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Can there exist an uncountable planar graph?

This usage of exist bothers me. In this context, my understanding is that it is used as a replacement for be. That looks very strange to me. However, I found it in the writing of a person who is very good at teaching and explaining, and I guess it might be actually correct. Is it?

EDIT: This is actually a title of a Mathematics Stack Exchange question.

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    Yes. It's perfectly grammatical. But if you ever heard the expression 'Can there exist ...' outside a university symposium (or EL website), I would be extremely surprised. It is probably better than the far more normal ordering 'Can a 7 foot spider exist?' (which would probably have an 'actually' inserted) here as it focuses emphasis in a better way. – Edwin Ashworth Jul 14 '14 at 8:14
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    @VividD Where does the question come from? It looks like mathematical jargon to me. It may be an odd way of speaking in general conversation, but to a mathematician it's a very normal way of asking the question. – Rupe Jul 14 '14 at 10:23
  • What bothers you about it? – Matt Gutting Jul 14 '14 at 10:34
  • @Matt, why is 'to exist' so special verb? I can't imagine any other verb in similar construction (other than 'to be'). – VividD Jul 14 '14 at 11:47
  • So your questions seem to be "Are there any other verbs besides be which can substitute in the construction Can there [VERB] [SUBJECT] '? – Matt Gutting Jul 14 '14 at 13:23
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This use of exist instead of be is common, not only in mathematics, but also in philosophy. Although in everyday life, we make little distinction, if any, between the two, in general, the verb be when used independently, seems to carry with it a sense of sentient existence, whereas exist lacks that connotation, and is therefore more "neutral".

Now, for the word order in the sentence. As Edwin Ashworth mentioned in his comment, in everyday language we would probably find a sentence like:

Can a 7 foot spider exist?

rather than

Can there exist a 7 foot spider?

However, in the fields of philosophy and mathematics, one usually is not interested in teh existence of such mundane phenomena which can so concisely be described.

You could phrase your sentence as:

Can an uncountable planar graph exist?

However, it is not unlikely that in a similar context I am not wondering about a mere uncountable planar graph, but one that has many more properties. I might wonder a about an uncountable, limited dimensional, planar graph that is not identical to an earlier-described construct.

Now, if I ask:

Can an uncountable, limited dimensional, planar graph that is not identical to an earlier-described construct exist?

The sentence becomes a lot less clear: halfway the sentence I start wondering what that thing you are describing is supposed to be able to do!

Therefore the main verb, exist is moved to the front of the sentence, so it is clear from the start that I want to know something about the possible existence of what I am about to describe:

Can there exist an uncountable, limited dimensional, planar graph that is not identical to an earlier-described construct?

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    Interestingly, the naturalness and neutralness of the there-based constructions is much higher if the verb is be, rather than exist: “Can there be a seven-foot spider?” is fine, whereas “Can a seven-foot spider be?” is archaic or awkward at best. – Janus Bahs Jacquet Jul 14 '14 at 10:58
  • True, "can a spider be?" is something I would expect in a theological treatise on the existence of souls in non-human animals... – oerkelens Jul 14 '14 at 11:06

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