Formalizing Natural Language Semantics

[PeteOlcott]

If you intentionally contradict yourself that makes you a liar and a waste of my time.

The system you are building is complete (by design), therefore it is necessarily inconsistent.

You know this (because Gödel'), and yet you are still doing it! One can safely infer that you are doing it knowingly and intentionally.

You are intentionally contradicting yourself. That makes you a liar and a waste of everybody's time.

(1) I can show that the Liar Paradox is an ill-formed truth-bearer.
(2) Since Tarski's whole Undefinability Theorem uses the Liar Paradox as it basis (1) Shows Tarski has no basis.
(3) Since Tarski Undefinability is analogous to Gödel Incompleteness showing that Tarski is wrong proves that Gödel is also wrong.

As easy as 1,2,3 as long as you follow my detailed reasoning of 1,2,3.

[Skepdick]

(1) I can show that the Liar Paradox is an ill-formed truth-bearer.

Maybe in your syntax. Not in mine.

(2) Since Tarski's whole Undefinability Theorem uses the Liar Paradox as it basis (1) Shows Tarski has no basis.

Sure. Quine has pointed out that analyticity is circular. Girard makes fun of Tarski through a lot of his work.

(3) Since Tarski Undefinability is analogous to Gödel Incompleteness showing that Tarski is wrong proves that Gödel is also wrong.

ROFL. That's not how it works. Just because that one proof of incompleteness is wrong doesn't mean that incompleteness (in general) is wrong.

This is called the fallacy fallacy.

And if you quit being so damn dogmatic about it, you would've noticed by now that Turing's halting problem is not formulated either in Tarski or Gödel's frameworks. It stands on its own two feet. It's such a simple proof that as far as I am concerned it is conceptually prior (though, historically latter) to Gödel or Tarski.

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.

As easy as 1,2,3 as long as you follow my detailed reasoning of 1,2,3.

I am not interested in your reasoning. I am interested in your universal algorithm. When it fails to do what you promise it will do, then you will know you are wrong.

[Scott Mayers]

Personally, I see BOTH as perspectively correct. And therein lies the problem. To be 'complete' in some universal logic, it may be ill-fated for requiring trivialize satisfaction. But it is nevertheless 'true' of Totality and if one wants to understand reality, one has to recognize the 'superiority' of such a presentation of a logic that can show HOW you also lead to the non-trivial logic of a subset of Totality.

So I think both of you are being stubborn here. Why not just express the 'conditions' you intend to get from the different logical approaches. Both are provably connected inimately just as Integration in Calculus is opposing to Differentiation in logic but meets up in the center as the "Fundamental Theorem of Calculus" nevertheless.

Because I share what both of you guys share in respect of logic, it would be interesting to see if we could just permit each to express the logic with the caveate of some 'condition' expressed prior to arguing whether the condition is or is not satisfying to all.

[Skepdick]

Personally, I see BOTH as perspectively correct. And therein lies the problem.

Uhuh!!! So you see that the halting problem BOTH has a universal solution and doesn't have a universal solution.

To be 'complete' in some universal logic,

In this 'universal logic' of yours, is the halting problem universally solvable or not?

it may be ill-fated for requiring trivialize satisfaction.

I think you are over-stating the severity of the problem.

But it is nevertheless 'true' of Totality and if one wants to understand reality, one has to recognize the 'superiority' of such a presentation of a logic that can show HOW you also lead to the non-trivial logic of a subset of Totality.

The 'superiority' of such a logic comes at a cost. If you want Totality then you have to give up recursion. You have to give up Turing completeness. By insisting I give up recursion and Turing completeness you are making my formal languages LESS EXPRESSIVE..

Because Turing Completeness buys you expressive power

And so, like all grown ups - you have to make a choice. if you are choosing to ride the fence when all evidence points to you that the fence does not exist - so be it.

So I think both of you are being stubborn here. Why not just express the 'conditions' you intend to get from the different logical approaches.

Because Pete is trying to limit my EXPRESSIVE POWER, by insisting that I am not 'allowed to use' certain grammatical structures.
And the only justification Pete offers in return is "I can't parse/evaluate it - so you are not allowed to use it!"
And then Pete is trying to 'shame me' into accepting his restrictions on my language by calling me a 'liar' - because that's the only way he knows how to control the narrative.

Pete is a grammar nazi and I have zero tolerance for his ilk.

it would be interesting to see if we could just permit each to express the logic with the caveate of some 'condition' expressed prior to arguing whether the condition is or is not satisfying to all.

Yeah! That is precisely what I am arguing for.

I insist that I am permitted to express a contradiction! And if your logic doesn't allow me to do that - fuck your logic.

Language/logic is for self-expression. You are either allowed to contradict yourself, or you have no free speech.

