From Osher Doctorow

I've argued for some time in previous years that mathematical/logical
existence or "there exists" and physical/physics existence are somewhat
related. If we can assert that "there exists x which is an element of
set X," then neither x nor X need be physically real and physically
existing, but in classical physics if x and X are physically
real/existing in the above context then there is some set X and element
x such that "there exists an x which is an element of X" is a
mathematical/logical proposition about mathematical/logical
existence/existentials. This actually carries over to
quantum/superstring/brane physics except where the Heisenberg
Uncertainty Principle (HUP) allegedly operates with conjugate variables
like position and momentum. Moreover, since black holes are part of
quantum/superstring/brane physics, the arguments of the previous
postings of this thread carry over to quantum physics, and regardless
of whether you believe in HUP or not it is absurd to delegate position
or its uncertainty to non-existence simultaneously with momentum or its
uncertainty. We may not either measure or observe them, but they do
not thereby lose their existence.

Saunders MacLane of U. Chicago, who recently passed away, developed
category theory with Eilenberg in an effort to largely eliminate sets
as the basic fundamental objects in mathematics (groups, algebras, etc.
are all sets). Garrett Birkhoff of Harvard, who had a superb
understanding of causation in differential equations, suggested that
his colleage MacLane get his Ph.D. in Germany, which MacLane proceeded
to do. Subsequently, much of MacLane's work followed the Heisenberg
agenda whether consciously or subconsciously. Existence is too
explicit as a set concept in mathematics/logic? Eliminate it by
dealing not with sets but "objects", which can be so abstractly and
weirdly defined that both the Heisenberg Uncertainty Principle and the
Prince De Broglie wave-particle duality no longer seem to clash with
our intuition from classical physics.

Of course, you could say that black holes also clash with our physical
intuition. But do they really? Have we not encountered the unknown
and failed to solve it, encountered the unknown and failed to observe
and detect it, encountered the unknown and failed to explain it? Have
we penetrated every closed surface, opened every closed box, even in
our brains/minds? I think that you know the answers to these
questions.

Osher Doctorow