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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 19:04:05 -0400
Organization: i2pn2 (i2pn.org)
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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.

Your misuse of the word "prove" just shows your utter ignorance of what 
you are talking about.

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 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.

> 
> Do you understand that no one needs to have any
> understanding of the proof to refute it when they
> can show that its conclusion is incorrect?
> 

Doesn't work that way. Since your "proof" that it is wrong is based on 
your own assumptions, all you prove is that your assumptions are untrue.