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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge (HoTT)
Date: Sun, 23 Mar 2025 17:53:17 -0400
Organization: i2pn2 (i2pn.org)
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On 3/23/25 5:00 PM, olcott wrote:
> On 3/22/2025 9:53 PM, Richard Damon wrote:
>> On 3/22/25 2:27 PM, olcott wrote:
>>> On 3/22/2025 12:34 PM, Richard Damon wrote:
>>>> On 3/22/25 12:11 PM, olcott wrote:
>>>>> On 3/22/2025 8:37 AM, Richard Damon wrote:
>>>>>> On 3/21/25 11:14 PM, olcott wrote:
>>>>>>> On 3/21/2025 9:31 PM, Richard Damon wrote:
>>>>>>>> On 3/21/25 8:47 PM, olcott wrote:
>>>>>>>>> On 3/21/2025 6:49 PM, Richard Damon wrote:
>>>>>>>>>> On 3/21/25 8:49 AM, olcott wrote:
>>>>>>>>>>> On 3/21/2025 3:57 AM, Mikko wrote:
>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> It is stipulated that analytic knowledge is limited to the
>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or
>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements
>>>>>>>>>>>>>>> of this set.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> A simple example is the first order group theory.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> When we begin with a set of basic facts and all inference
>>>>>>>>>>>>>>> is limited to applying truth preserving operations to
>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot 
>>>>>>>>>>>>>>> possibly
>>>>>>>>>>>>>>> be thwarted.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There is no computable predicate that tells whether a 
>>>>>>>>>>>>>> sentence
>>>>>>>>>>>>>> of the first order group theory can be proven.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Likewise there currently does not exist any finite
>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false
>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
>>>>>>>>>>>>
>>>>>>>>>>>> However, it is possible that someone finds a proof of the 
>>>>>>>>>>>> conjecture
>>>>>>>>>>>> or its negation. Then the predicate True is no longer complete.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The set of all human general knowledge that can
>>>>>>>>>>> be expressed using language gets updated.
>>>>>>>>>>
>>>>>>>>>> And thus your concept of truth breaks.
>>>>>>>>>>
>>>>>>>>>> Truth, by its definition is an immutable thing, but you just 
>>>>>>>>>> defined it to be mutable.
>>>>>>>>>>
>>>>>>>>>> How often do we need to re-verify our truths?
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>>> When we redefine logic systems such that they begin
>>>>>>>>>>>>> with set of basic facts and are only allowed to
>>>>>>>>>>>>> apply truth preserving operations to these basic
>>>>>>>>>>>>> facts then every element of the system is provable
>>>>>>>>>>>>> on the basis of these truth preserving operations.
>>>>>>>>>>>>
>>>>>>>>>>>> However, it is possible (and, for sufficiently powerful 
>>>>>>>>>>>> sysems, certain)
>>>>>>>>>>>> that the provability is not computable.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> When we begin with basic facts and only apply truth preserving
>>>>>>>>>>> to the giant semantic tautology of the set of human knowledge
>>>>>>>>>>> that can be expressed using language then every element in this
>>>>>>>>>>> set is reachable by these same truth preserving operations.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> But you aren't begining with basic facts, but with what has 
>>>>>>>>>> been assumed to be the basic facts. 
>>>>>>>>>
>>>>>>>>> That is not what I stipulated.
>>>>>>>>> When we begin with what actual are the set of basic
>>>>>>>>> facts and are only allowed to apply truth preserving
>>>>>>>>> operations to these basic facts then it is self-evident
>>>>>>>>> that True(X) must always be correct.
>>>>>>>>
>>>>>>>> But you can't stipulate that you cant' get to things that you 
>>>>>>>> can get to.
>>>>>>>>
>>>>>>>> If your system can define the Natural Numbers, then we get Godel 
>>>>>>>> and Tarski, and you can't stop it.
>>>>>>>>
>>>>>>>
>>>>>>> The entire semantics of G is defined in the body of human general
>>>>>>> knowledge that can be expressed in language henceforth called (BOK).
>>>>>>
>>>>>> Yes, and that is that there does not exist a number that satifies 
>>>>>> a particular involved Primative Recursive Relationship.
>>>>>>
>>>>>
>>>>> That you provide reasonable replies that show good
>>>>> insight some of the time seems to prove that you
>>>>> are capable of having good insight.
>>>>
>>>> So, you admit that I shows you something that breaks your claim?
>>>>
>>>
>>> Not at all. What I said and you agreed with
>>> it that G is provable in  in the same
>>> way the G is provable in meta-math.
>>
>> No it isn't as the GKEUL can't have the axioms that enumerate the 
>> axioms, and thus doesn't have the information needed to do the proof 
>> in the meta-math.(GKEUL)
>>
> 
> How-so-ever any human ever did this before (GKEUL)
> knows how to do that.
> 

But doesn't know WHICH numbering was used, and thus can't read the message.

Your problem is you still don't understand how this metasystem works, so 
you bravdo is just a bunch of lies, showing your stupidity.