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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 14:45:07 -0400
Organization: i2pn2 (i2pn.org)
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On 8/17/24 2:19 PM, olcott wrote:
> On 8/17/2024 1:10 PM, Richard Damon wrote:
>> On 8/17/24 2:04 PM, olcott wrote:
>>> 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.
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