When you describe a black hole (the kind of singularity you’re probably talking about) with our current theories (specifically general relativity), you arrive at the conclusion that they have zero volume, infinite density, etc.
But there is no experimental evidence for this, as we really can’t see what goes on inside a black hole.
We already know that general relativity is incomplete, failing to describe reality in certain situations. Ask a physicist who works with black holes and they’ll (probably) tell you that the singularity stuff is just another example of general relativity’s incompleteness.
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