I prefer to believe the universe exists and whatever is possible is synonymous with being physical law. Conscious subjective experience is one of those phenomena not excluded by physical law.
But then this article claims and you also seems to claim something like:
> But what if somewhere else some consciousness has intuitive experiences about numbers which differ from our intuitive experiences.
I don't see why minds with intuitions creates any burden for numbers. From my perspective Mathematics is at bottom a game of string manipulation. Interpretations of those strings often can be applied to understand/predict/manipulate the physical universe. But the only real thing is the universe itself not the subjective interpretations in the minds.
The minds are real, obviously, they exist in the universe. Integers are an interpretation of a particular string. Suppose some other mind is incapable of an intuitive understanding an interpretation that we as humans have; I don't see how the "integers" could possibly be affected.
None of us are concerned that dogs don't understand math. Why we be concerned about the minds of aliens and what they find intuitive?