July 19, 1996
One day, between a glass of champagne and a straight scotch, Gilles and I had a
discussion about truth and knowledge. I can't remember how it started; too
much alcohol and cigarettes, but likely it came from some sarcastic comments
from Gilles (I'm wondering why I added 'sarcastic' before 'comments from
Gilles'; I guess I like redundancies:)) about some
crazy/stupid/asshole/brainless people who believe they'll change the world by
forcing other people's minds to their own truth, or who believe they're right,
and (redundantly) that they have the truth. Ahum.... If you recognize
yourself in this description, please get out of this page quickly if you don't
want to have your beliefs ruined, and check out
http://moron.believer.com/~kill/them/all to see whether you're on the list. If
you're not sure, stay, be curious, and you're free to discuss the arguments as
much as you want....
Well, as I said, after 'moulte' (look it up in a French-English dictionary; I'm not in the mood today) glasses, we started chatting: What is truth? What I am going to explain (well, say I'm gonna try) is that truth is tighly linked to the language, and that the language is self-limited. Consequently, absolute truth does not exist after a certain level of "abstraction" and "complexity" (this level is indeed fairly simple). Today I only use intuitive notions to outline this conclusion. Next time I'll play with more powerful tools to go a little bit further.
Okay, let's try to show that the concept of truth is MUCH more complicated than most of the people may think. Of course, there are several ways to do it, more or less "effective", but I'm going to do it in an easy way for this time.
As far as I know, expressing anything needs a language. You can have a very poor language that expresses very simple notions, like the one you use with a microwave, which is nonetheless sufficient to correlate time and heat in an oven. The key point that I want to address can be stated as follows:
"Language" stands for any language that you may have heard of, e.g., French, English, Latin, Sanscrit, mathematics, or the language you use to program your VCR. The purpose of a language, which is nothing but a very formal set of sequences of symbols (characters), is to capture the "outside world". In other words, one maps the "words" of the language on "objects" and "concepts" (a chair, a bird, being hungry, love, peace, etc...). This mapping is called an interpretation, and we will say that the outside world is a "model" of the language.
Having a language and an interpretation that makes what you are interested in talking about (the outside world) a model of the language, you can start playing with the language and "deduce" facts from assumptions. This is called logic. Here starts the story of the mathematicians' dream of having a language from which one could derive all the theorems (i.e., the "true" facts). Pay attention here: We will call a "theorem" a sentence that can be derived (deduced) in your language. We will call a "truth" something that exists in your model, here the outside world. A first question:
The key question is:
...but do not take my statement as it! Discuss/refute/fight it, and I'll answer.
Olivier Coudert speaks French and English but, above all, UNIX. A mathematical artist, he concocts algorithms like Gerswin composed music, with so much passion that Silicon Valley lured him away from France to do as he so pleases. Most of the time he writes award-winning mathematical papers for esoteric conferences. And, when he is back down to earth he occasionally contributes to Swans.
Please, DO NOT steal, scavenge or repost this work without the expressed written authorization of Swans, which will seek permission from the author. This material is copyrighted © 1996, Olivier Coudert. All rights reserved.