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In other words, how can you presume the physical laws or logic of any other universe or domain outside this universe?

You misunderstand. Physical laws and science in general is highly context dependent i.e. it only applies to the universe we happen to live in. Mathematics can be applied to all possible universes, and is regularly. There is some application for proving mathematics in spaces that don't exist in our universe, so it isn't purely mental masturbation. Things like logic, which is grounded purely in mathematics, are transferable to all spaces and would work as well outside our universe as inside it. The presumption that most people have that mathematics only extends as far as the boundaries of our universe is wrong, and leads to idle speculation of dubious value.

The "how"s and "why"s are serious esoterica, so I won't go there. The only thing to remember is that physical laws only apply to our universe, but mathematics apply everywhere. Trying to get around inconvenient mathematics is a fool's errand in any universe/space. This means, among other things, that there can exist no universe where "liberal logic" is actually valid in any kind of mathematical sense.

Thank you for your explanation! However, I respectfully disagree.

I see no requirement that pi would be the same in an alternate universe, much less Schwarzchild, Riemannian or Euclidean Geometry and so forth.

I say this because space/time itself is a quality of the extension of field - physical laws - and may not be the same, or may be dimensionally skewed or not exist at all - in an alternate universe or domain.

Likewise, any logic conditioned on the arrow of time could be invalid in an alternate universe - even the concept of numbers (e.g. "three") requires a material existence, i.e. physical law.

For lurkers: What is Mathematics?

Things like logic, which is grounded purely in mathematics, are transferable to all spaces and would work as well outside our universe as inside it. The presumption that most people have that mathematics only extends as far as the boundaries of our universe is wrong, and leads to idle speculation of dubious value.

I think you are taking reason way too far when you say you can use it beyond the boundaries of our universe. How can one 'know' something which no one has any experience of? You can use reason and mathematics as science does to verify experiences, but reason alone cannot provide knowledge of something so foreign that no one has any experience of. In other words, knowing that 2+2=4 does not tell you what's for dinner.