Eugine_Nier comments on Second-Order Logic: The Controversy - LessWrong
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Simplicity is an important consideration. There are many more ways for complex universes to have violated our expectations already, while still making sapience possible, than for simple universes to have done so. That is, the space of simple universes is much more constrained by anthropic principles than is the space of complicated ones; so it is surprising that we seem to have found ourselves in a universe largely describable with very simple and uniform logic and mathematics, since there are many more ways to be complicated than to be simple. And this surprising fact may suggest that exotic logical, mathematical, or metaphysical structures do not exist, or are in some other respect not candidates for our anthropic reasoning. In other words, we can draw a tentative inductive conclusion regarding whether spacetime is nonstandard overall by considering all the ways in which our theories to date have been surprisingly successful and general while appealing almost exclusively to the simplest (which often corresponds to 'most standard,' with a few important caveats) conceivable systems. This won't be conclusive, but it's at least suggestive.
How do we know they haven't?
Interesting choice of example.
Not objecting to it, just interesting.