Prolog already refutes Tarski Undefinability

[Logik]

I spent 18 months designing this ultimate meta-language.
https://www.researchgate.net/publicatio ... y_YACC_BNF

Ohhh, you designed THE ULTIMATE meta-langauge?

Did you get any feedback from people like me?
Who have a particular use for meta-languages and a particular need for nonrestrictive semantics?

Your meta-language is nowhere near as expressive as Python.
In the same way that even though Python is written in C, C is nowhere near as expressive as Python.

What you cannot do is form undecidable sentences. The whole idea of
undecidable sentences was merely an artifact of insufficiently expressive
formal systems.

That's no my experience with formal languages. If you can write a parser you can parse it.

https://en.wikipedia.org/wiki/Regular_language

[PeteOlcott]

I spent 18 months designing this ultimate meta-language.
https://www.researchgate.net/publicatio ... y_YACC_BNF

Ohhh, you designed THE ULTIMATE meta-langauge?

Did you get any feedback from people like me?
Who have a particular use for meta-languages and a particular need for nonrestrictive semantics?

The ultimate Tarski metalanguage that can formalize any concept known to man.
More technically it expresses any order of higher order logic with explicit types
and a provability predicate.

I am not sure how it (or its cousin Lambda Calculus) could process strings of actual
characters. No one else could ever explain this to me.

[PeteOlcott]

What you cannot do is form undecidable sentences. The whole idea of
undecidable sentences was merely an artifact of insufficiently expressive
formal systems.

That's no my experience with formal languages. If you can write a parser you can parse it.

https://en.wikipedia.org/wiki/Regular_language

Of course its not your experience or anyone else's experience I just created this:
https://www.researchgate.net/publicatio ... ly_Refuted
Are you aware that a regular language is the weakest kind?

[Logik]

Of course its not your experience or anyone else's experience I just created this:
https://www.researchgate.net/publicatio ... ly_Refuted
Are you aware that a regular language is the weakest kind?

How do you measure "weakness" ?

[Logik]

Of course its not your experience or anyone else's experience I just created this:
https://www.researchgate.net/publicatio ... ly_Refuted

Oh my goodness. You have a terrible terrible misconception going on in your head.
You think academia is the only place where knowledge is acquired.

You think you just discovered something that has been intuitive to every practicing computer scientist for the last 50+ years



Experience (meaning!) comes before formalization.

[PeteOlcott]

Of course its not your experience or anyone else's experience I just created this:
https://www.researchgate.net/publicatio ... ly_Refuted
Are you aware that a regular language is the weakest kind?

How do you measure "weakness" ?

Expressiveness:
https://en.wikipedia.org/wiki/Chomsky_hierarchy

[Logik]

Expressiveness:
https://en.wikipedia.org/wiki/Chomsky_hierarchy

SO then I don't understand your point?

IF we had infinite memory, Python is a Type 0 grammar.

That's not a limitation of the language. It's a limitation imposed by Physics.

[PeteOlcott]

Of course its not your experience or anyone else's experience I just created this:
https://www.researchgate.net/publicatio ... ly_Refuted

Oh my goodness. You have a terrible terrible misconception going on in your head.
You think academia is the only place where knowledge is acquired.

You think you just discovered something that has been intuitive to every practicing computer scientist for the last 50+ years



Experience (meaning!) comes before formalization.

So how come all these smart guys never called out Kurt Gödel's big mistake?
The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F.
Raatikainen, Panu, "Gödel's Incompleteness Theorems", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition)

This refutes the above there are no such statements in any formal system F
https://www.researchgate.net/publicatio ... ly_Refuted

[Logik]

So how come all these smart guys never called out Kurt Gödel's big mistake?
The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F.
Raatikainen, Panu, "Gödel's Incompleteness Theorems", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition)

Because it's not a mistake. Godel talks about the INTEGERS.

A sufficiently powerful system can express things WAY BEYOND integers.

Also... they have. Constructive mathematicians haven't been giving a damn about Godel for ages.

The Halting problem and computational complexity is where it's at. Godel needs not be refuted because he's irrelevant.

