From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!qt.cs.utexas.edu!cs.utexas.edu!news Sun Dec  1 13:05:40 EST 1991
Article 1653 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca sci.philosophy.tech:1165 comp.ai.philosophy:1653
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!qt.cs.utexas.edu!cs.utexas.edu!news
>From: turpin@cs.utexas.edu (Russell Turpin)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Infinite is not the same as unbounded  (was: Zeleny)
Followup-To: sci.philosophy.tech
Date: 27 Nov 91 01:39:47 GMT
Organization: U Texas Dept of Computer Sciences, Austin TX
Lines: 31
Distribution: world,local
Message-ID: <kj5tr3INN1bc@cs.utexas.edu>
References: <5691@skye.ed.ac.uk> <1991Nov25.183929.2155@arizona.edu>

-----
In article <1991Nov25.183929.2155@arizona.edu> bill@NSMA.AriZonA.EdU (Bill Skaggs) writes:
>> Ok, I'll bite. What is the empirical evidence that my use of the name
>>"Zeleny" involves an infinite recursion?

In article <15252@castle.ed.ac.uk> cam@castle.ed.ac.uk (Chris Malcolm) writes:
> Ok. This is now stage 2 of the recursion. Keep posting on this thread
> until the horrible truth dawns :-)

Given the ambiguous smiley, I don't know whether Mr Malcolm
thinks his answer is legitimate and cute, or just cute.
Regardless of its cuteness, it is not legitimate. 

The recursion he describes will undoubtedly end in a finite 
number of steps before a googol years have passed.  Indeed,
I suspect we can safely describe a number beyond which no
human recursion will go, assuming each step takes some 
minimum time.

Abstract machines are not so limited.  A pushdown automata may
have to recurse to an arbitrary depth to recognize ever longer
instances of its language.  Its recursive depth is unbounded,
though finite for any particular input. 

Zeleny's argument requires not a very high upper bound, nor
evey a recursion that might require arbitrary depth depending
on the inputs in question.  Rather, it requires an actualized
infinity that occurs in some finite time.  This stretches my
credulity, but then, I am not a Platonist.

Russell


