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From: sinkkone@klaava.Helsinki.FI (Janne Sinkkonen)
Newsgroups: comp.ai.philosophy
Subject: Re: Continuous vs discrete (Zenon)
Message-ID: <SINKKONE.91Apr21224814@klaava.Helsinki.FI>
Date: 21 Apr 91 20:48:14 GMT
References: <384@molene.enst-bretagne.fr>
Sender: news@klaava.Helsinki.FI (Uutis Ankka)
Organization: University of Helsinki (Finland)
Lines: 70
In-Reply-To: beugnard@molene.enst-bretagne.fr's message of 19 Apr 91 14: 43:48 GMT
Originator: sinkkone@klaava

In article <384@molene.enst-bretagne.fr> beugnard@molene.enst-bretagne.fr (Antoine Beugnard and Didier Guy) write:

[...]  
> 4 - "a limit is eventually reached" (Achilles never reaches the
>     turtle until he does)

And 5 - saying "Achilles never reaches the turtle" makes sense only
        under some models, if you want to use all the words under the
	model with the same meanings they have in our everyday life.
        Within your model this is not possible.

>   Well, it is correct, because when you calculate limits, you obtain
>   that Achilles *could* reach the turtle at time t = N / (Va-Vt),
>   and at position ... which are the results obtained by more
>   classical models. To decide that this model is partial
>   (truncated), you have to assume that time and space are not
>   limited and then you can complete your modeling. But you have to
>   be *external* to your model. From the inside, your model is
>   definitivelly, for ever, correct, and Achilles cannot reach the
>   Turtle.

You could model every phenomenon in the nature by tranforming the time
axis somehow and by reformulating all the laws. As an example, let's
set n=-t, and say "we will never die".  This model is not even partial
(truncated). Even better, let's set n=t0 for odd values of n, and n=t1
for even values. This is a little truncated model, but calculation is
never terminating, as you would say (it is defined for all values of
n).

The problem is that "ever" and "never" are still external (in the same
sense as you say). You should do _the_same_transformation_ for these
two words, and to all others, as you do to the time axis. But then,
"inside" the model, _everything_ is as here outside.  This should be
no surprising, if the model is correct.

Thus, for a correct model, there is no such thing as
inside-model-world being different from the outside world. If there
was, then the model would be incorrect, or incomplete. 

Your model is incomplete, because inside it there does not exist all
the outside things: some timepoints are missed. As a result, some
concepts we use in this world are referring to something
nonexistential if translated inside to your model.

"Never" and "ever" belong to these words.

So, inside the Zenon model, it makes no sense saying:
"Achilles never reaches the turtle".

You could define a new word inside your model world, which means "not
for any value of n". But taking up all the context (remember that your
thoughts are also running together along Achilles and the turtle),
what it really means to "them" is by no means our "never".  At the
final gates of singularity, the model world is just the same as ours,
and then suddenly, it will be undefined. There is no eternity.

After these considerations, it should be clear why Zenon model is not
as good as our conventional. It is not false, but it is incomplete.
Incompleteness does not become apparent when compared to a
hypothetical real world, but when compared to our conventional
model.

>   Are you so troubled thinking time could be discrete?

Still repeating, I'm not. But this has nothing to do with Zenon.  I
think continuum is just a convenient mathematical abstraction, a nice
tool to work with. It is a form of infinity, and in the world there
is no infinities. (a subjective belief)

Janne