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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Sun, 18 Aug 2024 13:40:30 +0300
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On 2024-08-17 16:51:22 +0000, olcott said:

> On 8/17/2024 11:46 AM, Richard Damon wrote:
>> 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 
>> been "fixed", as it still wouldn't have been usable.
>> 
> 
> Defining that no set can be a member of itself would seem
> to do the trick.

It doesn't if there is another axiom that says or impies that the is a set
that contains itself, or if several axioms together imply that. If someting
provably exists then it exists even if you can prove that it does not
exist.

-- 
Mikko