ONT All Liar, No Paradox -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ALNP. Discussion Note 1
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
JA = Jon Awbrey
PD = Philip Dutton
Re: ALNP 1. http://stderr.org/pipermail/inquiry/2004-March/001297.html
In: ALNP. http://stderr.org/pipermail/inquiry/2004-March/thread.html#1297
Cf: ALNP. http://forum.wolframscience.com/showthread.php?s=&threadid=2667
JA: According to my understanding of it,
the so-called Liar Paradox is just the
most simple-minded of fallacies, involving
nothing more mysterious than the acceptance
of a false assumption, from which anybody can
prove anything at all.
PD: Let us pretend again that the universe has NKS rudiments.
Let us assume that the human thinking within the universe
is also a product of rudimentary NKS (simple programs,
algorithmic, etc.)
I think I've heard this one before --
| If we pretend that a tail is a leg,
| then how many legs does a dog have?
As good as I am at pretending, this would be a difficult pretense,
even for me. The way I pretend to understand it, the universe of
percourse that we drum up when we talk of "algorithmic rudiments",
and the whole repertoire of flim-flam paradigm-a-doodles that go
along with it, is just the space of recursive partial functions,
and last I counted there were only a countable number of these.
So the "universe at large" (UAL), unless it turns out to be
a "very large but still finite automaton" (VLBSFA), is just
sure to have all sorts of non-algorithmic happenings in it.
But even Aristotle already grasped the circumstance that
not all happenings in the world of phenomena fall within
the purview of science, but only the happenings that are,
as we say, "goings-on", in the sense of having a general
distribution throughout the experience of a community of
inquiry, in particular, persisting without limit in time.
Every method has a limit, indeed, the limit that makes it a method.
The more that one peers at the respective boundaries and interiors,
the more it begins to appear that the same limitation that gives a
method to science could very well be the same limitation to finite
means that stakes out the horizon of the computable.
To make a long story short, there is a sense of pretending that I can
entertain following directions with here, the sense in which a bit of
play-acting on some formal stage or other provides us with a model of
what goes on in the world outside the stage doors. But that requires
intelligent interpretation, not to mention cognizing the abbreviation,
the bias, the compression, and the distortion that is part and parcel
to the relationship between a reality and its finitary representation.
Jon Awbrey
PD: Well apparently, the rudiments allowed the universe
to "step" to this new universe configuration in which
the above assumption, which was false, was accepted.
PD: The act of accepting a false assumption
is apparently allowed by the algorithmic
rudiments.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o