Tarski Undefinability Theorem Succinctly Refuted

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PeteOlcott
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by PeteOlcott » Mon Apr 08, 2019 8:29 pm

Logik wrote:
Mon Apr 08, 2019 4:17 pm
PeteOlcott wrote:
Tue Apr 02, 2019 9:48 pm
Tarski Undefinability Theorem Succinctly Refuted
https://www.researchgate.net/publicatio ... ly_Refuted
I have stated it over and over again (and I keep demonstrating it).

Provide a logical statement which you think should evaluate to True or False.
This is the logical statement:
3) x ∉ Pr if and only if x ∈ Tr // page 275

This is the context
http://liarparadox.org/Tarski_Proof_275_276.pdf
Logik wrote:
Mon Apr 08, 2019 4:17 pm
IF I am allowed to control the value of any of your inputs (e.g the context) I will invent you a system (input to your framework) in which your theorem evaluates as False when you expect it to be True. AND a system in which your theorem evaluates as True when you expect it to be False.
You don't get to specify the context.

Logik
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Logik » Mon Apr 08, 2019 8:36 pm

PeteOlcott wrote:
Mon Apr 08, 2019 8:29 pm
This is the logical statement:
3) x ∉ Pr if and only if x ∈ Tr // page 275

This is the context
http://liarparadox.org/Tarski_Proof_275_276.pdf
No. You don't understand what "context' or "provable" means.

The (interpretative) context defines your grammar and semantics. The compiler/interpreter is your context.

"Provable" means an algorithm that satisfies your propositions.
An algorithm that decides whether x ∉ P given x and Pr
Another algorithm that decides whether x ∈ Tr given x and Tr.
And finally, an algorithm to decide if x ∉ P Implies x ∈ Tr is satisfied.
PeteOlcott wrote:
Mon Apr 08, 2019 8:29 pm
You don't get to specify the context.
Reality disagrees.

Everything in your context is either explicitly defined - or it doesn't exist.

PeteOlcott
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by PeteOlcott » Mon Apr 08, 2019 9:42 pm

Logik wrote:
Mon Apr 08, 2019 8:36 pm
PeteOlcott wrote:
Mon Apr 08, 2019 8:29 pm
This is the logical statement:
3) x ∉ Pr if and only if x ∈ Tr // page 275

This is the context
http://liarparadox.org/Tarski_Proof_275_276.pdf
No. You don't understand what "context' or "provable" means.

The (interpretative) context defines your grammar and semantics. The compiler/interpreter is your context.

"Provable" means an algorithm that satisfies your propositions.
An algorithm that decides whether x ∉ P given x and Pr
Another algorithm that decides whether x ∈ Tr given x and Tr.
And finally, an algorithm to decide if x ∉ P Implies x ∈ Tr is satisfied.
PeteOlcott wrote:
Mon Apr 08, 2019 8:29 pm
You don't get to specify the context.
Reality disagrees.

Everything in your context is either explicitly defined - or it doesn't exist.
In the above case the semantic meaning specified by Tarski governs the
interpretation of his proof.

You don't get to specify any other context besides Tarski and continue to
talk to me. That is the reality of it.

PeteOlcott
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by PeteOlcott » Tue Apr 09, 2019 12:00 am

Logik wrote:
Mon Apr 08, 2019 8:36 pm

"Provable" means an algorithm that satisfies your propositions.
An algorithm that decides whether x ∉ P given x and Pr
Another algorithm that decides whether x ∈ Tr given x and Tr.
And finally, an algorithm to decide if x ∉ P Implies x ∈ Tr is satisfied.
I do totally agree with this part although one is not free to form any algorithm if
one intends to conform to the actual notion of truth.

The algorithm must be based on the preexisting set of conceptions as
they are and is not free to represent the concept of a dog as a kind of cat.

One could make an algorithm that decides that anything that is an ice cream sundae
is true and everything else is false.

In this case the algorithm would essentially just be a liar.

Logik
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Logik » Tue Apr 09, 2019 7:40 am

PeteOlcott wrote:
Tue Apr 09, 2019 12:00 am
I do totally agree with this part although one is not free to form any algorithm if
one intends to conform to the actual notion of truth.
There is no single, universal, generally accepted notion of "truth" to be conformed to.
There are as many theories of truth as there are philosophers.

