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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Sat, 17 Aug 2024 11:35:17 -0500
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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.

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