"Robert Perkins" wrote in message

The upshot of Goedel's Incompleteness Theorem is mathematical proof
that "any self-consistent axiomatic system powerful enough to describe
integer arithmetic will allow for propositions about integers that can
neither be proven nor disproven from the axioms." [from the Wikipedia
article on Goedel]

Euclidean geometry is more powerful than integer arithmetic.

Interesting POV. I gather that you're not a physicist. Empirical experiment
is still the gold standard. You haven't identified which parts of SR fall
falt under this type of confrontation. You haven't identified *any* current
physical models which whither under the light of empirical testing.

That is, logical systems powerful enough to be useful will contain
unprovable axioms. So the question, "Which [axiom or theorem] in
mathematics can't be proven or shown false that is the basis for all
other math?" is simply an utterly unanswerable question, given a
powerful enough system. Goedel proved it years ago. What *can* be said
is that "some axioms are unprovable, which doesn't mean they're false
or true."

Mathematics itself is today in a state alongside physics and most
natural science, of great uncertainty about the "Great Unknowables",
therefore, while depending on mathematical fundamentals will be
remarkably and consistently useful (can't compute a weight and balance
and then observe performance, or watch your climb rate go down as
altitude goes up, without noticing that), you just never know if your
system will stand up to new stuff.

That's the same as saying that you'll never know anything. About anything.
Your musings about science today being in a state of great unknowing ignores
most of recent scientific history. (When *everything* was unknown.)

Kind of like religion, that way, which works for most people. Until it
doesn't. Except for mine, of course. :-)

Nothing like religion at all. You haven't made any case for that statement.

le moo