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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Fri, 21 Mar 2025 07:48:25 -0400
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On 3/20/25 10:49 PM, olcott wrote:
> On 3/20/2025 8:31 PM, Richard Damon wrote:
>> On 3/20/25 11:02 AM, olcott wrote:
>>> On 3/20/2025 8:09 AM, Mikko wrote:
>>>> On 2025-03-20 02:42:53 +0000, olcott said:
>>>>
>>>>> It is stipulated that analytic knowledge is limited to the
>>>>> set of knowledge that can be expressed using language or
>>>>> derived by applying truth preserving operations to elements
>>>>> of this set.
>>>>
>>>> A simple example is the first order group theory.
>>>>
>>>>> When we begin with a set of basic facts and all inference
>>>>> is limited to applying truth preserving operations to
>>>>> elements of this set then a True(X) predicate cannot possibly
>>>>> be thwarted.
>>>>
>>>> There is no computable predicate that tells whether a sentence
>>>> of the first order group theory can be proven.
>>>>
>>>
>>> Likewise there currently does not exist any finite
>>> proof that the Goldbach Conjecture is true or false
>>> thus True(GC) is a type mismatch error.
>>
>> In other words, you are admitting you logic system isn't properly 
>> defined.
>>
>>>
>>> When we redefine logic systems such that they begin
>>> with set of basic facts and are only allowed to
>>> apply truth preserving operations to these basic
>>> facts then every element of the system is provable
>>> on the basis of these truth preserving operations.
>>>
>>
>> But your idea of a "logic system" isn't what logic is, while you claim 
>> your idea apply to it.
>>
>> Remember, you don't get to change the rules for an existing system.
>>
> 
> If I am showing the details of exactly logic can be transformed
> into correct reasoning without losing anything besides inconsistency
> and undecidability THEN I DO GET TO SUPERSEDE AND OVERRIDE THE
> RULES OF EXISTING SYSTEMS WITH MY CORRECTIONS.

Except you aren't, and you don't.

Please show the accepted rule that allows you to change the rules?

You do get to create your own logic system, if you are willing to do the 
actual work (If you can figure out how to do it) but you don't get to 
change the existing systems, and you claims you do just shows that you 
don't understand what you are talking about and are just committing a 
giant fraud,

> 
>> You can say that in Olcott Logic, that a Truth Predicate can exist, 
>> but you first have to convince people that they should care because 
>> you logic system can do something useful.
>>
> 
> Try and show anything that the set of all knowledge that
> can be expressed in language doesn't know that other
> formal systems do know.

But your claim isn't about knowledge, but about truth.

For instance, we KNOW that the Goldbach conjecture MUST be either True 
or False, but by your system True(GC) is False (and thus by the rules of 
immutable truth, it must NEVER be provable) and False(GC) is False, and 
thus also can't change, and thus your system can't meet the requirement 
that we know that one of them must be true.

> 
>> Since, by your admittion, it can't handle the properties of the 
>> Natural Numbers, as a statement about one of those properties is a 
>> "type mismatch error", you show how limited your system is.
>>
> 
> Natural numbers themselves don't actually have
> any properties other than an ordered set of finite
> strings of digits. Operations can be defined on the
> basis of this single property. These derived
> operations are not actually properties themselves.

You can try to make that lie, but it doesn't work. Your problem is that 
you don't understand what the Natual Numbers are, as just being that 
order set of strings, means that the operations exist, and the 
properties of those operation exist. Natural Numbers are DEFINED by an 
axiometic system (several different ways, but they all turn out to be 
the same system). Fro this the basics of the Arithmetic of the Natural 
Numbers turns up as a fundamental property of them, and thus the needed 
mathematics is shown and has the properties it has, because just by the 
existance of infinite set of Natural Numbers.

Note, one problem with trying to "define" them as just an ordered set of 
strings, is that to BE the Natural Numbers, there needs to be a 
countable infinity of them, and thus you need some way to make that full 
infinity, and not just say it is the finite set I wrote. That rule to 
create it is what creates the properties.

> 
>> The problem is until you can actually define what you can do in your 
>> system in a precise manner, it is just worthless.
>>
> 
> Yes of course even people with a million IQ would have
> no idea what can possibly be done with elements of the
> set of all knowledge that can be expressed using language.
> When you use the term "inference" with these million IQ
> people they think you are saying "in fer rents", like you
> owe rent and are OK with paying it.

Just proves that you don't understand what you are talking about.

A set, no matter what it is of, is not a logic system.

Sorry, but you are just proving your stupidity.

> 
>> So, in WORTHLESS Olcott logic, we have an unproven claim (since you 
>> haven't established enough of a system to prove something in it) about 
>> your truth predicate, but until someone has a use for your system, 
>> that is pretty worthless.
> 
>