There are all kinds of theories formal and informal.

Theory is often a logic, after philosophy.

Logic has inductive and deductive inference,
formally for proofs or as via derivation rules,
of statements in the language of the objects
of the theory.

This has causality about first principles and final cause.

There are properties of theories:
constancy (monotonicity)
consistency (contradictions can't be derived)
completeness (there are no derivations about the objects not in the theory)
concreteness (the theory is a model of reality).

"The" "Theory of Everything" has all these properties,
if it's to be believed that causality always holds.

Fundamental theory or foundations has the goal
of some least axiomatics as define a theory with
the most of consistency and completeness (and
usually constancy for monotone logics, and
concreteness for practical theories).

In mathematics for example, we might look to
set theory, type theory, number theory, and geometry.
(Together.) In physics examples include relativity
and quantum mechanics (or statistical mechanics)
along with a theory of gravity, these days about a
unified field theory about the physical interpretation
of objects (in a fundamental framework of numerical
resources in space and time).

Working theories, toy theories, ad hoc theories,
there's a continuum of theories then for some
usual idea that one suffices, then as for what
it wouldn't be accessible, but all efforts in
theory approach it.

Platonism includes the idea that numbers (or
the objects of mathematics) are real things.
This for example would be a continuum.

Instead of a multiple worlds hypothesis,
it is a theory that only one of the theories
is concrete. This doesn't necessarily imply
determinism, particularly where rational agency
exists, but it leaves all possibility in the realm
of theory (or the abstract).

Natural theory is an idea that any rational agency
could arrive at, more or less, this theory.

Theory and theism are closely related,
with usual monotone theories or monotheism.
(Or, not.)

Monism then is a usual idea that there is a theory
for everything, one Platonist's continuum of
numerical resources, a true theory or the
theory of truth.

Then here in physics there's symmetry and conservation
(or, violation as transition, state and change) as fundamental,
this idea of space contraction as things change is that as
things change it's always at rest here the (quasi-)Euclidean
space over a ray of time.

"The scintillation theory provides no means for
polarization effects and none are expected."

Well put.

Mathematics _owes_ physics more and better
mathematics of infinity and infinitesimals.
(Continuum theory.)

It's coming along with quasi-invariant measure
theory, Ramsey theory and etc. Also the super-classical
about the usual fluid and wave models of transport
and for example the Mach cone and models of
attenuation, dissipation, and dispersion besides
truncation is where the extremes, that result in
the means, that define physics are. (I.e., the
potential fields are super-classical and real.)
The trans-Planckian and other approaches to
the continuous nature of the space-time continuum
go a long way toward a holistic theory with
the classical as a result in the middle.

(... about the Planckian regime and the hidden sector.)

Quantum mechanics has a lot going on toward
normalization as not just de-re-normalization.

Page 133 (a few pages above):

"... concerns the possibility of using the notion of
asymptotic density, as used in number theory,
as a mathematical tool for discriminating sizes
of infinite sets of natural numbers. [...] According
to this notion the set of even numbers has density 1/2,
....".

Finite sets don't need asymptotic density,
to compare their sizes,
simply computing the count of elements of
each to the maximum of the range of each,
of their population counts as however "count"
is implemented.

I.e., according to parsimony, two finite sets
always have a finite union.