nowhere else; it is to say it does not exist.*
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*Denying that things exist "outside space and time" is not to rule out the possibility of multiple space-time domains. If the universe is "closed" (finite but unbounded) there may be universes other than ours. Objects in these "parallel universes" are outside our space-time continuum, but not "outside space and time." They have coordinates within their own local continuum, and also within a larger coordinate system that embraces our universe, as well.
We proceed to the second version of Claim #1: God is omnipresent. On my desk before me is a half-cupful of cold coffee. If God is everywhere, He is presumably in that cup. If I pour out the coffee, God will presumably remain in the cup (although part of Him would also have been poured out with the coffee). If I launch the cup into the vacuum of high orbit, still God will remain in the cup. We thus face another question similar to our earlier one: how do I tell a cup containing God from an empty cup? And if the two states of affairs cannot be distinguished, why not opt for the simpler, i.e., the empty cup?
The believer may now say, "God is not 'in' the cup in the same way that the coffee is 'in' the cup. The coffee is contained in the cup, but God is immanent in all things; it is His presence in it that sustains the cup. If God were not immanent in the cup it could not exist."
But this latter is surely an empirical claim. "If God were removed from the cup (or was to remove Himself from it) it would cease to exist" is of the same form as "If the latent heat were removed from the coffee, it would freeze." But the believer will not likely be able to remove God from the cup, or persuade Him to remove Himself; he will not be able to show that his claim is true. He thus predicates a property of the cup but does not show how a cup with this property differs from one that lacks it. Of course (the believer tells us), this property is not lacked by anything; it is a property of all things whatsoever. But we can certainly imagine that things might lack this property and yet exist. How do we tell, then, a universe in which all things possess this property from one in which things lack this property but exist anyway? If we have no way to decide whether our universe is made up of the first kind of objects or the second, why not (again) choose the simpler story?
We can no doubt imagine a universe in which all things exhibit a certain property; one, say, in which all things are blue. The inhabitants of this universe will not notice that all things are blue, and will not even have a word in their language for "blue" (or any other color, if all things are blue). Yet by hypothesis, all things in their universe are blue, whether they realize it or not. And so (says the believer) is God in all things in our universe.
Now the first thing to realize about this scenario is that there is a difference between what we outside observers are entitled to say about the blue universe and what its inhabitants are entitled to say (recall that it is what we are entitled to say that is at issue here). Being able to perceive colors ourselves (and aware that there are many colors), we, if we behold this imagined universe, are entitled to say all things in it are blue. We can distinguish blue things from orange and purple things, and can therefore have evidence, namely the evidence of our senses, that things in the blue universe are blue. The inhabitants, on the other hand, never having seen a color other than blue, have no concept of color; they can't have any evidence for the claim that things in their universe are blue. They have no point of reference; they are in the position we (in our universe) are in with respect to the conjecture (mentioned by Russell) that the universe, and everything within it, is doubling in size every second. Because no conceivable observation could confirm this conjecture, it is vacuous; no one is entitled to claim that the universe is doubling in size every second because no one can produce supporting evidence -- even though it may well be doubling in size every second (we dismiss this conjecture simply because it is uneconomical: if the universe is doubling in size every second, then we will need some account of the mechanism driving this expansion, etc.). Being similarly in want of evidence, the inhabitants of the blue universe are not entitled to claim all things in their universe are blue.
Imagine, however, that eventually the blue people discover the wave theory of light and produce a spectrometer. They measure the wavelengths of light reflected by things in their universe and discover that all things reflect at the same wavelength. Being imaginative, they propose that light might exist at other wavelengths, and call the wavelength with which they're familiar "blue.” They are now entitled to do this (and they are also obliged to demonstrate their hypothesis by actually producing light of another color).
It may be that God (regarded as some so far undiscovered property) is present in all things. But only someone in possession of evidence (or who can at least say what would count as evidence) is in a position to so claim. Until such evidence presents itself the claim is of the same status as the claim that the universe is doubling in size every second.
There is another possible problem with God's omnipresence: God is presumed to be a being. But are not beings necessarily local? It seems to be necessary for the identification of any being that the being have limits; that we be able to determine where the being begins and ends. Else how do we identify the being as a being? Suppose someone invites us to a zoo in another universe to gaze upon the incredible omnipresent elephant. Would we be able to see anything but an endless expanse of gray? How would we know we did not behold, instead, an omnipresent mouse? Or merely a dense fog?
Endowing any object with natural attributes carried to infinity is to invite conceptual mayhem, particularly when several are predicated simultaneously. Within our common conceptual framework only space and time can be extended to infinity in an orderly way. The logics of such formulae as "infinite wisdom," "infinite benevolence," "infinite power," "infinite knowledge," "infinite being," et cetera, are undeveloped; we have no consensus as to how such expressions ought to function. And if we attempt to interpret them using the logics of their component terms, we easily derive contradictions. An obvious example is the classical "problem of evil": if God is simultaneously omnipotent, omniscient, and infinitely beneficent, how does one explain the existence of evil? Another: if God is omnipotent and immutable, can He change Himself? Or if, per Anselm's definition, God is "that which nothing greater than can be conceived," then He must be able to conceive a being greater than Himself. For if He cannot, then we can conceive a greater being, namely one who can conceive a being greater than himself. So if God is that which nothing greater than can be conceived, then He is not. And so on.
I am doubtful whether the notion of an "infinite being" can be made coherent (although I grant that the above problem of visualizing an infinite elephant seems less troublesome in the case of a being which is also invisible and intangible). The concept of infinity, itself, is not a problem; the set of integers is a coherent infinity, and perhaps the universe is a spatio-temporal infinity of some cardinality. The question is whether a being (and the properties of a being) can coherently be described as infinite; whether "infinite being" may not be a predicative construct of the same ilk as "round square." I admit my uncertainty on this point, and welcome any arguments in opposition to my tentative conclusion. I would insist, however, that any proposed clarification preserve the differences between beings and things which are not beings, and that after "clarification" such things as elephants and mice continue to count as beings.