Re: D1. Summary: Separate computer science ontology from philosophical ontology
John,
you are right in that it would be practically impossible to find the right
book out of the library of Babel, but the point was to show that it is not
impossible. another way to formulate it: if a theory exists now, then it
exists also in the library of Babel. An analogy: if x is computable, then it
is Turing machine computable.
Note also that the book would exists in Aristotle's language. Now, I bet it
wouldn't take too long for Aristotle to understand it: he could understand
it, even if he would no accept it as true. It cannot be a matter of some
mathematics that was not invented in Aristotle's times. I think that
everything, every mathematical and physical theory, can be explained in very
simple terms. And that is a real challenge of knowledge representation:
there are so many theories, that bunching them up and explaining them in
simple terms has a value in itself.
The only guideline I can give in reaching the as perfect and as simple as
possible ontology, is to use the axiomatic method and natural language, but
without any rules of inference, because it is quite impossible to have rules
of inference on natural language, don't you think? In any case, the task is
the most interesting task imaginable, that is, if one gets any kicks out of
rehearsing logical analysis.
Avril
Lainaus "John F. Sowa" <sowa@bestweb.net>:
> Avril,
>
> As I've said many times, I believe that a large part of ontology
> is empirical, and there is no way to have a completed ontology
> until we have a complete science -- and we are very far from
> "the end of science".
>
> But I have never denied that it might be possible to have a
> completed science and ontology at some point in the indefinite
> future. And I won't deny that at least a significant part of
> such an ideal science and ontology might be found somewhere
> in your extremely large, but finite list of books:
>
> AS> Take e.g. all 500-page books: all the 500-page long
> > combinations of unicode symbols. One of these books must be
> > a pretty good candidate for the PPO, since the set of these
> > book contains about all that can be written.
>
> A really good ontology with all the justifications and proofs would
> probably require many more than 500 pages. However, I would agree
> that a good summary of the top levels of the world's best ontology
> could probably be written in about 500 pages. Unfortunately, there
> are several problems with that idea:
>
> 1. Enumerating all possible Unicode character strings of 500 pages
> in length would take far longer than the age of the universe
> to generate and perform the most rudimentary gibberish-removing
> exercises. (See "The Library of Babel" by Borges for some of
> the issues.)
>
> 2. Even for strings of characters that are not gibberish, there is
> no guarantee that they would be written in any language humans
> today could read. There are over 6,000 existing languages today,
> and many more thousands or perhaps millions of languages that had
> been spoken on earth and untold numbers of conceivable languages
> that might be spoken in the future or in some far away galaxy.
> The likelihood that anyone on earth today could read a book
> that was generated is extremely small.
>
> 3. Even if some excellent ontology happened to turn up very early
> in the enumeration in a recognizable language, there would be no
> way to determine whether it was indeed the best of all possible
> ontologies -- especially since the justification would probably
> take much, much more than 500 pages.
>
> 4. Even if, by some rarest of rare possibilities, there was a solid
> proof that the ontology was the best possible and it could be
> included in that 500 pages, that proof might depend on some
> extremely advanced mathematics and science that would be far
> beyond the capabilities of our present scientists to understand.
>
> For example, suppose somebody went back in a time machine and gave
> Aristotle a copy of Penrose's book _The Road to Reality_, which is
> a good summary of today's physics (but in more than a thousand pages).
> Since nobody in ancient Greece could read English, nobody would know
> what it said. Even if they could decipher it, that book is a very
> terse summary that is hard to read even by college graduates today
> who have studied math & physics. Furthermore, that book does not
> specify how to carry out all the experiments with equipment that
> would be inconceivable in ancient Greece.
>
> When you multiply all the extremely small probabilities above,
> the implication is that there is no way to avoid the hard work
> of doing the dirty work in the laboratories.
>
> John
>
>