Actual Infinity in Reality?

[possibletarian]

So there could be some universe where A could be both A and not A?!

We don't know, but if there were, we couldn't cogently describe it or anything about it by reference to a system of axioms derived from this universe where...so far as we know (and that's not exactly a full throated invocation of inviolable truth, now is it, lol)...such is not the case.

Logic, as a system, has all the limitations of this universe..plus whatever additional limitations arise from the axioms of the system itself -and- those who employ it.

Hell, even in -this- universe the system wasn't always formed as such.  We didn't discover these "laws" all at once...and I don't know how we could know if we'd found the very last piece yet..today.  Propositional logic may still be incomplete just in this world, and whatever else that's left, if there;s anything left, may invalidate some axiomatic x...just as it has in the past.  The continued existence of paradox strongly implies that we haven;t gotten it quite right..somehow.

I'm always cautious when 'possible' worlds are used to argue anything, they are at best imaginary worlds and don't represent reality (as in what actually happened or is happening)  at all.  We have no way of knowing if even a single atom could be in a different place from what is.

Imaginary worlds are the reserve of a mind that wishes to discuss non existent alternatives to the reality we know, or story makers who want to create some fantasy.

As for logic I agree it is rather limited to the same minds that make stuff up, It's our version of what we think should be given our understanding of what we observe the world around us to be. We seem to have lost the ability to simply say we don't know, logic simply will not help if we lack information on which to base it.