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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Fri, 16 Aug 2024 17:40:56 -0500
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On 8/16/2024 5:19 PM, Richard Damon wrote:
> On 8/16/24 6:16 PM, olcott wrote:
>> On 8/16/2024 5:03 PM, Richard Damon wrote:
>>> On 8/16/24 5:35 PM, olcott wrote:
>>>> On 8/16/2024 4:05 PM, Richard Damon wrote:
>>>>> On 8/16/24 4:39 PM, olcott wrote:
>>>>>> On 8/16/2024 2:42 PM, Richard Damon wrote:
>>>>>>> On 8/16/24 2:11 PM, olcott wrote:
>>>>>>>> On 8/16/2024 11:32 AM, Richard Damon wrote:
>>>>>>>>> On 8/16/24 7:02 AM, olcott wrote:
>>
>>>>>>>>>>
>>>>>>>>>> *This abolishes the notion of undecidability*
>>>>>>>>>> As with all math and logic we have expressions of language
>>>>>>>>>> that are true on the basis of their meaning expressed
>>>>>>>>>> in this same language. Unless expression x has a connection
>>>>>>>>>> (through a sequence of true preserving operations) in system
>>>>>>>>>> F to its semantic meanings expressed in language L of F
>>>>>>>>>> x is simply untrue in F.
>>>>>>>>>
>>>>>>>>> But you clearly don't understand the meaning of "undecidability"
>>>>>>>>
>>>>>>>> Not at all. I am doing the same sort thing that ZFC
>>>>>>>> did to conquer Russell's Paradox.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> If you want to do that, you need to start at the basics are 
>>>>>>> totally reformulate logic.
>>>>>>>
>>>>>>
>>>>>> ZFC didn't need to do that. All they had to do is
>>>>>> redefine the notion of a set so that it was no longer
>>>>>> incoherent.
>>>>>>
>>>>>
>>>>> I guess you haven't read the papers of Zermelo and Fraenkel. They 
>>>>> created a new definition of what a set was, and then showed what 
>>>>> that implies, since by changing the definitions, all the old work 
>>>>> of set theory has to be thrown out, and then we see what can be 
>>>>> established.
>>>>>
>>>>
>>>> None of this is changing any more rules. All
>>>> of these are the effects of the change of the
>>>> definition of a set.
>>>>
>>>
>>> No, they defined not only what WAS a set, but what you could do as 
>>> basic operations ON a set.
>>>
>>> Axiom of extensibility: the definition of sets being equal, that ZFC 
>>> is built on first-order logic.
>>
>>
>>>
>>> Axion of regularity/Foundation: This is the rule that a set can not 
>>> be a member of itself, and that we can count the members of a set.
>>>
>> This one is the key that conquered Russell's Paradox.
>> If anything else changed it changed on the basis of this change
>> or was not required to defeat RP.
> 
> but they couldn't just "add" it to set theory, they needed to define the 
> full set.
> 
> I think you problem is you just don't understand how formal logic works.
> 

I think at a higher level of abstraction.

All that they did is just like I said they redefined
what a set is. You provided a whole bunch of details of
how they redefined a set as a rebuttal to my statement
saying that all they did is redefine a set.

My redefinition of formal system does this exact same
sort of thing in the same way. I do change the term
{logical operation} to {truth preserving operation}.
Other than that the only thing that is changed is
the notion of {formal system}. I don't even change
this very much.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer