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Message from discussion The empty string as a code [was: InvalidInput Decider 2012-05-02]
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Peter Olcott  
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 More options May 17 2012, 6:18 am
Newsgroups: comp.theory, sci.logic
From: Peter Olcott <OCR4Screen>
Date: Thu, 17 May 2012 05:18:57 -0500
Local: Thurs, May 17 2012 6:18 am
Subject: Re: The empty string as a code [was: InvalidInput Decider 2012-05-02]
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On 5/17/2012 12:07 AM, Bryan wrote:

> Peter Olcott wrote:
>> Bryan wrote:
>>> Peter Olcott wrote:
>>>> I am not saying that it could not mean something, yet attaching any
>>>> meaning to it would form an inaccurate mathematical mapping between the
>>>> specified semantic meanings.
>>> Whether that's meaningful enough to qualify as wrong is debatable, but
>>> it sure ain't right. Peter, check your four theory books. Notations
>> I am speaking from a mathematics of semantics point of view and thus not
>> bound by arbitrary prior conventions within the Theory of Computation.
> That pretty well settles whether it was meaningful enough to be wrong.
> Peter, in science and math it's actually better to say something
> precisely wrong that to spew that kind of mess. There's a phrase for
> it: "not even wrong".

Now I have a better way to express this.
Within the context of a correct translation from one symbolically
specified set of semantic meanings into another symbolic representation
that is required to be semantically identical to the first set of
semantic meanings, taking the the contents of the empty string to mean
anything at all would form an incorrect translation because this would
change the specified meaning from the lack of any specified meaning into
something that is not the lack of any specified meaning.

It looks like the way that you guys have been using mathematical
mappings (which would be correct within the specified context of
mathematics) would allow the following question to have a correct answer:

What color is you age green or blue?
{Green is mapped to >= 50 years and blue is mapped to < 50 years}

 From the point of view of the mathematics of the meaning of words, the
above mapping would only be allowed if it is explicitly stated as a
hypothetical exception to the foundational rules, much like the case of
pretending that parallel lines meet, or that there really is a square
root of a negative number.

> Have you yet able to understand the table on on page 233 of Dexter
> Kozen's 1997 book, /Automata and Computability/? Previously you had
> thought he made some kind of error there, because you could not
> comprehend mapping from all strings onto all TM's. Have you grasped
> that much yet?
> http://groups.google.com/group/comp.theory/msg/2a6ce517b0e39ae8


 
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