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From: ins_ampm@jhunix.UUCP (Michael P McKenna)
Newsgroups: net.puzzle
Subject: Re: truth machine clarification**2
Message-ID: <2109@jhunix.UUCP>
Date: Wed, 5-Mar-86 18:41:16 EST
Article-I.D.: jhunix.2109
Posted: Wed Mar  5 18:41:16 1986
Date-Received: Sat, 8-Mar-86 02:52:03 EST
References: <423@watdragon.UUCP> <2664@pucc-h> <394@link.UUCP>
Reply-To: ins_ampm@jhunix.ARPA (Michael P McKenna)
Organization: Johns Hopkins Univ. Computing Ctr.
Lines: 27

In article <394@link.UUCP> msb@link.UUCP writes:
>> In article <423@watdragon.UUCP> gawilson@watdragon.UUCP (Graham Wilson) writes:
>> >Consider a machine which is used to create true sentences (for example,
>> >the sentence "A dog is a dog" is true).  If the machine is "complete",
>> >then it could, given time, produce the set of ALL true sentences.  If the
>> 		^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>> >machine is "consistent", then all the sentences that it produces will be
>> >true.
>> >
>> >Question:  Can such a machine exist (even in theory)?
>> 
>> The machine cannot produce the set of ALL true sentences unless that set
>> is finite.  I think you meant to say any given true sentence would eventually
>> be produced by the machine.
>> -- 
>> Dave Seaman	  					pur-ee!pucc-h!ags
>
>You can't even guarantee that any given true sentence would eventually be
>produced by the machine unless the set is finite.

You mean countable.  If the set is countable there exists a 1 to 1
correspondence with the set of positive integers.  Thus each true
statement can be associated with a unique integer.  We need only
specify that the machine produces the statements in this order to
guarantee that any true statement is eventually produced.

                                                        Dwight S. Wilson