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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Sun, 18 Aug 2024 14:33:16 +0300
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On 2024-08-17 19:54:51 +0000, olcott said:

> On 8/17/2024 2:41 PM, Richard Damon wrote:
>> On 8/17/24 3:12 PM, olcott wrote:
>>> On 8/17/2024 1:45 PM, Richard Damon wrote:
>>>> On 8/17/24 2:19 PM, olcott wrote:
>>>>> On 8/17/2024 1:10 PM, Richard Damon wrote:
>>>>>> On 8/17/24 2:04 PM, olcott wrote:
>>>>>>> On 8/17/2024 12:51 PM, Richard Damon wrote:
>>>>>>>> 
>>>>>>>> In other words, you are just admitting you don't understand how logic works.
>>>>>>>> 
>>>>>>>> If you CHANGE an existing axiom, everything that depended on that axiom 
>>>>>>>> needs to be re-verified.
>>>>>>>> 
>>>>>>>> If you ADD a new axiom, it doesn't affect ANY argument that doesn't try 
>>>>>>>> to use it, and thus doesn't affect Russel's Paradox.
>>>>>>> 
>>>>>>> OK.
>>>>>>> 
>>>>>>> I add the definition for the True(L, x) predicate
>>>>>>> and every instance of the notion of True changes
>>>>>>> in every formal mathematical logic system.
>>>>>>> 
>>>>>> 
>>>>>> But either that changes what that instance means,
>>>>> 
>>>>> When I stipulate what True(L,x) means then that is done.
>>>>> It does not go on and in any circle endlessly redefining itself.
>>>> 
>>>> Nope. You can say for YOUR usage, what you mean by True(L,x). You can't 
>>>> force others to use that,
>>> 
>>> Likewise ZFC is a mere opinion that most everyone chooses to ignore.
>> 
>> No, it isn't an "opinion", it is a set of definitions, and the logic 
>> system that comes out of them.
>> 
>> People are of course allowed to choose which ever set theory they want 
>> to use, but if they choose to use Naive Set Theory, they have the 
>> problem that it is known to be inconsistant, and thus any "proof" they 
>> build is suspect.
>> 
>> They can also shoose some other Set theory  Theory, maybe even just ZF, 
>> or to one of the derived theorys like Morse-Kelly, or to something 
>> different like one of the New Foundations Systems. The key is you tend 
>> to need to specify if you differ from ZFC which is generally considered 
>> the default.
>> 
>> You seem to be having trouble with the words you are using.
>> 
> 
> Not that. I am taking the hypothetical extreme position
> to see where you set your own boundaries on this.
> 
>>> 
>>>> or reinterprete what others have said or proven based on you 
>>>> stipulation, in fact, by stipulating that definition, anythig that uses 
>>>> any other definition of it becomes out of bounds for your argument.
>>>> 
>>>>> 
>>>>> Everything in logic the depended on some notion of True is
>>>>> changed. Any logic operations that were not truth preserving
>>>>> are discarded. The notion of valid inference is also changed
>>>>> because it was not truth preserving.
>>>>> 
>>>> 
>>>> And needs to be reproved to see if it is still true.
>>>> 
>>>> 
>>>>> When a conclusion is not a necessary consequence of all of its
>>>>> premises then the argument is invalid.
>>>>> 
>>>> 
>>>> Right, so YOUR argument here is invalid.
>>>> 
>>> 
>>> It is proven totally true entirely on the basis of the
>>> meaning of its words. Math conventions to the contrary
>>> simply ignore this.
>>> 
>> 
>> Nope. You are just proving by the meaning of the words that you are 
>> totally ignorant of how logic works.
>> 
>> Sorry, but that is the facts.
>> 
> 
> Logic is currently defined to work contrary to the way that
> truth itself actually works.

The classical logic is empirically correct.
As Aristotle says, we use the ordinary rules of inference
because nobody has ever observed a situation where a valid
inference from true premises gives a false conclusion.


-- 
Mikko