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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 13:21:32 -0600
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On 3/2/2025 1:13 PM, dbush wrote:
> On 3/2/2025 2:11 PM, olcott wrote:
>> On 3/2/2025 1:04 PM, dbush wrote:
>>> On 3/2/2025 1:57 PM, olcott wrote:
>>>> 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.
>>>>
>>>
>>> That's not what incompleteness means.
>>>
>>> For example, Robinson arithmetic is incomplete because the true 
>>> statement "no number is equal to its successor" has *only* an 
>>> infinite connection to its truthmaker.
>>>
>>
>> That is a ridiculously stupid thing to say and you know it.
>> I may not be alive in a month. Quit f-cking around with
>> my life's work.
>>
> 
> That you don't know the definition of the terms you're using is not a 
> rebuttal.

When formal systems can be defined in such a way that they are not
incomplete and undecidability cannot occur it is stupid to define
them differently.

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