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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 14:22:51 +0300
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On 2024-08-17 18:04:24 +0000, olcott said:

> On 8/17/2024 12:51 PM, Richard Damon wrote:
>> On 8/17/24 1:41 PM, olcott wrote:
>>> On 8/17/2024 12:39 PM, Richard Damon wrote:
>>>> On 8/17/24 1:22 PM, olcott wrote:
>>>>> On 8/17/2024 12:13 PM, Richard Damon wrote:
>>>>>> On 8/17/24 12:51 PM, olcott wrote:
>>>>>>> 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.
>>>>>>> 
>>>>>>> 
>>>>>> 
>>>>>> But usable, until integrated into a Formal Logic system.
>>>>>> 
>>>>> 
>>>>> No. Just tacking it on at the end of set theory gets rid of RP.
>>>>> 
>>>> 
>>>> Nope, because you can just ignore any axiom you don't want to use.
>>>> 
>>> 
>>> It is part of the definition of a set thus cannot be correctly
>>> ignored.
>>> 
>> 
>> In other words, you are just admitting you don't understand how logic works.
>> 
>> If you CHANGE an existing axiom, everything that depended on that axiom 
>> needs to be re-verified.
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