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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sun, 2 Mar 2025 12:57:21 -0600
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On 3/2/2025 12:22 PM, dbush wrote:
> On 3/2/2025 1:10 PM, olcott wrote:
>> On 3/2/2025 11:19 AM, dbush wrote:
>>> On 3/2/2025 12:14 PM, olcott wrote:
>>>> On 3/2/2025 11:11 AM, dbush wrote:
>>>>> On 3/2/2025 12:08 PM, olcott wrote:
>>>>>> On 3/2/2025 11:00 AM, dbush wrote:
>>>>>>> On 3/2/2025 11:53 AM, olcott wrote:
>>>>>>>> On 3/2/2025 10:28 AM, dbush wrote:>>> So how does changing the 
>>>>>>>> definition of truth prevent systems from
>>>>>>>>> existing that contain true statements that have *only* an 
>>>>>>>>> infinite connection to their truthmaker?
>>>>>>>>
>>>>>>>> *This <is> how actual truth has always worked*
>>>>>>>>
>>>>>>>> If expression X has a connection to a truth-maker then
>>>>>>>> X is true otherwise X is untrue, yet possibly not false.
>>>>>>>> It does not matter what kind of connection this is.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> You didn't answer the question.
>>>>>>>
>>>>>>
>>>>>> Sure I did
>>>>>>  >> It does not matter what kind of connection this is.
>>>>>>
>>>>>> It does not matter whether the connection is infinite
>>>>>> or not so STFU about it.
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> Dishonest dodge.
>>>>>
>>>>> You stated that your definition of truth prevents systems from 
>>>>> existing that contain true statements that have *only* an infinite 
>>>>> connection to their truthmaker.
>>>>>
>>>>> So how does that happen?
>>>>
>>>> I never said anything like that.
>>>>
>>>
>>> Yes you did:
>>>
>>> On 3/1/2025 11:46 PM, olcott wrote:
>>>  > Incompleteness cannot possibly exist when true means
>>>  > has a truth-maker and untrue means has no truth-maker
>>>  > and false mean ~X has a truth-maker.
>>
>> Your paraphrase of that was terribly incorrect.
>> Has a truth-maker has always been the only correct
>> way to determine True(x) superseding and replacing
>> the ill-formed notion of provability.
>>
> 
> I merely substituted the term "incompleteness" with it's official 
> definition.  That you don't understand that definition is not a rebuttal.
> 
> That you attempted to change the idea of "provability" doesn't change 
> the fact that "incompleteness" still refers to the original idea of 
> "provability".
> 
> A system is incomplete if it contains one or more true statements that 
> contain *only* an infinite connection to their truthmakers.
> 
> That doesn't change despite your idea of "truth", so incompleteness 
> still exists.

One can define a system of arithmetic that does not allow
summing the integers 5 and 3. Such a system would be
incomplete as an artificial contrivance.

The notions of undecidability and incompleteness are this
same sort of artificial contrivance.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer