Eliminating undecidability in formal systems

[Logik]

The groundbreaking discovery is that I derived a very slight change to the way that formal
systems are defined such that incompleteness is impossible in any of these formal systems.

I literally just demonstrated to you why your system is incomplete.

It is raining outside.
I went outside unprotected.
I didn't get wet.

Because it was only raining on one side of the street.

A complete system does not permit falsification.

[PeteOlcott]

The groundbreaking discovery is that I derived a very slight change to the way that formal
systems are defined such that incompleteness is impossible in any of these formal systems.

I literally just demonstrated to you why your system is incomplete.

It is raining outside.
I went outside unprotected.
I didn't get wet.

Because it was only raining on one side of the street.

A complete system does not permit falsification.

OK that is a good point. I was just providing a simple
explanation of what I meant by the facts do not add up to true.

Sound deductive inference from true premises to true conclusions adds up to true.
Any other equivalent representational system also adds up to true.
Nothing else adds up to true.

I really did provide the means to eliminate incompleteness from all formal systems.
Incompleteness cannot be expressed in any formal system implementing my changes.

[Logik]

I really did provide the means to eliminate incompleteness from all formal systems.
Incompleteness cannot be expressed in any formal system implementing my changes.

And I simply pointed out to you that all of the "incompleteness" you have removed from your formal system now hides behind one term "adds up".

Sufficiency.

[PeteOlcott]

I really did provide the means to eliminate incompleteness from all formal systems.
Incompleteness cannot be expressed in any formal system implementing my changes.

And I simply pointed out to you that all of the "incompleteness" you have removed from your formal system now hides behind one term "adds up".

Sufficiency.

Within the specific context of the Tarski proof
(not all the other extraneous stuff that you brought up) how so?

The ONLY thing that I did was make undecidability inexpressible,
that has nothing to do with sufficiency, it remains unchanged.

[Logik]

Within the specific context of the Tarski proof
(not all the other extraneous stuff that you brought up) how so?

Because you keep trying to put up artificial goal posts like the "within the context of the tarski proof".

The proof doesn't exist in a vacuum. And no matter how hard you try to create this vacuum - it's artificial.

That's the pitfall of Type 0 Chomsky grammars. Symbols have no meaning without context.

The ONLY thing that I did was make undecidability inexpressible,
that has nothing to do with sufficiency, it remains unchanged.

Why do you want to make decidability inexpressible?!?!

How would I express it to you then?

[PeteOlcott]

Within the specific context of the Tarski proof
(not all the other extraneous stuff that you brought up) how so?

Because you keep trying to put up artificial goal posts like the "within the context of the tarski proof".

The proof doesn't exist in a vacuum. And no matter how hard you try to create this vacuum - it's artificial.

That's the pitfall of Type 0 Chomsky grammars. Symbols have no meaning without context.

The ONLY thing that I did was make undecidability inexpressible,
that has nothing to do with sufficiency, it remains unchanged.

Why do you want to make decidability inexpressible?!?!

How would I express it to you then?

All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences.

All of my attention is focused on refuting this one sentence which is the generalized conclusion of both the Tarski and Gödel proofs.

My reasons for doing this are extraneous to whether or not I did this. Can you stay focused on this until it is resolved?

[Logik]

All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences.

All of my attention is focused on refuting this one sentence which is the generalized conclusion of both the Tarski and Gödel proofs.

My reasons for doing this are extraneous to whether or not I did this. Can you stay focused on this until it is resolved?

You will have much better luck coming from a Chomsky angle.

Learn about compilers. Invent your own, super-duper expressive language, write its compiler in itself.

You will gain intuitions/concepts from direct experience that are really difficult to communicate in English.

But just off the top of my head. Here is an undecidable sentence:

for all x: x = x, x ∈ Integers

It's an infinite loop.

[PeteOlcott]

All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences.

All of my attention is focused on refuting this one sentence which is the generalized conclusion of both the Tarski and Gödel proofs.

My reasons for doing this are extraneous to whether or not I did this. Can you stay focused on this until it is resolved?

You will have much better luck coming from a Chomsky angle.

Learn about compilers. Invent your own, super-duper expressive language, write its compiler in itself.

You will gain intuitions/concepts from direct experience that are really difficult to communicate in English.

I have already completely accomplished this in totality.
You may be able to validate my results in as little as five minutes
of concentrated effort.

I have already written compilers. I have already created whole
new formal systems with unlimited expressive power. All this
is moot. You only have to have very focused concentration on
the original message of this single post.

[Logik]

I have already completely accomplished this in totality.
You may be able to validate my results in as little as five minutes
of concentrated effort.

I have already written compilers. I have already created whole
new formal systems with unlimited expressive power. All this
is moot. You only have to have very focused concentration on
the original message of this single post.

OK, but I have a mind for spotting falsifiers.

So tell me how you would decide this sentence in your system:

for all x: x = x, x ∈ Integers

My intuition tells me you will appeal to the identity axiom.

[PeteOlcott]

I have already completely accomplished this in totality.
You may be able to validate my results in as little as five minutes
of concentrated effort.

I have already written compilers. I have already created whole
new formal systems with unlimited expressive power. All this
is moot. You only have to have very focused concentration on
the original message of this single post.

OK, but I have a mind for spotting falsifiers.

So tell me how you would decide this sentence in your system:

for all x: x = x, x ∈ Integers

My intuition tells me you will appeal to the identity axiom.

I will give you the simplest answer. That expression would be true.
For the purpose of this post all inference is entirely on the basis of
the conventional meaning of the logic symbols, thus no axioms are needed at all.

[Logik]

I will give you the simplest answer. That expression would be true.

1. How did you decide that?
2. https://repl.it/repls/AcclaimedJubilantTasks

[PeteOlcott]

I will give you the simplest answer. That expression would be true.

How did you decide that?

The conventional meaning of the logic symbols.

[Logik]

The conventional meaning of the logic symbols.

https://repl.it/repls/AcclaimedJubilantTasks

The notion of "conventional" doesn't work with semantics.

The meaning of "=" doesn't work with non-numbers.

What does it mean to compare one cat to another cat? Are you testing for identity or type?

[PeteOlcott]

The conventional meaning of the logic symbols.

https://repl.it/repls/AcclaimedJubilantTasks

The notion of "conventional" doesn't work with semantics.

Although you might not understand how it does, it still does.

[Logik]

The conventional meaning of the logic symbols.

https://repl.it/repls/AcclaimedJubilantTasks

The notion of "conventional" doesn't work with semantics.

Although you might not understand how it does, it still does.

OK, if you are going to lecture me on things you have nothing other than academic experience with, I am out.

What does it mean to compare one cat to another cat? Are you testing for identity or type?