I am not *comfortable* allowing logic itself to be something like a fact of our universe -- maybe it is something more like a necessity for any universe, or at least for any intelligible universe. — Srap Tasmaner
It ought to help to strip "logic" down to its ultimate simplicities. We do grant it too much psychological status, even though we don't then want to eliminate it as the thread of "cosmic intelligibility" that runs through life and mind too.
The metaphysics of the systems view goes back to Anaximander's apeiron and the general Greek enthusiasm for understanding nature as a dialectic, a unity of opposites.
What it boils down to is the logical principle that whatever doesn't self-contradict is free to be the case. Peirce encoded this in his dichotomy of tychism~synechism – freedoms and the habits of constraint that must emerge once everything starts happening and discovers how that mass of interacting results in its own restricting limits.
If you have to argue against any principle, this would seem the hardest to refute.
Something popping out of nothing doesn't compute. There is no logic in that. But somethingness being whatever is left after a great clash of clashing contrarieties does compute. It is an undeniable conclusion. Everythingness is its own filter as all that is simply symmetric will eliminate itself, leaving whatever is uncancellably asymmetric as a possibility.
If you step one metre left and one metre right, nothing has effectively changed. But if you step one metre left and it is over the edge of a cliff, now you have an event that can't so easily be cancelled out.
This is exactly the logic of the path integral that extracts a concrete world from the probabilities of particle fields. The calculation takes all possible particle events and then discovers the degree to which all the many options cancel each other out.
The vast weight of the possibilities are symmetric – virtual particle pairs that create and annihilate without leaving any trace. But this self-winnowing eventually leaves some "collapsed" actual particle event making its mark on the world.
So both in our earliest metaphysics and our best current physical models, the same deep logical trick is at work. Something emerges out of a self-cancelling sum over everything. We have a foundational truth that we can rely on. Or at least pragmatism tells us no other principle has better survived the test.
I should add that dichotomies encode asymmetries, or hierarchical order.
If everything simply self-cancelled, then that would indeed leave nothing. So what can survive all the cancellation is the dichotomous order that gives reality two complementary directions in which to be forever moving apart from itself.
Again, that is the metaphysics of the quantum view. The Universe is eternally cooling and spreading – spreading because it cools, and cooling because it spreads.
In any instant, from the level of individual quantum vacuum fluctuations, the world has grown both larger and cooler. This in itself is enough to promote some of the self-cancelling virtual pairs to long-term reality.
At the event horizon of a black hole or the edge of the visible universe, you have even the briefest-lived self-annihilating pairs being separated for just long enough to find themselves existing in different lightcones or world lines.
Back during the hot dense fury of the Big Bang, inflation itself was separating virtual fluctuations with enough vigour to keep even a lot of very short-lived particles going. There was a lot of crud to spill into a rapidly cooled void and reheat it with the matter we are familiar with as the lucky survivors.
So the objection to maths and logic is largely to do with the way these fields have wandered off as their own research subjects, remote from the concerns of natural philosophy - the tradition that connects ancient metaphysics to modern physics.
Maths is hell of an arbitrary exercise in the freedoms from physical reality that it grants itself. The logic choppers likewise have strayed from the constraints of pragmatics.
But what we mean by an intelligible cosmos is in fact so simple in terms of its logic and maths that this isn't a great problem. The Darwinian principle of cosmic self-selection tells us somethingness is the product of a symmetry-breaking so rigorous that it left behind only uncancellable asymmetry. The dichotomy that results in the hierarchy.
In the end, the cooling~expanding Universe will end in its Heat Death. All the crud will get broken down into the faintest rustle of a quantum vacuum and exported across cosmic horizons. It will still be something of course, but as near to absolute nothingness as we can intelligibly conjecture.