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From: ags@pucc-h (Dave Seaman)
Newsgroups: net.puzzle
Subject: Re: truth machine clarification**2
Message-ID: <2694@pucc-h>
Date: Wed, 12-Mar-86 10:14:50 EST
Article-I.D.: pucc-h.2694
Posted: Wed Mar 12 10:14:50 1986
Date-Received: Fri, 14-Mar-86 05:43:18 EST
References: <423@watdragon.UUCP> <2664@pucc-h> <394@link.UUCP> <2109@jhunix.UUCP> <11581@watnot.UUCP>
Reply-To: ags@pucc-h.UUCP (Dave Seaman)
Organization: Purdue University Computing Center
Lines: 28

In article <11581@watnot.UUCP> rmariani@watnot.UUCP (Rico Mariani) writes:
>It is possible for a machine to generate a countably infinite number
>of truths in a finite amount of time.  

True, if you allow the machine to run infinitely fast, but in computability
theory it is the finiteness or non-finiteness of the number of operations
that is significant.  References to "time" are merely a linguistic convenience
based on the assumption that the machine runs at a uniform finite rate.

>Dave Seaman made a comment about the number of true sentences over a finite
>alphabet being necessarily countable, this is true if you assume that all
>sentences are of finite length however this is not such a reasonable 
>assumption to make (we can't make statements about arbitrary real numbers
>unless we either allow an infinite alphabet or sentences of arbitrary
>length).

Very well, I will grant you BOTH an infinite (countable) alphabet and 
sentences of "arbitrary" (i.e. finite) length.  The number of sentences is 
still countable.  This does mean we cannot make statements about arbitrary
real numbers (only countably many numbers can be "named"), but that is not news.

Obviously one can speak of infinite sequences of characters, but I see no
justification for calling these "sentences."  A "sentence" is a sequence of
symbols which can be parsed according to the rules of some language.  Any
language which can be expressed in EBNF form has sentences of finite length
only.
-- 
Dave Seaman	  					pur-ee!pucc-h!ags