[PeteOlcott]

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

http://liarparadox.org/Peter_Linz_HP%28 ... 319%29.pdf

[Skepdick]

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

Pete, you are a moron.

Proving that the Halting proofs are incorrect, is not the same thing as solving the halting problem.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

That is not a universal solution to the halting problem. That is just an algorithm which provably halts.
You have re-invented Walther recursion.

In order to solve the halting problem I expect you to provide an algorithm, which can decide whether an arbitrary program, written in an arbitrary language will halt.

The word "arbitrary" means that you don't get to choose the program or the language in which it's written in.

It means that I get to choose the program/language. it also means that your algorithm MUST WORK for ALL programs written in ALL programming languages.

[PeteOlcott]

Personally, I see BOTH as perspectively correct. And therein lies the problem. To be 'complete' in some universal logic, it may be ill-fated for requiring trivialize satisfaction. But it is nevertheless 'true' of Totality and if one wants to understand reality, one has to recognize the 'superiority' of such a presentation of a logic that can show HOW you also lead to the non-trivial logic of a subset of Totality.

So I think both of you are being stubborn here. Why not just express the 'conditions' you intend to get from the different logical approaches. Both are provably connected inimately just as Integration in Calculus is opposing to Differentiation in logic but meets up in the center as the "Fundamental Theorem of Calculus" nevertheless.

Because I share what both of you guys share in respect of logic, it would be interesting to see if we could just permit each to express the logic with the caveate of some 'condition' expressed prior to arguing whether the condition is or is not satisfying to all.

>>>>>>>> Some expressions of language are stipulated to be true and some
>>>>>>>> relations between expressions of language are stipulated to be
>>>>>>>> truth preserving.

Expressions of language that are stipulated to be true can be verified as completely true entirely based on their meaning.

Any expression of language in this set can be proved to be true by tracing through the connected set of meanings that makes this expression of language true.

From the stipulated definitions that [all dogs are mammals] and [all mammals are animals] we can conclude that [all dogs are animals].

Copyright 2020 Pete Olcott

[Scott Mayers]

Personally, I see BOTH as perspectively correct. And therein lies the problem.

Uhuh!!! So you see that the halting problem BOTH has a universal solution and doesn't have a universal solution.

To be 'complete' in some universal logic,

In this 'universal logic' of yours, is the halting problem universally solvable or not?

No. It is incomplete with respect to a finite time. If you allow time as a static dimension, then technically this could solve the problem but would require a rule that uses contradiction to SEPARATE into two different universes and what I use for my theory. But as you already know, this is considered, "trivial" (permits a third value) and makes many particular problems still non-resolvable other than as "indeterminate" as an answer.

Because Totality would contain absolutely all, the kind of machine that would permit completion is itself Totality which is never "complete" but you can still close it in using limits and Calculus. I don't know if I care to be concerned about it specifically because my own theory will likely not be even presentable in my lifetime to any satisfaction. But it would be something that would/should be a part of it at some point to give others confidence that such a theory itself is possible prior to expecting anyone to read such a paper if I get that complete.

But it is nevertheless 'true' of Totality and if one wants to understand reality, one has to recognize the 'superiority' of such a presentation of a logic that can show HOW you also lead to the non-trivial logic of a subset of Totality.

The 'superiority' of such a logic comes at a cost. If you want Totality then you have to give up recursion. You have to give up Turing completeness. By insisting I give up recursion and Turing completeness you are making my formal languages LESS EXPRESSIVE..

Because Turing Completeness buys you expressive power

And so, like all grown ups - you have to make a choice. if you are choosing to ride the fence when all evidence points to you that the fence does not exist - so be it.

I don't know what you are thinking on recursion. But as I just mentioned, with respect to Totality, it is 'complete' by label and yet never complete in 'times'. But given all possibilities in Totality takes in all the continuum of infintes, including time, physics itself would be 'complete' with respect to it but not necessarily provable by expected standards. It doesn't exclude any possibility.

it would be interesting to see if we could just permit each to express the logic with the caveate of some 'condition' expressed prior to arguing whether the condition is or is not satisfying to all.

Yeah! That is precisely what I am arguing for.

I insist that I am permitted to express a contradiction! And if your logic doesn't allow me to do that - fuck your logic.

Language/logic is for self-expression. You are either allowed to contradict yourself, or you have no free speech.
[/quote]
?? You sound schizoid here. What are you meaning when you say that "I insist that I am permitted to express a contradiction!" if you are already in agreement to the Incompleteness Theorem you are challenging Pete about?

My approach is to accept multivariable realities and have a means to construct/reconstruct what reality is from an Absolute Nothing as the only constant and pointers to it or other pointers, in a set theoretical way.

