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

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.
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.
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.
The problem is until you can actually define what you can do in your system in a precise manner, it is just worthless.
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.