Not everything is
cut and dried,
not everything is
black and white,
"not nothing is not everything": "is".
The complementary dual, is a higher level mental construct,
than the opposite.
The dialectic isn't for asymmetry, though it's applied that way,
it's for symmetry.
The difference between "versus" and "vis-a-vis",
is one has a loser and the other's not a game.
The inductive impasse, reflects that there are cases for induction
that never complete, but, in the continuous and in time, they do.
It's the continuous and the uniform in time, infinitely-divisible,
that's about the simplest prototype of a model of change, in
a model of state.
The, inductive impasse either way, is simply reflected in what
are points in a line, how they are drawn, and, points on a line,
and how they divide, what is the drawn-out and what is the divided,
making line-continuity first then besides signal-continuity,
for field-continuity.
The, "meeting in the middle", the "middle of nowhere",
is the center of the square of opposition and the dialectic,
in the complementary duals, about for example the point,
the local, the global, and the total.
The anaphora and cataphora, nouns, the synthetic and analytic, adjectives,
the continuous and discrete, complements, here what's generally put
first is the universals, that work out same as "void".
So, the context of the oscillating and the attenuative, for
the restitutive and dissipating, is that the oscillating radiates
while the attenuative has a floor, in a "default" or "ground" model.
There are others, where the tendencies and propensities reflects
actions or states. This is used to define the thermodynamic and
anything else which is open in physics.
The kinetic, and laws of motion, here is addressed with a dialectic,
about this, for example "Zeno's starter". This is about "what is the
impulse" or the singularity of beginnings, of change, which are
first modeled as perfect inelastic collisions, but physics is an open
system. So anyways this idea of derivative stopping is about powers
and inverse powers and their derivatives, and for a model of addition
formulae or index formulae, about an operator calculus of higher,
and, lower, orders of acceleration, with respect to displacement
and rest, with respect to time (singular). The idea is to work up
that the C^\infty functions who eventually in some order have
a derivative that's zero, that there's a family of functions whose
integrals eventually reflect a constant, these being symmetrical
in positive and negative powers, for "Newton's Zero-eth Laws".