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From: ags@pucc-h (Dave Seaman)
Newsgroups: net.puzzle
Subject: Re:  New Puzzle (Clarification by Author)
Message-ID: <2679@pucc-h>
Date: Fri, 28-Feb-86 13:51:13 EST
Article-I.D.: pucc-h.2679
Posted: Fri Feb 28 13:51:13 1986
Date-Received: Sat, 1-Mar-86 16:34:04 EST
References: <478@watdragon.UUCP>
Reply-To: ags@pucc-h.UUCP (Dave Seaman)
Organization: Purdue University Computing Center
Lines: 22

In article <478@watdragon.UUCP> gawilson@watdragon.UUCP (Graham Wilson) writes:
>With respect to the puzzle I recently submitted concerning the
>Sentence-producing machine, there is something I wish to clarify:
>
>The comment that the machine is complete if, given time, it could
>produce all true sentences should have been the machine is complete
>if there does not exist a true sentence which the machine could not
>produce.  The original wording presents a problem if the number of
>true sentences is uncountably infinite (there is no problem if the
># is countably infinite).  

There is no chance that the number of true sentences can be uncountable,
since there are are only countably many sentences, regardless of truth
value.  There are only finitely many sentences of length N, for each N.

The number of sentences which can be produced by the machine in any
given time is finite.  If there are infinitely many true sentences, the 
best you can say is that any given true sentence is eventually produced 
by the machine.  There is never a time when all true sentences have
been produced.
-- 
Dave Seaman	  					pur-ee!pucc-h!ags