>There are now many different logics which allow for
>partial inconsistency, self-reference, etc.
Indeed, the new "market" is exploding. We have fuzzy logic which solves the
classic paradox by calling it a half truth, there is August Stern's Matrix Logic
which operates with four truth values: True, False, True and False, Neither True
Nor False. And there are myriads others. This is both exciting and at the same
time a little scary. With these new logics, logic takes the full step into the
maths. It becomes more and more problematic to speak of mathematical truths
since we at the same time have to specify which logic this truth is relative to.
In other words, the new logics may be the beginning of mathematical relativism.
The hope is, of course, that there turns out to be a finite number of
hyper-logics. If not, we will see a chaos of logics.
Logic has always been an integral part of human thinking. There has been
little room for hyper-logics. It will be very interesting to see if our culture
manages to make this kind of thinking intuitive.
Personally I believe this fragmentation of logic shows what philosophers have
known for a very, very long time: language is intrinsically wounded. It cannot
be complete and consistent at the same. This is basically what Godel discovered
as well. Maturana is only a biologist, yet he framed the only flaw of language
in a simple statement:
"There are always more linguistic relations than there are linguistic
descriptions in a given language."
This beautiful statement could easily be called sociology's version of the
Incompleteness theorem.
Onar.