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

PeteOlcott wrote:
Tue Apr 09, 2019 12:00 am
The algorithm must be based on the preexisting set of conceptions as
they are and is not free to represent the concept of a dog as a kind of cat.

One could make an algorithm that decides that anything that is an ice cream sundae
is true and everything else is false.

In this case the algorithm would essentially just be a liar.
You are missing something really, really vital in your own cognition.

Before you know whether something is a dog or a cat first you have to recognize it for what it is. Pattern-matching.
Dogs and cats are difficult to confuse, so that's not a good example, but lets say you have to determine whether something is a dog or a wolf.

If you incorrectly classify a god as a wolf, or a wolf as a dog - you've just made an error. Type I and Type II errors

The easiest way to demonstrate this gap in recognizing the role of recognition is to ask you this question:

Is this true or false? A = А

The answer is here: https://repl.it/repls/RoastedVainQueryplan

Now. Admit that you got the answer wrong and tell me. Were you lying?

Logik
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Logik » Tue Apr 09, 2019 7:45 am

PeteOlcott wrote:
Mon Apr 08, 2019 9:42 pm
In the above case the semantic meaning specified by Tarski governs the
interpretation of his proof.
How do you know that you are interpreting the specification the way Tarski intended it to be interpreted?

Tarski made the specification in system T (his own mind)
You are parsing the specification in system P (your mind).

Are you sure T(specification) ⇔ P(specification) ?

As I already argued, you ignore intentionality.

The fundamental problem with your approach is that you have no universal system for parsing the grammar, syntax and semantic rules.

Which is precisely the problem a compiler/interpreter solves.
PeteOlcott wrote:
Mon Apr 08, 2019 9:42 pm
You don't get to specify any other context besides Tarski and continue to
talk to me. That is the reality of it.
Yes. I do. Look. I am doing it right now.

I have switched contexts and I am still talking to you.

Because all the "rules" you have laid down are best intentions, but unenforceable in practice. And if rules can't be enforced, they will be broken. Whether by accident or by intent. Might as well be sooner rather than later.

That is the reality of it ;)

It is almost as if you don't understand why use computers for boring, repetitive tasks. Because they are REALLY GOOD at following rules. Over and over and over.

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Speakpigeon
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Re: Tarski Undefinability Theorem Reexamined

Post by Speakpigeon » Wed Apr 17, 2019 10:20 am

A_Seagull wrote:
Thu Apr 04, 2019 9:50 pm
PeteOlcott wrote:
Thu Apr 04, 2019 4:06 pm
A_Seagull wrote:
Thu Apr 04, 2019 10:28 am
Lol
Unless you are just playing games I would estimate that you may not have a deep enough
understanding of these things to provide any useful feedback.
Thank you, but I prefer not to debate with children.
Your unwillingness to articulate and argue your claims seems a recurring feature.
So, I'm intrigued.
Could you direct me to at least some of your posts where you think you display your wits and knowledge by articulating your ideas and arguing your point in an intelligent and rational way?
I don't expect any meaningful answer but maybe you could surprise me.
Could you direct me at the thread you've started, too. I can't find them.
EB

Logik
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Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Wed Apr 17, 2019 11:09 am

Speakpigeon wrote:
Wed Apr 17, 2019 10:20 am
Your unwillingness to articulate and argue your claims seems a recurring feature.
(...)
Could you direct me at the thread you've started, too. I can't find them.
Your willingness to argue for the sake of it and past the point where your premises have been proven flawed is a recurring feature.

Both in threads you've started and in threads you respond to.

It's quite tedious to deal with your ignorance.

