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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 13:50:01 -0600
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On 11/9/2024 1:32 PM, Alan Mackenzie wrote:
> olcott <polcott333@gmail.com> wrote:
> 
>> The assumption that ~Provable(PA, g) does not mean ~True(PA, g)
>> cannot correctly be the basis for any proof because it is only
>> an assumption.
> 
> It is an assumption which swifly leads to a contradiction, therefore must
> be false.  

You just said that the current foundation of logic leads to a 
contradiction. Too many negations you got confused.

When we assume that only provable from the axioms
of PA derives True(PA, g) then (PA ⊢ g) merely means
~True(PA, g) THIS DOES NOT LEAD TO ANY CONTRADICTION.

> But you don't understand the concept of proof by
> contradiction, and you lack the basic humility to accept what experts
> say, so I don't expect this to sink in.
> 


>>> We know, by Gödel's Theorem that incompleteness does exist.  So the
>>> initial proposition cannot hold, or it is in an inconsistent system.
> 
>> Only on the basis of the assumption that
>> ~Provable(PA, g) does not mean ~True(PA, g)
> 
> No, there is no such assumption.  There are definitions of provable and
> of true, and Gödel proved that these cannot be identical.
> 

*He never proved that they cannot be identical*

The way that sound deductive inference is defined
to work is that they must be identical.

A conclusion IS ONLY true when applying truth
preserving operations to true premises.

It is very stupid of you to say that Gödel refuted that.

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