Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sun, 2 Mar 2025 16:11:14 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <9c836636d16b24d34f502c282df63bdfd3b397b0@i2pn2.org>
References: <vnh0sq$35mcm$1@dont-email.me>
 <0f7cd503773838ad12f124f23106d53552e277b8@i2pn2.org>
 <vpbknk$3qig2$1@dont-email.me> <vpc560$3sqf7$1@dont-email.me>
 <vpd5r4$2q85$2@dont-email.me>
 <7e3e9d35d880cfcad12f505dfb39c5650cdd249e@i2pn2.org>
 <vpfo75$js1o$1@dont-email.me>
 <f3c8332f4b42f8e085d4d4dac017ccc8a0dc5a5f@i2pn2.org>
 <vpgt6o$tiun$1@dont-email.me>
 <3cf165ef9793e844dc9d5db82aecbc47f9545367@i2pn2.org>
 <vpiubu$1fvqe$1@dont-email.me>
 <080bf2b1c322247548c6ec61c9f054359062ccd4@i2pn2.org>
 <vpj8c9$1hivf$3@dont-email.me>
 <6fc61a762b56308f9919993f29ba3e77f7ba84c7@i2pn2.org>
 <vpl2q5$23vks$6@dont-email.me>
 <41ca355a1f535e767e17d3f4df3d404eb1e61cef@i2pn2.org>
 <vplr1t$28j3a$2@dont-email.me> <vps1n5$3k4j1$1@dont-email.me>
 <vptbtg$3rlov$2@dont-email.me> <vpuhf0$57aa$1@dont-email.me>
 <vpvost$bjn9$5@dont-email.me>
 <d40c6a96b85a9efc4de8d05178f8d0ff4e85bc8f@i2pn2.org>
 <vq0bil$f3k3$5@dont-email.me>
 <0c13204eabb5d28a0ff0b1c463404416fd535888@i2pn2.org>
 <vq0om6$kqua$6@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 2 Mar 2025 21:11:14 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="2552192"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
In-Reply-To: <vq0om6$kqua$6@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US

On 3/2/25 12:00 AM, olcott wrote:
> On 3/1/2025 7:25 PM, Richard Damon wrote:
>> On 3/1/25 8:17 PM, olcott wrote:
>>> On 3/1/2025 3:58 PM, Richard Damon wrote:
>>>> On 3/1/25 2:58 PM, olcott wrote:
>>>>> On 3/1/2025 2:45 AM, Mikko wrote:
>>>>>> On 2025-02-28 22:04:31 +0000, olcott said:
>>>>>>
>>>>>>> On 2/28/2025 4:04 AM, Mikko wrote:
>>>>>>>> On 2025-02-26 01:33:48 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 2/25/2025 5:58 PM, Richard Damon wrote:
>>>>>>>>>> On 2/25/25 1:40 PM, olcott wrote:
>>>>>>>>>>> On 2/25/2025 12:15 PM, joes wrote:
>>>>>>>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott:
>>>>>>>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 2/24/25 6:11 PM, olcott wrote:
>>>>>>>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 2/22/2025 9:56 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 2/22/25 1:42 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/22/2025 3:25 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2025-02-22 04:44:35 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 2/21/25 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Sure I do.
>>>>>>>>>>>>>>>> A Systems is semantically sound if every statement that 
>>>>>>>>>>>>>>>> can be proven
>>>>>>>>>>>>>>>> is actually true by the systems semantics,
>>>>>>>>>>>>>>> That is very good.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> in other words, the system doesn't allow the proving of 
>>>>>>>>>>>>>>>> a false
>>>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>> That is not too bad yet ignores that some expressions 
>>>>>>>>>>>>>>> might not have
>>>>>>>>>>>>>>> any truth value.
>>>>>>>>>>>>>> Which has nothing to do with "soundness".
>>>>>>>>>>>>> When any system assumes that every expression is true or 
>>>>>>>>>>>>> false and is
>>>>>>>>>>>>> capable of encoding expressions that are neither IT IS 
>>>>>>>>>>>>> STUPIDLY WRONG.
>>>>>>>>>>>
>>>>>>>>>>>> In honour of Gödel this is usually called "incomplete".
>>>>>>>>>>>>
>>>>>>>>>>> Where "incomplete" has always been an idiom for stupid wrong.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, only in your faulty logic.
>>>>>>>>>>
>>>>>>>>>> Incomplete means that there are some truths that can't be 
>>>>>>>>>> proven in the system.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> That comes from stupidly failing to require {true in the system}
>>>>>>>>> to require {proven in the system}. Fix this one stupid mistake
>>>>>>>>> and all of incompleteness goes away.
>>>>>>>>
>>>>>>>> No, that merely means that "true in the system" is incomplete in 
>>>>>>>> some
>>>>>>>> systems (e.g., natural numbers). There are sentences that are 
>>>>>>>> true in
>>>>>>>> practical applications of the system but not in the system itself.
>>>>>>>> That is not a defect as it does not prevent useful practical 
>>>>>>>> aplications.
>>>>>>>
>>>>>>> The bottom line here is that expressions that do not have
>>>>>>> a truth-maker are always untrue. Logic screws this up by
>>>>>>> overriding the common meaning of terms with incompatible
>>>>>>> meanings. Provable(common) means has a truth-maker.
>>>>>>
>>>>>> Logic doesn't care about truths and truth makers except in the 
>>>>>> (usually
>>>>>> uninteresting) special cases where truth makers are found in the 
>>>>>> logic
>>>>>> itself.
>>>>>>
>>>>>
>>>>> Incompleteness(math) and Undecidability(logic) are
>>>>> artifacts of defining the term provable(math)
>>>>> in a way that is inconsistent with provable(common)
>>>>> {shown to be definitely true by whatever means}.
>>>>>
>>>>
>>>> Nopw, because shown(common) requires a finite sequence to show to 
>>>> someone, as people can not see all of an infinite sequence
>>>>
>>>
>>> If the Goldbach conjecture is true and there is only
>>> an infinite sequence as its truth-maker then this
>>> infinite sequence <is> its proof(common)
>>> {shown to be definitely true by whatever means}.
>>>
>>
>> No, an infinite sequence is not a "proof" as you can not SHOW an 
>> infinite sequence.
>>
> 
> Whatever makes an expression true is its truth-maker.
> Any expression not having a truth-maker is not true.
> LP cannot possibly have a truthmaker.
> 

It does if it was defined as ~True(LP), as the True Predicate becomes 
its proximate truth-maker, derived from the truth that the True 
predicate determined.

Unless you are going to admit that your True predicate based its "false" 
answer on logic without a truth maker. For True(x) to return false, it 
is making the assertion that there is no path to a truth-maker for its 
input, if it can't assert that, it can't answer false.

You don't seem to understand the difference between an actual logical 
predicate, and just refering to the truth of a statement.