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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 14:20:14 +0300
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On 2024-08-17 17:41:51 +0000, olcott said:

> 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
>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> 
>>>>>>>> 
>>>>>>>> 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).
>>>>>>> 
>>>>>>> Once I specify the architecture others can fill in the details.
>>>>>>> 
>>>>>> 
>>>>>> Yes, the ROOT was that change, but you don't understand that if they 
>>>>>> JUST did that root, and not the other work, Set theory would not have 
>>>>>> been "fixed", as it still wouldn't have been usable.
>>>>>> 
>>>>> 
>>>>> Defining that no set can be a member of itself would seem
>>>>> to do the trick.
>>>>> 
>>>>> 
>>>> 
>>>> But usable, until integrated into a Formal Logic system.
>>>> 
>>> 
>>> No. Just tacking it on at the end of set theory gets rid of RP.
>>> 
>> 
>> Nope, because you can just ignore any axiom you don't want to use.
>> 
> 
> It is part of the definition of a set thus cannot be correctly
> ignored.

You don't need to use an axiom if you can without it do what you want.
The definition of proof says that every axiom can be used in a proof.
It does not say that every axiom must be used.

-- 
Mikko