Thanks, I see your point.

What I see different from your conclusion
is that Frege's universe, didn't define itself
some well-founded inductive set (omega)
as a constant in the language.

Frege's theory didn't have trans-finites.
It doesn't have defined some "well-founded infinity",
but only quantifies over infinite elements
as for whatever results(s) so follow.

Comprehension, i.e., quantification,
over Frege's inductive elements,
is defined, i.e. added to ZF,
not named for a structure in ZF,
with adding a constant to the language:
omega the inductive set.

Frege's omega would be Frege's Russell set, found wrong,
Zermelo's omega was Frege's Russell set, claimed not wrong.

So, why can ZF just define away the contradiction?

Restriction of comprehension contradicts
what otherwise the axioms establish
expansion of comprehension.

Then, about that "contradiction doesn't exist",
is: in an altogether consistent theory.

(For example in a Comenius language where
the Liar/Russell/... simply establish a prototype
of a fallacy in the language, to reject.)

This idea of a fall gravity is that instead of
each massy body (i.e., frames on down to
particles) perpetually working
to draw together in the Newtonian
or stake the curvature in the Einsteinian,
that instead, there's a universal field of the gravific,
matter and its associated inertia occupying it.

This was considered by Fatio/LeSage as a
push gravity, contra Newtonian's pull gravity,
where here instead it's a fall gravity as there's
no notion that each massy body is a constantly
working system with influence over each other
throughout the universe.

(Gravity is well known to be proportional to
inverse square, which though attenuating is
still non-zero everywhere for each pair-wise
combination of frames, eg particles.)

Then, the idea of a two-body system is
that instead of a pair of strings (wires)
each pulling the other, that about them
both is the entire field of the universe,
that the inertia of the objects is that
they are at rest, not that they work,
that the line between them only happens
to be what it is the center of a potential,
and that the maximum value of the force
vector in the gravitic field, is the maximum
value of the potential vector in the gravific
field.

Then, this isn't like "ultramundane corpuscles"
of Fatio/LeSage, though that's descriptive,
instead that the objects happen to fall together,
instead of that they pull each other or are pushed
both.

I.e. the classical system is actually defined
by this super-classical regime.

Cf. Allais effect.