“they [the elves] hold that all Creation of any sort must be in Eä [the actual, existing universe], proceeding from Eru in the same way, and therefore being of the same Order. They do not believe in contemporaneous non-contiguous worlds except as an amusing fantasy of the mind. They are (say they) either altogether unknowable, even as to whether they are or are not, or else if there are any intersections (however rare) they are only provinces of one Eä” (Morgoth’s Ring 252)
Does this mean that there are no possible, alternate worlds at all, or just that there are no actual worlds that are not already “contiguous” with, and hence part of, this world? Compare this with St. Thomas:
The very order of things created by God shows the unity of the world. For this world is called one by the unity of order, whereby some things are ordered to others. But whatever things come from God, have relation of order to each other, and to God Himself, as shown above (Q[11], A[3]; Q[21], A[1]). Hence it must be that all things should belong to one world. Therefore those only can assert that many worlds exist who do not acknowledge any ordaining wisdom, but rather believe in chance, as Democritus, who said that this world, besides an infinite number of other worlds, was made from a casual concourse of atoms. (ST 1.47.3)
The Flame Imperishable 
A very interesting question, thank you!
I was strongly reminded of Tolkien’s 1954 reply to Mr. Peter Hastings, in which Tolkien wrote:
“Since the whole matter from beginning to end is mainly concerned with the relation of Creation to making and sub-creation (and subsidiarily with the related matter of ‘mortality’), it must be clear that references to these things are not casual, but fundamental: they may well be fundamentally ‘wrong’ from the point of view of Reality (external reality). But they cannot be wrong inside this imaginary world, since that is how it is made.
We differ entirely about the nature of the relation of sub-creation to Creation. I should have said that liberation ‘from the channels the creator is known to have used already’ is the fundamental function of ‘sub-creation’, a tribute to the infinity of His potential variety, one of the ways in which indeed it is exhibited, as indeed I said in the Essay. I am not a metaphysician; but I should have thought it a curious metaphysic – there is not one but many, indeed potentially innumerable ones – that declared the channels known (in such a finite corner as we have any inkling of) to have been used, are the only possible ones, or efficacious, or possibly acceptable to and by Him!
‘Reincarnation’ may be bad theology (that surely , rather than metaphysics) as applied to Humanity; and my legendarium, especially the ‘Downfall of Númenor’ which lies immediately behind The Lord of the Rings, is based on my view: that Men are essentially mortal and must not try to become ‘immortal’ in the flesh. But I do not see how even in the Primary World any theologian or philosopher, unless very much better informed about the relation of spirit and body than I believe anyone to be, could deny the possibility of re-incarnation as a mode of existence, prescribed for certain kinds of rational incarnate creatures.”
Carpenter, Humphrey; Tolkien, Christopher (2012-12-13). The Letters of J. R. R. Tolkien (Kindle Locations 4001-4014). HarperCollins Publishers. Kindle Edition. #153, draft letter to Peter Hastings, September 1954
It seems to me that Tolkien’s explanation of Elvish beliefs from Laws and Customs among the Eldar is in good accordance with the ideas he describe to Mr. Hastings, where he essentially argues that it is unknowable whether God would use reincarnation as “a mode of existence” (presumably in some, also unknowable, ‘other’ world).
And of course there is then also the whole question of modern physics with its suggestions of many-worlds interpretations of quantum physics … but that would, I think, be taking the discussion too far :-)
Seems to be a rejection of possible world semantics on the basis that anything that actually is is part of this actual world.
Metaphysically speaking, I am the Universe, and if I choose to accept the tenet that what ‘is,’ is – then that is proof enough. However, Tolkien would seem to contradict himself in that he has ‘permitted’ and ‘recognised’ the existence of Tom Bombadil, Old Man Willow, and the Watcher in the Water – all recognised characters so proclaimed to be “in Middle-earth, but not of it.” To my thoughts, this would proclaim an ‘other world’ acceptance, as these would need to come from somewhere.
Old Man Willow was also implicitly cited as an example of all things in Arda Marred being at risk of Fall, including trees. So I’d hesitate to take it as an example of something “in Middle-Earth, but not of it”.
In any case, the problem described in the original quotes is one that modern scientific cosmology has as well – if other universes are indeed separate, we have no way to observe them and as such, dealing with them can not precisely be called scientific, since they are inherently untestable. If, on the other hand, they interact with ours, can they, and ours, really be called “universe(s)”, since they evidently don’t describe a “whole”?
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I think that second part of your sentence is accurate that the fragment you gave admits it possible that there may exist other ‘worlds’ but they are simply part of Ea :) and so technically within the same world as a whole, and now how the wraith world, the Unseen and Aman removed from circles of the world fit in? Well in the same manner it would seem. Aman is still physical and accessible through Straight Road and the Unseen is second layer of reality or appears to be :) it’s normally invisible and there exist within it things unseen in primary plane. That’s what I think anyway :).