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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 13:51:04 -0400
Organization: i2pn2 (i2pn.org)
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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
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
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