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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 10:12:37 -0500
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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.

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