Re: How a True(X) predicate can be defined for the set of analytic knowledge

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.