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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis ---
Date: Sun, 3 Nov 2024 08:16:33 -0600
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On 11/3/2024 5:53 AM, Mikko wrote:
> On 2024-11-02 11:43:02 +0000, olcott said:
> 
>> On 11/2/2024 4:09 AM, Mikko wrote:
>>> On 2024-11-01 12:19:03 +0000, olcott said:
>>>
>>>> On 11/1/2024 5:42 AM, Mikko wrote:
>>>>> On 2024-10-30 12:46:25 +0000, olcott said:
>>>>>
>>>>>> ZFC only resolved Russell's Paradox because it tossed out
>>>>>> the incoherent foundation of https://en.wikipedia.org/wiki/ 
>>>>>> Naive_set_theory
>>>>>
>>>>> Actually Zermelo did it. The F and C are simply minor improvements on
>>>>> other aspects of the theory.
>>>>
>>>> Thus establishing the precedent that replacing the foundational
>>>> basis of a problem is a valid way to resolve that problem.
>>>
>>> No, that does not follow. In particular, Russell's paradox is not a
>>> problem, just an element of the proof that the naive set theory is
>>> inconsistent. The problem then is to construct a consistent set
>>> theory. Zermelo proposed one set theory and ZF and ZFC are two other
>>> proposals.
>>
>> My view is that the same kind of self-reference issue that
>> showed naive set theory was inconsistent also shows that the
>> current notion of a formal system is inconsistent.
> 
>  From the proof of the exstence of Russell's set it is easy
> to prove that 1 = 2. As long as no proof of 1 = 2 from a
> self-reference in a formal system is shown there is no
> reason to think that such system is inconsisten. 

In other words you presume yourself to be all knowing about this.

> And the
> existence of insonstent formal systems does not mean that
> the notion of a formal system is inconsistent.
> 

The notion of formal systems is incoherent because they
rule that self-contradictory expressions prove that the
system is incomplete rather than the expression is incorrect.

>> When we handle this self-reference differently then this issue
>> is resolved.
> 
> No proof ot that, either.
> 
>> When a formal system is ONLY a sequence of truth preserving
>> operations applied to a consistent set of expressions that
>> have been stipulated to be true then expressions that would
>> otherwise show incompleteness are rejected because they have
>> no path to true or false.
>>

You can't ignore this.
The above is the essence of my whole system
of thought.

>>> The foundation of all these theories is classical logic.
>>>
>>
>> The key error of classical logic is that it diverged from the
>> model of the syllogism where there is always a path to true or
>> false or the syllogism is ill-formed.
> 
> Classical logic does not substantially diverge from the model of
> syllogism. 

When modern logic divides the formal system from the underlying
semantics there is no direct path to True(L,x) within the system,
thus no way to reject self-contradictory expressions on the basis
that they have no path to true or false.

> It iextends it for situations that cannot be covered
> with syllogistic logic. Presentational differences follow mainly
> from the needs of the additional coverage.
> 
> No error has been shown in classical logic.
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer