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You know, the field, of, formal methods, and particularly
here, "the terminal in the interminable", all the issues
involved and resolved in the supposition and dispatch and
resolution and what can't be logical paradox, it's of interest.
You guys' love spats though, it's more like, "get a room".
That the classical is sort of singular, and, there's
a sort of super-classical the multiplicity, has that
here, for models of computation and models of knowledge,
and certification of the results as it were, "proof", in
theory, has pretty much that if there's thrashing and flailing
it's not being done correctly, pretty much has that
you have to get above this stuff, if there's not something
_new_ in the post, it's _noise_, if there's not a proper
novel, derivative statement, it's not _signal_, _information_.
About information and free information in physics, and
models of computation, which work on information, that
their input and output is work and information, has that
actors and agents can use information and perspective,
to effect their own inputs, and besides the Aristotle's
entropy and Leibniz' entropy, and the source and/or sink
of destiny and these kinds of things, makes for the old
"Scylla and Charybdis" bit: "keep it in the middle".
Now it's established that ZFC includes a restriction of
comprehension, and that somebody like Mirimanoff introduced
what became the Axiom of Regularity, and it's an opinion
and a stipulation and there are other, there are the others,
that if you really want to know then it involves learning
about Mirimanoff's, or, your own, "extra-ordinary", "l'extraordinaire",
because otherwise trying to stretch the limits of theory
within the limits of the ordinary theory, results that
"the theories the theories the theories: meta-fragment theory",
either is or isn't a theory, and it's true.
It's true that some people don't know that ordinals and sets
are fundamentally different and though that they have ready
models of the initial that build infinite limits and completions
in terms of each other, that the theory of "the universe of
the logical objects", has that it's matters of perspective,
and perspicuity, for universals and particulars and these
kinds of things, and type theory and "inverting the diamond",
the universe of relations of type, it starts being easier
to have critical analysis always included instead of
picking a fixed course when neither will do.
Maybe it would help to introduce an "Aristotle's demon",
what he does is arbitrarily re-orders and disarrays and
sequence of syllogisms, so that of course only the relevant
result coherent, and what was in any way plainly dependent
on contradiction or not compounded the induction by all
matters of deduction, is not constructivists and results
not intuitionist.
Now, one might aver, "there's no Aristotle's demon and
there's no Maxwell's demon", yet, yet it's rather provable,
or not, one way or the other, and, anybody who makes and
stays the course between the rock and the hard place,
is highly dependent that they do and don't exist.
I.e., the idea is, "there's no Aristotle's demon and
there's no Maxwell's demon", but, anybody who thinks
about it sort of rather is their own Aristotle's angel
and Maxwell's angel.
Now, I've just kind of invented this idea of "Aristotle's
demon", but the idea is that the apparatus and mechanics
of robust theorem-proving depend on it not mattering
whether it exists, or not.
In these sorts cases, the "quasi-modal", is yet a mode,
just as classical theory is just a singularity,
so, it's called critical reasoning, and, often enough
it's the development of the dialectic to maintain
the development of a dialectic, that otherwise results
these sorts, ..., kook fights, that result poisoning the
well, tragedizing the commons, when here we have a
free theory where "Aristotle's demon can't destroy
comprehensive critical categorical closure".
https://en.wikipedia.org/wiki/Maxwell%27s_demonWhich the quasi-modal is not.
So, Aristotle's demon, or Aristotle's gremlin,
here is a concept that takes, for example, any
sorts plain fallacious rhetoric, on its own,
and results for example "must both be wrong".
Thus it is upon you to always be making work
for Aristotle's gremlin, for Maxwell's will do none.