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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 13:32:51 +0300
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On 2024-08-17 14:45:45 +0000, olcott said:

> 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.

Yes they did. They did show that the new system is similar enough to
the old systems to be called "set theory" and sufficiently useful.

-- 
Mikko