[self-interest] On "Meta," with a trick question at the end.
Albertina Lourenci
lourenci at lsi.usp.br
Wed Jan 17 14:53:34 UTC 2001
Randy Smith wrote:
Hi Randy:
> Don't forget to look at the trick question at the end
> of this note. Meanwhile....
>
> > > > what is meta-programming? >
> Hey, how about the metaness of the following, which refers to
> itself and is therefore meta? "If this sentence is true, it is
> not meta, otherwise it is meta."
>
> Is it an empty trick or does it reveal a problem with the
> meta/nonmeta distinction?
>
Well I do not think that this construction is perfectly clear
however Douglas Hofstadter, deeply concerned with the
science of consciousness throws some light on this.
In the book Gódel, Escher and Bach: an eternal braid
Hofstadter gives examples where he illustrates the strange
loops in the work of Bach and Escher. It seems a conflict
happens between the finite and infinite and a strong sense
of paradox. Intuitively Hofstadter thought something
mathematical was involved here. And indeed in the
last century K Gödel uncovered a Strange Loop in the
mathematical systems that had origin in the translation
of an ancient paradox in philosophy in mathematical
terms. This is the so called paradox of the Cretan Epimenides
or the Paradox of the Liar. He made an imortal statement.
All Cretan are liars. A version of this statement is simply
I am lying or the The statement is false. This rudely violents
the dichotomy assumed about statements in false and true.
If you think it is true, immediately triggers the thinking
it is false. Once decided it is false, it triggers the
thinking it is true.
The Epimenides' s paradox is a Strange Loop like the
Print Gallery from the graphical artist Escher, where the
spectator looks at a picture that transforms itself into
a city that shelters the gallery where he is!
But what's the relationship with math?
This is what Gödel discovered. His idea was to use
the mathematical thinking to explore the mathematical
thinking by itself. This notion of making mathematics
introspective proved to be well successful and his richest
implication was Gödel's most famous discovery:
the theorem of incompleteness. What the theorem
states and what is proved are two different things.
This is discussed in the book. It can be summarized
as follows This statement about the number theory
does not find proof in the system of Mathematical
Principles. Hence provability is a weaker notion than
truth, in spite of the axiomatic system involved.
It is also a consequence that an infinite truth can
not be condensed in a finite theory.
Curiously this book was very important
for the unfolding of my ideas, and this statement
about provability
has always been my inner voice.And it never fails.
So it is the same problem with physics being scientific
and metaphysics not scientific.
Fortunately this gap has been being fulfilled by
postquantum physicists as well as philosophers
such as Popper and so on.
Best wishes
Albertina
>
> --Randy
--
.----------------------------------------------------------.
| Albertina Lourenci |
| PhD in Architecture and Urbanism |
| post-doctorate researcher |
| Laboratory of Integrated Systems University of Sao Paulo |
| Avenida Professor Luciano Gualberto, 158 Travessa 3 |
| CEP: 05508-900 |
| Sao Paulo Sao Paulo State Brazil |
| Voice: +55 011 818 5254 |
| Fax: +55 11 211 4574 |
.----------------------------------------------------------.
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