Date: Thu, 15 May 1997 08:51:37 +0800 (CST)
From: Liano Sharon <lsharon-AT-ms2.hinet.net>
Subject: Re: Liano's paradoxies




On Wed, 14 May 1997, John Morss wrote:

> thankyou Liano, I think this is really helpful: some comments:

	Glad they were usefull.

 
> (Liano:)
> 
> >there is an important sense in which Achilles &Tortoise is in fact not a
> >paradox in the
> >same way that the Liar is a paradox.
> 
> sure, surely the A & T problem would be identical to the Achilles problem,
> or Tortoise problem, 

	I'm not sure I understand how the whole of the problem (A&T) is 
identical to the problem of either of the participants taken separately.  
This may make sense, but I'm not sure.  Can you elaborate?


> its a problem about how it is possible to talk about
> movement per se (not about how to talk specifically about relative
> movement/speed)?

	Right, the problem comes from how we look at movement itself and not 
from how we look at the movement of two things relative to each other.  
Or put another way, the problem comes from how we look at the movement of 
any object in relation to its frame of reference, and not from how we 
look at the movement of an object in relation to another object in the 
same frame of reference.


> (does Deleuze's term 'speed' avoid or solve these issues? ok, I know theres
> relavant stuff on Lewis Carroll in Diff and Rep.)
> A&T is also, if one wishes it to be, a pedagogical demonstration of the
> deceptiveness of our senses versus our intellect,

	Exactly.  This also demonstrates our over reliance on artificial 
moodes of reasoning.  Achilles and the Tortoise was a paradox for so long 
only because those who saw it as such refused to reason the way the 
universe reasons and instead insisten on reasoning according to some 
arbitrary set of formalized rules.  Then another equally arbitrary set of 
formalized rules came along (calculus) and suddenly if you reasoned this 
way the paradox dissapeard.  But it should be emphasized that the rules 
and axioms of modern mathematics are no less arbitrary and no less prone 
to contradiction then were the rules of the system of reasoning that led 
A&T to be seen as a paradox.  (I am calling A&T a paradox here purely 
becasue that is the convention, but I want to point out that under the 
distinction I make between paradox and contradiction, A&T has always been 
a contradiction in the drawing rooms and closely argued papers of those 
who considered it a problem, and was only manifested as a true paradox on 
the race track where no one worried about it, and instead just ran).


> A appears to overtake the
> tortoise rather easily (unless some1 shouts "heel!") but of course it can
> be 'shown' (sic) that he can't have done... he must, perhaps, already have
> been in front and thus our memory is decieving us, etc etc. Still not a
> paradox which surely involves a clash of two tokens of the same type/level
> etc, a conflict between 2 things that should converge. The sort of thing
> that causes computers to self-destruct on Star Trek., eg,  [as Liano points
> out,]
> "_This_ sentence is not true" or
> >"I'm lying _now_".

	Exactly, these computers find that in the instant of these 
statments, they cannot realize paradox, but must fight against a 
contradiction in which they themselves occupy both sides, so they fight a 
three way battle:  Computer Vs. Contradiction, where Contradiction = 
(computer vs. computer).  A three way battle in which theythemselves 
occupy all three positions, and this continues to bifurcate untill they 
confront themselves infinitely many times over.




> Another point... if we were (per impossibile???) to 'do away with'
> traditional (Aris) logic, ther'd then be no paradoxes...

	In an earlier post I made a distinction between a paradox and a 
contradiction, if you look at that distinction carefuly, I think you'll 
see why I think that the move away from traditional logic could result 
int the absence of contradictions, but not in the absence of paradoxes.  
To elaborate a little, wile it is logic which makes both contradictions 
and paradoxes seem wierd, the essence of a contradiction is preciesly 
this wierdness, while the essence of a paradox is the exploration of the 
universe as it is under the assumption that any group of things can in fact 
be co-existant.  That is, paradox accepts as possible and even 
acctual what contradiction rejects as wierd and impossible, but paradox 
is not defined in terms of contradiction, rather, contradiction is an 
archical reaction to pparadox.  Thus, 
if we give up traditional logic, contradictions may well dissapear, but 
paradoxes will remain, though they will ceasse being wierd.


	What do you think?


Your Friend,

	Liano