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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sat, 9 Nov 2024 19:19:15 -0500
Organization: i2pn2 (i2pn.org)
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On 11/9/24 6:37 PM, olcott wrote:
> On 11/9/2024 2:58 PM, Richard Damon wrote:
>> On 11/9/24 2:50 PM, olcott wrote:
>>> 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.
>>
>> Nope, becuase
>>
>> TRUE is based on ANY sequence of steps, including an infinite sequence.
>>
>> PROVABLE is based on only a FINITE sequence of steps.
>>
> 
> Instead of the term provable I refer to a sequence
> of truth preserving operations. Because some people
> can untangle what I mean by this I must digress for
> them to the term provable. I always means a sequence
> of truth preserving operations.

So, which of your definitions allow for an INFINITE chains of 
operations, and which allow for only finite chains operaitions.

Classic logic, defines TRUTH to allow for the infinite chain, while a 
PROOF allows for only a finite chain,



> 
>>>
>>> A conclusion IS ONLY true when applying truth
>>> preserving operations to true premises.
>>
>> Which might be infinite, and thus not a proof.
>>
> 
> I always mean [truth preserving operations] when this
> exceeds the person's capacity to understand I have to
> dumb it down and lose some of the precise meaning.

So, do you mean an INFINITE chain of them or only a FINITE chain of them.

And, which operations allowed in "Normal" logic, are you intending to 
remove from the list?

Any you are thinking of adding?

and Why?

This seems just like your typical diversion to create your own terms 
that you refuse to actual come up with a definite definition.

> 
>>>
>>> It is very stupid of you to say that Gödel refuted that.
>>>
>>
>> Because he did, for the actual definitions, not your false one.
>>
>> Sorry God you are that can't undetstand what a infinite thing is.
> 
>