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From: olcott <NoOne@NoWhere.com>
Date: Sat, 18 Jul 2020 10:14:17 -0500
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On 7/17/2020 11:09 PM, Keith Thompson wrote:
> olcott <NoOne@NoWhere.com> writes:
>> On 7/17/2020 8:01 PM, Keith Thompson wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>> On 7/17/2020 6:06 PM, Keith Thompson wrote:
>>> [SNIP]
>>>>> What Gödel proved, if I understand correctly, is that <HANDWAVE>if a
>>>>> theory is expressive enough that it can actually have self-contradictory
>>>>> expressions, then it *is* either incomplete or inconsistent</HANDWAVE>.
>>>>> (Perhaps someone else can restate that in more formal and/or accurate
>>>>> terms.)
>>>>
>>>> They would hate the way that you said it, yet you said the way that it
>>>> really is.
>>>
>>> By "they", I presume you mean the other participants in these
>>> discussions.  I'd be interested in their opinions of my summary.
>>>
>>> But I think you just admitted that any sufficiently expressive theory
>>> is either incomplete or inconsistent.  Is that really what you mean?
>>> (Yes or no, please.)
>>
>> It is mischaracterized as "incomplete" for the following reasons:
>>
>> A theory that is sufficiently expressive to form syntactically correct
>> yet semantically incorrect expressions meets the definition of
>> "incompleteness" only because it is insufficiently expressive to
>> detect and reject semantically incorrect expressions.
> 
> Non-answer ignored.
> 

You asked a yes or no question that had no correct yes or no answer.
You might as well have asked how many feet long is the color of my car.

>>>>> I have asked you a number of times whether it's the way the *word*
>>>>> "incomplete" is defined that you have a problem with, and whether using
>>>>> a different word for the concept that "there is some sentence φ such
>>>>> that (T ⊬ φ) and (T ⊬ ¬φ)".  Once you divorce that concept from the
>>>>> baggage of the English meaning of "incomplete", do you still have a
>>>>> problem with Gödel's proof?
>>>>>
>>>>> It's rather telling, I think, that you haven't answered that.
>>>>
>>>> If we called a formal system "super doodle" on the basis that it could
>>>> not prove that lies are true, I would be OK with that.
>>>>
>>>> If we call a formal system "incomplete" on the basis that it cannot
>>>> prove that lies are True, I have a big problem with that.
>>>
>>> PAY ATTENTION TO THE FOLLOWING.  I'VE WRITTEN IT SEVERAL TIMES AND
>>> YOU HAVE IGNORED IT.
>>>
>>> If I ask you a yes or no question, I request that you include
>>> the word "yes" or "no" in your answer, preferably at or near the
>>> beginning -- or explain why neither "yes" nor "no" would be an
>>> appropriate answer.  If you fail to do that, I will IGNORE your
>>> answer.  If you think that's unreasonable, feel free to explain why.
>>
>> My whole point of many hundreds of posts is that some yes or no
>> questions have no correct yes or no answer.
> 
> Some do.  Some don't.  So say so explicitly *in response to the
> yes or no question*.  If your response is neither yes, nor no,
> nor an explanation of *why* neither yes nor no is meaningful,
> I will ignore it.

I always give an explanation that you always ignore. We could say that 
all formal systems are incomplete on the basis that they can't make you 
a sandwich and wash the dishes afterwards. This would be a perversion of 
the use of the term "incomplete".

Although Q lacks the commutativity of addition and cannot prove or 
disprove formulas expressing the commutativity of addition the formula 
for the commutativity of addition: ∀x∀y (x + y = y + x) is not a WFF of 
Q, so Q is not incomplete even in the conventional sense.

It does superficially seem to make sense that when a formal system can 
neither prove nor disprove one of its own WFF that the formal system 
should be called incomplete, until we look at it deeper:




The set of sentences of the formal system that are satisfied by a 
specific model of this system are the true sentences of this model of 
this system.

The set of sentences of the formal system such that their negation is 
satisfied by a specific model of this system are the false sentences of 
this model of this system.

The set of expressions of the formal system such that neither the 
expression nor its negation are satisfied by a specific model of this 
system are the expressions that are not sentences of this model of this 
system.

> 
>> When you ask a man that has never been married:
>> Have you stopped beating your wife yet: (Yes or No)?
>> What is the correct answer?
> 
> English is often ambiguous.  You could say that the question is
> ill-formed because "your wife" doesn't refer to anything.  You could say
> that the answer is simply "yes" because there does not exist a time
> before which he beat his wife and after which he didn't.  In a formal
> system, that ambiguity could be avoided.

If we are being totally precise and treating the question as a 
mathematicaly formalism then we must reject the question as incorrect.

> 
>>> I actually had some things to say about what you wrote above,
>>> but I'll keep them to myself.
>>>
>>> For someone who posts so many words, you seem singularly uninterested
>>> in communicating.
> 


-- 
Copyright 2020 Pete Olcott