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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Sat, 17 Aug 2024 12:46:57 -0400
Organization: i2pn2 (i2pn.org)
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On 8/17/24 12:35 PM, olcott wrote:
> On 8/17/2024 11:28 AM, Richard Damon wrote:
>> On 8/17/24 11:47 AM, olcott wrote:
>>> On 8/17/2024 10:33 AM, Richard Damon wrote:
>>>> On 8/17/24 11:12 AM, olcott wrote:
>>>>> On 8/17/2024 9:53 AM, Richard Damon wrote:
>>>>>> On 8/17/24 10:45 AM, olcott wrote:
>>>>>>> On 8/17/2024 9:40 AM, Richard Damon wrote:
>>>>>>>> On 8/17/24 12:05 AM, olcott wrote:
>>>>>>>>> On 8/16/2024 5:57 PM, Richard Damon wrote:
>>>>>>>>>> On 8/16/24 6:40 PM, olcott wrote:
>>>>>>>>>>> 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.
>>>>>>>>>>
>>>>>>>>>> No, you don't, unless you mean by that not bothering to make 
>>>>>>>>>> sure the details work.
>>>>>>>>>>
>>>>>>>>>> You can't do fundamental logic in the abstract.
>>>>>>>>>>
>>>>>>>>>> That is just called fluff and bluster.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> 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.
>>>>>>>>>>
>>>>>>>>>> Showing the sort of thing YOU need to do to redefine logic
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I said that ZFC redefined the notion of a set to get rid of RP.
>>>>>>>>> You show the steps of how ZFC redefined a set as your rebuttal.
>>>>>>>>
>>>>>>>> No, you said that "ALL THEY DID" was that, and that is just a LIE.
>>>>>>>>
>>>>>>>> They developed a full formal system.
>>>>>>>>
>>>>>>>
>>>>>>> They did nothing besides change the definition of
>>>>>>> a set and the result of this was a new formal system.
>>>>>>>
>>>>>>
>>>>>> I guess you consider all the papers they wrote describing the 
>>>>>> effects of their definitions "nothing"
>>>>>>
>>>>>
>>>>> Not at all and you know this.
>>>>> One change had many effects yet was still one change.
>>>>>
>>>>
>>>> But would mean nothing without showing the affects of that change.
>>>>
>>>
>>> Yet again with your imprecise use of words.
>>> When any tiniest portion of the meaning of an expression
>>> has been defined this teeny tiny piece of the definition
>>> makes this expression not pure random gibberish.
>>>
>>> Meaningless does not mean has less meaning, it is
>>> an idiom for having zero meaning.
>>> https://www.britannica.com/dictionary/meaningless
>>>
>>>
>>>
>>
>> And your statements have NO Meaning because they are based on LIE.
>>
>> We can not use the "ZFC" set theory from *JUST* the definition, but 
>> need all the other rules derived from it.
> 
> The root cause of all of the changes is the redefinition
> of what a set is. Likewise with my own redefinition of a
> formal system by simply defining the details of True(L,x).
> 
> Once I specify the architecture others can fill in the details.
> 

Yes, the ROOT was that change, but you don't understand that if they 
JUST did that root, and not the other work, Set theory would not have 
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