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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Mon, 11 Nov 2024 10:53:21 -0500
Organization: i2pn2 (i2pn.org)
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On 11/11/24 9:35 AM, olcott wrote:
> On 11/11/2024 4:26 AM, Mikko wrote:
>> On 2024-11-11 03:08:36 +0000, olcott said:
>>
>>> On 11/10/2024 3:52 AM, Mikko wrote:
>>>> On 2024-11-09 18:05:38 +0000, olcott said:
>>>>
>>>>> On 11/9/2024 11:58 AM, Alan Mackenzie wrote:
>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>> On 11/9/2024 10:03 AM, Alan Mackenzie wrote:
>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>> On 11/9/2024 5:01 AM, joes wrote:
>>>>>>>>>>>>>>>>>> On 11/8/24 12:25 PM, olcott wrote:
>>>>>>
>>>>>>>>>>>>>>>>>>> That formal systems that only apply truth preserving 
>>>>>>>>>>>>>>>>>>> operations
>>>>>>>>>>>>>>>>>>> to expressions of their formal language that have been
>>>>>>>>>>>>>>>>>>> stipulated to be true cannot possibly be undecidable 
>>>>>>>>>>>>>>>>>>> is proven
>>>>>>>>>>>>>>>>>>> to be over-your-head on the basis that you have no 
>>>>>>>>>>>>>>>>>>> actual
>>>>>>>>>>>>>>>>>>> reasoning as a rebuttal.
>>>>>>>>>> Gödel showed otherwise.
>>>>>>
>>>>>>>>> That is counter-factual within my precise specification.
>>>>>>
>>>>>>>> That's untrue - you don't have a precise specification.  And 
>>>>>>>> even if you
>>>>>>>> did, Gödel's theorem would still hold.
>>>>>>
>>>>>>>>> When truth is only derived by starting with
>>>>>>>>> truth and applying truth preserving operations
>>>>>>>>> then unprovable in PA becomes untrue in PA.
>>>>>>
>>>>>>>> No.  Unprovable will remain.
>>>>>>
>>>>>>> *Like I said you don't pay f-cking attention*
>>>>>>
>>>>>> Stop swearing.  I don't pay much attention to your provably false
>>>>>> utterances, no.  Life is too short.
>>>>>>
>>>>>
>>>>> That you denigrate what I say without paying attention to what
>>>>> I say <is> the definition of reckless disregard for the truth
>>>>> that loses defamation cases.
>>>>>
>>>>>> Hint: Gödel's theorem applies in any sufficiently powerful logical
>>>>>> system, and the bar for "sufficiently powerful" is not high.
>>>>>>
>>>>>
>>>>> Unless it is stipulated at the foundation of the notion of
>>>>> formal systems that ~Provable(PA, g) simply means ~True(PA, g).
>>>>>
>>>>>>> Unprovable(L,x) means Untrue(L,x)
>>>>>>> Unprovable(L,~x) means Unfalse(L,x)
>>>>>>> ~True(L,x) ^ ~True(L, ~x) means ~Truth-Bearer(L,x)
>>>>>>
>>>>>> If you're going to change the standard meaning of standard words, 
>>>>>> you'll
>>>>>> find communicating with other people somewhat strained and difficult.
>>>>>>
>>>>>
>>>>> ZFC did the same thing and that was the ONLY way
>>>>> that Russell's Paradox was resolved.
>>>>>
>>>>> When ~Provable(PA,g) means ~True(PA,g) then
>>>>> incompleteness cannot exist.
>>>>
>>>> But it doesn't. "Provable(PA,g)" means that there is a proof on g in PA
>>>> and "~Provable(PA,g)" means that there is not. These meanings are don't
>>>> involve your "True" in any way. You may define "True" as a synonym to
>>>> "Provable" but formal synonyms are not useful.
>>>
>>> We can ALWAYS prove that any expression of language is true or
>>> not on the basis of other expressions of language when we have a
>>> coherent definition of True(L,x).
>>
>> Not relevant. 
> 
> It <is> relevant in that it does refute the Tarski
> Undefinability theorem that <is> isomorphic to incompleteness.
> 
>> The meaning of "Provable(PA,g)" does not depend on
>> the definition of "True(L,x)". "Provable(PA,g)" is false because
>> there is no proof of g in PA. For the same reason "Provable(PA,~g)"
>> is false.
>>
> 
> There is no proof of Tarski's x in his Theory only
> because x is incoherent in his theory.
> https://liarparadox.org/Tarski_275_276.pdf

Nope, you are ignoring the work before which he mentions as establishing x.

So, you are guilty of lying by making baseless assumptions because of 
your ignornace. This can not be an "honest mistake" as you have been 
told previously of the error, so repeating them is just a reckless 
disregard for the truth.


> 
>     Let {T} be such a theory. Then the elementary
>     statements which belong to {T} we shall call the
>     elementary theorems of {T}; we also say that
>     these elementary statements are true for {T}.
>     Thus, given {T}, an elementary theorem is an
>     elementary statement which is true.
>     https://www.liarparadox.org/Haskell_Curry_45.pdf
> 
> Haskell Curry is referring to a set of expressions that are
> stipulated to be true in T.
> 
> We define True(L, x) to mean x is a necessary consequence of
> the Haskell Curry elementary theorems of L.
> (Haskell_Curry_Elementary_Theorems(L) □ x) ≡ True(L, x)
> 
> x = "What time is it?"
> True(English, x) == false
> True(English, ~x) == false
> ∴ Not_a_Truth_Bearer(English, x)
> 
> Under math rules we would declare that English is incomplete
> because neither x nor ~x is provable in English.

Except that "English" is not a formal logic system, so the definition 
doesn't apply, and you are shown to just be an idiot that doesn't 
undetstand what he is talking about.

> 
>> There are actually infinitely many sentences of PA that could be used
>> instead of g to show incompleteness but one is enoubh.
>>
>>> That Gödel relies on True(meta-math, g) to mean True(PA, g)
>>> is a stupid mistake that enables Incomplete(PA) to exist.
>>
>> Gödel proved Provable(meta-math, "~Provable(PA,g) ∧ ~Provable(PA,g)").
>>
> 
> That is the same thing as proving:
> This sentence is not true: "This sentence is not true" is true.
> 

Nope, and your repeating it proves you to be an idiotic pathological liar.