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On the other hand, there is no substantive content in metaphysics (at least as far as ontology goes) if the statements do not pick out real entities.

You've just committed the fallacy of begging the question -- you assumed the truth of mathematical realism in this line, and arguably in a couple others.

If mathematical realism is false, various parts of your argument start to crumble.

I fail to see how the quoted portion of my comment assumes mathematical realism. I could see how other parts of my comment might suggest I'm assuming MR. Assuming you meant to reference the portions where I talk about how the results of mathematics tells us something about the world, modal structural realism[1] is an underappreciated interpretation of mathematics.

[1] https://plato.stanford.edu/entries/nominalism-mathematics/#M...

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