For example, "truth" is defined in formal logic with respect to, again, formal models with an infinite
number of formal symbols in them. It is not defined with respect
to some vague "correspondence" with external reality.

Actually, science is just about such correspondences with external reality.

I haven't argued that logic alone is a substitute for science, measurement, experimentation, refutation, correction, adjustment, model-building

All I was saying is that the semantics that define the meaning with respect to each
other of symbols and symbol-relationships is formal and, within each given
well-formed framework, inarguable.

whereas the semantics of the mapping of formal models to their "supposed" subject is
not, itself, formal (yet anyway), and hence is suspect as to whether we understand it or
get it right all the time. With science, all we have is:

"this formal symbol system (theory) A
seems to correspond better to our current observations than any competing
formal symbol system (theory) B (that we've conceived of so far), so we'll
consider A (as a whole) to be TRUE i.e.
"the best observation-corresponding theory" (for now.)

This scientific process works pretty well
but is somehow loosy-goosy and unsatisfying. Do theories which replace
other older, now discredited theories, keep getting better and better? Probably yes.
But what is the limit of that? Is there one? Or a limit in each domain about which
we theorize? But hold on, most of the scientific revolutions tell us that we had a nice
theory, but were theorizing about a badly-scoped, badly conceptualized idea of what
the "domain" was. A better theory is usually a better set of formal, interacting concepts
which map to a slightly (or greatly) differently defined and scoped external domain than the
last theory mapped to. None of this is very straightforward at all.

For example, would you go out on a limb and say that Einstein's theories are
the "best" (and only "true") way of modelling the aspects of physics he was concerned
with? If so, would you be equally confident that his theories cover "essentially
all the important issues" in that domain? Or might someone else, someday, re-conceptualize
a similar but not 100% overlapping domain, and create an even more explanatory
theory of fundamental physics than he came up with? Can we ever say for sure,
until that either happens or doesn't?

You can interpret the history of science in two ways: either we were just really
bad at it back then (in Newton's day) and wouldn't make those kind of mistakes
in our theory formation today, or you can say, no we're about as good at it as always,
maybe a little more refined in method but not much, and we'll continue to get
fundamental scientific revolutions even in areas we see as sacrosanct theory today.
And the new theory will not so much "disprove" the existing one (as Einstein
didn't really "disprove" Newton) but rather will be just relegating the old theory
to be an approximate description of a partially occluded view of reality.
And then one day, will the same thing happen again to that new theory? Is
there an endpoint? What would the definition of that endpoint be?


As far as I know, there is no good formulation of
a formal connection between a formal system and """"""reality""""" <-unbalanced quotes, the secret
cause of asymmetry in the universe. How's that for a
"quining" paragraph?

I don't understand your "secret cause of asymmetry in the universe" point. We understand some things about symmetry breaking in particle physics theories, via gauge theories and the like. If you want more than this, you'll have to expand on what you mean here.
It is a Koan (kind of). A self-referential, absurd example of a notion that an imbalance in a formal symbol system (the words I'm using, and the quotes) could possibly be the cause of
asymmetry in the physical universe. It is an attempt to highlight the problems we get into
when we confuse the properties of a model with the properties of the thing we are
TRYING to model with it.

"Quining" is the use of self-reference in sentences, often to achieve paradox. It is
a childish ploy. e.g. of a Quine:

"Is not a sentence" is not a sentence.

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