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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology
 providing situational context.
Date: Sat, 22 Mar 2025 11:25:13 -0500
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On 3/22/2025 10:54 AM, Mikko wrote:
> On 2025-03-22 15:00:44 +0000, olcott said:
> 
>> On 3/22/2025 7:05 AM, Mikko wrote:
>>> On 2025-03-21 22:47:04 +0000, olcott said:
>>>
>>>> On 3/21/2025 3:10 PM, Richard Heathfield wrote:
>>>>> On 21/03/2025 11:48, Richard Damon wrote:
>>>>>> On 3/21/25 5:33 AM, Richard Heathfield wrote:
>>>>>
>>>>> <snip>
>>>>>
>>>>>>>
>>>>>>> But what if they were /both/ right? It was an obvious worry, and 
>>>>>>> so arose the great question: is mathematics consistent?
>>>>>>>
>>>>>>> And Gödel proved not only that it isn't, but that it can't be.
>>>>>>>
>>>>>>> Fortunately, to date inconsistency has tended to surface only in 
>>>>>>> corner cases like the Halting Problem, but Gödel's Hobgoblin 
>>>>>>> hovers over mathematics to this day.
>>>>>>>
>>>>>>
>>>>>> Godel didn't prove that Mathematics wasn't consistent. He proved 
>>>>>> that it couldn't be proved to BE consistant within itself.
>>>>>
>>>>> Yes, I rather overstated the case. Sorry about that.
>>>>
>>>> Or we could simply define the rules for constructing a
>>>> formal system such that inconsistency cannot exist.
>>>
>>> That is possible. An example is Horn clauses, which is the theory behind
>>> Prolog. If the logic has no negation operator there is no posiibility to
>>> express an inconsistency. But even then the question whether there is an
>>> unprovable sentence is problematic.
>>
>> The body of human general knowledge that can be expressed
>> in language cannot possibly have any unprovable expressions
>> when truth preserving operations are the only category of
>> inference steps allowed.
> 
> There are unprovable expressions that may in future be in the body
> of expressible human general knowledge.
> 

The body of knowledge excludes unknown things that are
instantly added to this set as soon as they are known.

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