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ChristianKl comments on Consistent extrapolated beliefs about math? - Less Wrong Discussion
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As long as you aren't clear what you mean with "exist" the rest of the argument is build on quicksand.
How so? The argument is about disbelieving intuitions about "existence" when they seem to contradict well-known math results.
If you start to reject naive assumptions about 'existence' the straightforward way is to do ontology and get a concept of 'existence' that's not naive.
In logical positivism there the attitude that you don't need to do any ontology, but when it comes to issues like this that just isn't helpful.