organization levels

[Mitsuharu Hadeishi]

I would guess that such a technique (to describe logical levels of abstraction
formally, i.e., syntactically) would fail (except as metaphor) because
it is often the case that the abstracted level of a formal system is not
itself formally describable (at least not in a manner which is easily
defined).  That is, one would not be able in all cases to define the
set of relations on the "meta-" field in any kind of well-defined manner
(though such relations might well exist in the original system).  Mathematics
versus metamathematics, physics versus "metaphysics".  I.e., the "meta-"
fields are not describable from within the language of the fields themselves,
and this is often, I think, the case because the meta-fields are not
formally describable in a well-defined manner (at least not a manner which
is easily fathomable by human beings).  I am, of course, simply speaking
through my hat: this seems to me to be the case, but I have not come up
with an ironclad argument as yet.  I just put the idea out for consideration
by those who might be able to clarify the issue.

Mitsu