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Topic: Validating Natural Language Statements (and Mathematical Propositions)
Replies: 2   Last Post: Jan 10, 2014 10:21 AM

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 Ben Bacarisse Posts: 1,972 Registered: 7/4/07
Re: Validating Natural Language Statements (and Mathematical Propositions)
Posted: Jan 10, 2014 9:30 AM

Peter Olcott <OCR4Screen> writes:

> On 1/9/2014 7:35 PM, Ben Bacarisse wrote:
>> Peter Olcott <OCR4Screen> writes:
>>

>>> On 1/9/2014 4:57 PM, Ben Bacarisse wrote:
>>>> Peter Olcott <OCR4Screen> writes:
>>>>

>>>>> On 1/9/2014 11:05 AM, Ben Bacarisse wrote:
>>>>>> Peter Olcott <OCR4Screen> writes:
>>>>>>

>>>>>>> On 1/9/2014 10:35 AM, Ben Bacarisse wrote:
>>>>>>>> Peter Olcott <OCR4Screen> writes:
>>>>>>>> <snip>

>>>>>>>>> In logic a statement is a meaningful declarative sentence that is
>>>>>>>>> either true or false...
>>>>>>>>> a) It must be meaningful (it can not be gibberish).
>>>>>>>>> b) It must be declarative.
>>>>>>>>> c) It must have a Boolean value from the set of: {true, false}.
>>>>>>>>>
>>>>>>>>> It seems to me that every natural language statement or mathematical
>>>>>>>>> proposition must at least meet the above minimum standard to be
>>>>>>>>> considered (syntactically and semantically) correct.

>>>>>>>> Given some specified enumeration of TMs (I could specify exactly which
>>>>>>>> one, but that's tedious and doesn't alter much) the statement:
>>>>>>>>
>>>>>>>> "Turing machine number 246 always halts regardless of the initial
>>>>>>>> content of the tape"
>>>>>>>>
>>>>>>>> meets all three criteria, yes? Is there any such statement (i.e. the
>>>>>>>> same words but with 246 replaced by some other natural number) that does
>>>>>>>> not meet these three criteria?

>> <snip>
>>>>> I did not want to get into an endless debate based on your failure to
>>>>> comprehend that an identically worded sentence may meet or fail to
>>>>> meet the criterion measure for a correct statement/proposition
>>>>> depending upon which of two distinct frames-of-reference that this
>>>>> sentence is tested against.

>>>> is reasonable to ask if another statement can be so classified.

>>> I just answered it. In the case of the HP it depends on the
>>> frame-of-reference context
>>> that the sentence is being evaluated.

>> No, but you have now. Your previous remark was general, but if you
>> consider it to have been an answer, you are saying that it applies in
>> the case of my example. Anyway, we have an answer: "it depends on the
>> frame of reference".
>>
>> That's not true.

> Yes it is true.
>

>> It is true or false without any reference to anything
>> other than the meanings of the things in the question

> The meanings change depending upon who you ask.

No. The meanings of everything involved in the question is properly
specified. What is it that changes meaning? The enumeration that has
been written out formally? The definition of a Turing machine? My
example question has one and only one meaning.

And what has "who" got to do with it? Are you talking about asking
people halting questions? Of so you are not talking about the halting
problem.

>> -- the enumeration
>> used and the definition of a TM. Specifically (as you bring it up
>> later) there is no frame of reference where it has no correct answer or
>> where it is ill-defined.

> You still fail to comprehend this.

Here's an idea: tell me what it is that changes meaning so that the
answer is different or non-existent in some frames of reference. Just
start which what meaning changes. You don't even have to explain what
a frame of reference is -- I'll take it that such things matter in the
case of my example -- just say what changes meaning.

It can't be hard. The definition of a TM is only a few lines with words
like "set" and "tuple". The standard lexicographic ordering of tuples
that represent TMs is fussy to write down, but I don't think you'll find
anything there whose meaning is dependent on some frame of reference.
The definition is halting is also only a few lines. How does the
meaning of my example question end up with no correct answer in some
frames of reference?

<snip>
> Outside of the frame-of-reference of the potential halt decider the
> question has a correct Boolean answer.
> Inside the frame of reference of the potential halt decider neither
> true nor false is correct.

No. Tell me what meaning has changed. What alters so that there is no