[Scott Mayers]

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

http://liarparadox.org/Peter_Linz_HP%28 ... 319%29.pdf

We already recognize that you can solve any particular problem by careful exhaustion. What can't be done is to have a finite machine be able to FIND ALL the possible programs as 'haltable' finitely.

[Skepdick]

No. It is incomplete with respect to a finite time.

That's not really in your control, is it? It depends entirely on the time-complexity of the problem and the size of your inputs.

If you allow time as a static dimension, then technically this could solve the problem but would require a rule that uses contradiction to SEPARATE into two different universes and what I use for my theory.

"Separating into two different universes" is nothing more than a non-deterministic Turing machine cloning itself. Concurrency/Parallelism. You are arriving at the doorstep of P vs NP.

Because Totality would contain absolutely all, the kind of machine that would permit completion is itself Totality which is never "complete" but you can still close it in using limits and Calculus.

Naturally. Numerical methods (sheer brute force) is the only way to solve some problems. Whether you will be successful or not at this still depends on the computational resources at your disposal. Space, Time, Entropy.

I don't know what you are thinking on recursion. But as I just mentioned, with respect to Totality, it is 'complete' by label and yet never complete in 'times'. But given all possibilities in Totality takes in all the continuum of infintes, including time, physics itself would be 'complete' with respect to it but not necessarily provable by expected standards. It doesn't exclude any possibility.

You are confusing your perspectives here. A priori vs a posteriori.

A posteriori any function which has halted (past tense) is "Total". This is an empirical assertion and needs not be "proven".
A priori some functions can be proven to be Total. E.g we can prove that they WILL halt (given enough time).

Neither of those two functions address the issue of totality with respect to recursive functions. There are some recursive functions that may not terminate. EVER. Even if they had infinite time/memory - they will continue to run for for eternity. One trivial example of such a function is an infinite loop.

?? You sound schizoid here. What are you meaning when you say that "I insist that I am permitted to express a contradiction!" if you are already in agreement to the Incompleteness Theorem you are challenging Pete about?

I am in agreement with the incompleteness theorem AND the completeness theorem.

I agree in as much as I understand the implications of each theorem. There exists a trade-off (read: choice) between consistency, completeness and unrestricted recursion.

Choose any two.

Pete has chosen Consistency + Completeness.. Therefore he has given up the expressive power of recursion for Walther recursion which is provably terminating (read: finite) form of recursion.

That may be an acceptable loss to Pete, but it's not an acceptable loss for me.

[PeteOlcott]

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

http://liarparadox.org/Peter_Linz_HP%28 ... 319%29.pdf

We already recognize that you can solve any particular problem by careful exhaustion. What can't be done is to have a finite machine be able to FIND ALL the possible programs as 'haltable' finitely.

What I have accomplished is deriving the complete encoding (written in x86 machine language) of a halt decider that decides halting for the set of halting problem counter-examples as defined by the Peter Linz H_Hat.

[Skepdick]

a halt decider that decides halting for the set of halting problem counter-examples.

Pete, you are handling counter-examples on case-by-case basis. You are literally demonstrating that your solution is not universal!

How much more obvious than that does it get?

[PeteOlcott]

a halt decider that decides halting for the set of halting problem counter-examples.

Pete, you are handling counter-examples on case-by-case basis. You are literally demonstrating that your solution is not universal!

How much more obvious than that does it get?

On what basis could you possibly justify the presumption that I am handling the counter-examples on a case by case basis? The Peter Linz H_Hat is a template that species an infinite set of Turing Machine descriptions.

[Skepdick]

On what basis could you possibly justify the presumption that I am handling the counter-examples on a case by case basis?

1. On the basis of you saying so.

What I have accomplished is deriving the complete encoding (written in x86 machine language) of a halt decider that decides halting for the set of halting problem counter-examples as defined by the Peter Linz H_Hat.

2. If you had a universal solution you would've published the source code by now.

The Peter Linz H_Hat is a template that species an infinite set of Turing Machine descriptions.

Ohhh. You have an actual infinite set of Turing Machines? Show it to me!

[PeteOlcott]

To prove the Halting problem wrong is to produce an algorithm that solves the halting problem universally. We are still waiting.

To prove that the Halting Problem proofs are incorrect I only have to show how
halting is decided for the Halting Problem proof counter-examples.

I now have written the Peter Linz H_Hat in "C" so that it examines the x86
machine language of itself and decides halting on itself.

http://liarparadox.org/Peter_Linz_HP%28 ... 319%29.pdf

We already recognize that you can solve any particular problem by careful exhaustion. What can't be done is to have a finite machine be able to FIND ALL the possible programs as 'haltable' finitely.

All of the conventional self referential Halting Problem counter-examples are shown to be decidable by my x86 encoded halt decider.