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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 13:13:12 -0400
Organization: i2pn2 (i2pn.org)
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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).
>>>
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