Hello Farsight,
In Geons, Black Holes and Quantum Foam (the 2000 paperback edition) Wheeler says something similar on page 235, only with "spacetime" in place of "space". He is actually quoting from another of his books, A Journey into Gravity and Spacetime, but I don't have access to that right now. The version you gave (with "space") doesn't appear anywhere in Wheeler's writings as far as I can see, but I admit I don't had the time or will to make an exhaustive search. Could you post a link so I may see the quote in its original context?
The reason I ask is this: in my experience it is not uncommon to see "spacetime" referred to as a "four-dimensional space" or simply a "space". This is actually a perfectly correct use of terminology - see [1] for the technical meaning of "space", for example. It may be that some ambiguity could arise when we start talking about spacelike hypersurfaces (which are also "spaces", though 3-dimensional, and correspond closely to the everyday meaning of "space"), but the context and the actual mathematics being presented would be enough to resolve the ambiguity for someone familiar with the subject.
To put it mildly, I would consider it a safe bet that Wheeler is not confused about the distinction between the four-dimensional space we call "spacetime", and the 3-dimensional "spaces" it contains as spacelike hypersurfaces. It is virtually certain to me that either (a) it is a misquote, or (b) the quote is accurate, but in context the meaning of "space" is seen to be "spacetime", rather than something like "spacelike hypersurface". If you could dig up the source for that quote I'm sure we could verify that.
Best regards.
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References:
[1] en.wikipedia.org/wiki/Space_(mathematics)
(Apparently I need 15 posts or more before I can post links.)