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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Analytic Expressions of language not linked to their semantic
 meaning are simply untrue
Date: Sat, 3 Aug 2024 22:07:08 -0400
Organization: i2pn2 (i2pn.org)
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On 8/3/24 7:46 PM, olcott wrote:
> On 8/3/2024 6:04 PM, Richard Damon wrote:
>> On 8/3/24 2:40 PM, olcott wrote:
>>> On 8/3/2024 12:53 PM, Richard Damon wrote:
>>>> On 8/3/24 12:24 PM, olcott wrote:
>>>>> On 8/3/2024 11:06 AM, Richard Damon wrote:
>>>>>> On 8/3/24 9:44 AM, olcott wrote:
>>>>>>> On 8/3/2024 4:50 AM, Mikko wrote:
>>>>>>>> On 2024-08-02 12:19:31 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 8/2/2024 1:43 AM, Mikko wrote:
>>>>>>>>>> On 2024-07-31 14:46:17 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 7/31/2024 3:03 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-07-30 13:40:55 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 7/30/2024 2:33 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-07-29 00:44:41 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The truth about every expression of language that can be 
>>>>>>>>>>>>>>> known
>>>>>>>>>>>>>>> to be true on the basis of its meaning expressed in 
>>>>>>>>>>>>>>> language is
>>>>>>>>>>>>>>> that a lack of connection simply means untrue.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Does that really mean something? If the significance of 
>>>>>>>>>>>>>> the lack of
>>>>>>>>>>>>>> connection is restricted to sentences where the connection 
>>>>>>>>>>>>>> exists
>>>>>>>>>>>>>> then it seems that you are talking about nothing.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://plato.stanford.edu/Entries/analytic-synthetic/
>>>>>>>>>>>>> I had to redefine the analytic side of the analytic/synthetic
>>>>>>>>>>>>> distinction because Quine convinced most everyone that this
>>>>>>>>>>>>> distinction does not exist.
>>>>>>>>>>>>
>>>>>>>>>>>> You cannot redefine side wihout redefining the other side 
>>>>>>>>>>>> and the
>>>>>>>>>>>> distinction itself. Is your redefinition equivalent to the one
>>>>>>>>>>>> at https://plato.stanford.edu/Entries/analytic-synthetic/ or 
>>>>>>>>>>>> did
>>>>>>>>>>>> you find out that that distincition is not the one that exists?
>>>>>>>>>>>
>>>>>>>>>>> Quine got totally confused by synonymity. He never understood
>>>>>>>>>>> that the term {Bachelor} was defined in terms of
>>>>>>>>>>> (~Married + Adult + Male).
>>>>>>>>>>
>>>>>>>>>> It is not a good idea to lie about other people.
>>>>>>>>>>
>>>>>>>>>> When reqding Quine, you should ask yourself why your presentation
>>>>>>>>>> is much less convincing than Quine's.
>>>>>>>>>
>>>>>>>>> Try and show the details of how I am incorrect.
>>>>>>>>
>>>>>>>> What you said (quoted above) about Quine is insulting and 
>>>>>>>> unjustified,
>>>>>>>> which alone is wrong.
>>>>>>>>
>>>>>>>
>>>>>>> The bottom line here is that every objection that he could
>>>>>>> have possibly made is addressed by this augmentation to
>>>>>>> the definition of {analytic truth}
>>>>>>>
>>>>>>> *Original definition* of {Analytic truth}
>>>>>>> Every expression of (formal or natural language) that is
>>>>>>> true on the basis of its meaning...
>>>>>>>
>>>>>>> *Is augmented by this*
>>>>>>> within a system of reasoning is only true when this
>>>>>>> expression is linked by truth preserving operations to
>>>>>>> its meaning within this system using this language.
>>>>>>>
>>>>>>> The superset of all of these systems that contains all
>>>>>>> analytic truth is called {the accurate model of the actual world}.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> And so you agree that Godel's G is True in PA.
>>>>>>
>>>>>
>>>>> It seems that you are the only one that believes that
>>>>> there are any sequence of truth preserving operations
>>>>> from G to the axioms of PA showing that G is true in PA.
>>>>>
>>>>
>>>> You are sorely mistaken in that beleif, but that error is caused by 
>>>> your ignorance of the topic.
>>>>
>>>> Anyone who understands Godel's proof would understand that fact.
>>>>
>>>> Note, you have the sentence backwards, the sequence is from the 
>>>> axioms to G, not G to the axioms.
>>>>
>>>> That just shows you don't understand how to do logical proofs.
>>>>
>>>> We know what we can demonstrate by a sequence from the axioms to the 
>>>> statement.
>>>>
>>>> We can form an actual proof for each individual number, but just 
>>>> cranking the Relationship (which will always have a finite number of 
>>>> steps) showing that this number does not satisfy the relationship.
>>>>
>>>> By just chaining the infinite set of these proofs for every number, 
>>>> we get that infinite chain of steps that establish G as true.
>>>
>>>
>>> Ah I see now.
>>> There is not a proof with an infinite sequence of steps
>>> that proves G in PA as you claimed. Instead an infinite
>>> set of proofs fails to prove G in PA.
>>
>> There is no such thing as a proof with an infinite number of steps.
>>
>> That is like talking about a triangle with 5 sides.
>>
>>
>> The infinite sequence of steps shows that G is true, as it shows that 
>> no number exists that statisfies the given PRR, which is exactly what 
>> G claims.
>>
> 
> That is not a sequence of steps in PA
> It is an infinite set of finite sequences of steps in PA.

which can be placed end to end to form a single sequence.

> 
>> Your misuse of the word "prove" just shows your utter ignorance of 
>> what you are talking about.
>>
> 
> That was my mistake.
> 
>> The infinite set of proofs DOES estabilish that G is true, as G is a 
>> statment that claims that no number satisfied that relationship. 
>> Having a proof for every possible that it doesn't satisfiy that 
>> relationship, shows that G is in fact true, as no number can exist 
>> that falsifies G.
>>
> 
> Yet PA is incapable of evaluating this.

Of course it is capable.

> I don't think that PA can even represent more than
> one proof at a time, so it is no sequence of steps in PA.

Why do you say that?

Do you have a source of that?

Note, PA could be the field of Peano Arithmatic.

> 
>>>
>>> Yet that would be back to the simple version of G that
>>> merely claims to be unprovable in PA. Not some other
>>> different highly abstract relationship that you had
>>> been claiming.
>>
>> There is no such G, except in your imagination.
>>
> 
> *Gödel stated that this was his intention*
> ...We are therefore confronted with a proposition which asserts
> its own unprovability. 15 ... (Gödel 1931:40-41)
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