[Logik]

Expressiveness:
https://en.wikipedia.org/wiki/Chomsky_hierarchy

Are you familiar with the notion of para-consistency?

https://en.wikipedia.org/wiki/Paraconsistent_logic

Paraconsistent logics are propositionally weaker than classical logic; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate everything that classical logic does. In some sense, then, paraconsistent logic is more conservative or cautious than classical logic. It is due to such conservativeness that paraconsistent languages can be more expressive than their classical counterparts including the hierarchy of metalanguages due to Alfred Tarski et al. According to Solomon Feferman [1984]: "…natural language abounds with directly or indirectly self-referential yet apparently harmless expressions—all of which are excluded from the Tarskian framework." This expressive limitation can be overcome in paraconsistent logic.

Python allows me to construct para-consistent logics!
That is what error-handling is all about.

English is a para-consistent logic. That's why is expressively more powerful than formalisms. Because you can ignore errors.

[PeteOlcott]

So how come all these smart guys never called out Kurt Gödel's big mistake?
The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F.
Raatikainen, Panu, "Gödel's Incompleteness Theorems", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition)

Because it's not a mistake. Godel talks about the INTEGERS.

A sufficiently powerful system can express things WAY BEYOND integers.

Also... they have. Constructive mathematicians haven't been giving a damn about Godel for ages.

The Halting problem and computational complexity is where it's at. Godel needs not be refuted because he's irrelevant.

His (and Tarski's) general result apply to formal systems of arithmetic AND GREATER, thus applying to every formal system.

I have also refuted this
http://liarparadox.org/Peter_Linz_HP(Pages_318-319).pdf

I have defined the precise algorithm such that H correctly decides halting for input pair: (Ĥ, Ĥ).
This result is generalizable to the other proofs.

[PeteOlcott]

Expressiveness:
https://en.wikipedia.org/wiki/Chomsky_hierarchy

Are you familiar with the notion of para-consistency?

https://en.wikipedia.org/wiki/Paraconsistent_logic

Paraconsistent logics are propositionally weaker than classical logic; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate everything that classical logic does. In some sense, then, paraconsistent logic is more conservative or cautious than classical logic. It is due to such conservativeness that paraconsistent languages can be more expressive than their classical counterparts including the hierarchy of metalanguages due to Alfred Tarski et al. According to Solomon Feferman [1984]: "…natural language abounds with directly or indirectly self-referential yet apparently harmless expressions—all of which are excluded from the Tarskian framework." This expressive limitation can be overcome in paraconsistent logic.

Python allows me to construct para-consistent logics!
That is what error-handling is all about.

English is a para-consistent logic. That's why is expressively more powerful than formalisms. Because you can ignore errors.

Yes it is simply a nutty idea that was tried out because no one had a decent solution for undecidability.

[Logik]

His (and Tarski's) general result apply to formal systems of arithmetic AND GREATER, thus applying to every formal system.

That is a conceptual non-starter for me. Arithmetic is not foundational to formal systems OR logic.

This is the paradigm disagreement I was talking about right at the beginning.
IF you accept set theory/arithmetic as foundational to Mathematics then Godel's work is valid
IF you accept type theory as foundational to Mathematics then Godel's work is irrelevant.

But, of course wtf explained this to you when he mentioned the axiom of choice.

AC applies to your own choice. What is the foundation of mathematics? Set theory or type theory?

BECAUSE you have CHOSEN type theory you are getting the results you are getting.

[Logik]

Yes it is simply a nutty idea that was tried out because no one had a decent solution for undecidability.

Nonsense dude. It's a nutty idea because the human mind can't store a billion GUIDs - one for every semantic.
It's a nutty idea because if you were in charge of "human knowledge" the dictionary would be list of GUIDs.

You thought Mandarin was bad with 100k hieroglyphs. You will invent a language that no human could learn in 100 lifetimes.
And therefore - you will build a system form which no knowledge can be extracted.

We equivocate and contradict each other ALL THE TIME. And it doesn't matter. Informal languages are a mess and that's why they work so well.
Because they are flexible and they evolve rapidly.

The notions of usability and indexing are foreign to you.
https://en.wikipedia.org/wiki/Term_indexing

Language (and thus logic) is just a tool.
https://www.youtube.com/watch?v=TDiENpmpY78

If you care to watch the video above you would recognize that a unified ontology is a pipe dream across different paradigms.
You are straddling paradigms! The set-theoretic and the type-theoretic.

[Logik]

Yes it is simply a nutty idea that was tried out because no one had a decent solution for undecidability.

Let me put it in far simpler terms. If you solved decidability - you have necessarily decided if P = NP.