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A_Seagull
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Re: Tarski Undefinability Theorem Reexamined

Post by A_Seagull » Wed Apr 17, 2019 9:46 pm

Speakpigeon wrote:
Wed Apr 17, 2019 10:20 am
A_Seagull wrote:
Thu Apr 04, 2019 9:50 pm
PeteOlcott wrote:
Thu Apr 04, 2019 4:06 pm

Unless you are just playing games I would estimate that you may not have a deep enough
understanding of these things to provide any useful feedback.
Thank you, but I prefer not to debate with children.
Your unwillingness to articulate and argue your claims seems a recurring feature.
So, I'm intrigued.
Could you direct me to at least some of your posts where you think you display your wits and knowledge by articulating your ideas and arguing your point in an intelligent and rational way?
I don't expect any meaningful answer but maybe you could surprise me.
Could you direct me at the thread you've started, too. I can't find them.
EB
The short answer is .. No.

The slightly longer answer is: No, No, no..

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Arising_uk
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Re: Tarski Undefinability Theorem Reexamined

Post by Arising_uk » Wed Apr 17, 2019 11:22 pm

Logik wrote:... But here is the TL;DR. Physics produces models of the world in the language of Mathematics. As physics discovers new phenomena (ones that we have never experienced before), phenomena for which we have no language for - physicists go looking to Mathematicians for the language to express this experience. The output of Physics is Mathematics. ...
That is theoretical physics where does experimental physics lie in this model?

Logik
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Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Wed Apr 17, 2019 11:47 pm

Arising_uk wrote:
Wed Apr 17, 2019 11:22 pm
That is theoretical physics where does experimental physics lie in this model?
Not at all. Park physics aside for a second. Language (logos, logic) is a tool for self-expression.

A tool for describing/narrating your own experiences. So if you can construct poetry with English, you can construct poetry with Mathematics.
You just need good command and understanding of your tools. And (the important bit) no rules!

As Richard Feynman said: What I cannot create I do not understand.

Computer scientists create formal languages.

What experimental physicists have been doing for ever and ever is run to Mathematicians and ask "Do you have anything that can help here?".
And what mathematicians have been bitching about is how Physicists bastardize their "beautiful mathematics".

What boggles my mind is that physicists can't construct the Mathematics they need from first principles! What? Just bloody describe what you experienced!

Express what happened in a formal language. Program dammit ! I side with physicists here. Screw "beauty" - if it's stupid an it works it isn't stupid.

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A_Seagull
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Re: Tarski Undefinability Theorem Reexamined

Post by A_Seagull » Thu Apr 18, 2019 5:37 am

Arising_uk wrote:
Wed Apr 17, 2019 11:22 pm
Logik wrote:... But here is the TL;DR. Physics produces models of the world in the language of Mathematics. As physics discovers new phenomena (ones that we have never experienced before), phenomena for which we have no language for - physicists go looking to Mathematicians for the language to express this experience. The output of Physics is Mathematics. ...
That is theoretical physics where does experimental physics lie in this model?
The theoretical physics must match the experimental results... if not it goes out the window.

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Speakpigeon
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Speakpigeon » Thu Apr 18, 2019 7:57 am

Most of the time, for new theories, physicists have to invent themselves the mathematical tools necessary to their theories. And for a long while, mathematical theories were models of physical entities, or modelled after, or inspired by, physical entities, like arithmetic or Euclid's geometry.
EB

Logik
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Logik » Thu Apr 18, 2019 8:02 am

Speakpigeon wrote:
Thu Apr 18, 2019 7:57 am
Most of the time, for new theories, physicists have to invent themselves the mathematical tools necessary to their theories. And for a long while, mathematical theories were models of physical entities, or modelled after, or inspired by, physical entities, like arithmetic or Euclid's geometry.
EB
That is all mathematics and logic are. Models.
That is all concepts are. Models.

That is all science does. Constructs models of reality, however all models are wrong - some are useful.

The map is not and never will never be the territory.

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Speakpigeon
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Re: Tarski Undefinability Theorem Succinctly Refuted

Post by Speakpigeon » Thu Apr 18, 2019 8:10 am

String theory shows that theoreticians don't work by constantly checking that their theories "match physical results".
Copernicus caused a revolution by asserting something that contradicts the evidence of provided by our senses about the physical world that the Sun moves in the sky.
Astronomers maintained for a long time their belief in Newton's theory of Gravitation even though their own observations repeatedly and consistently showed the orbit of Mercury disproved Newton. Until Einstein could precisely explain the previously unexplained 43'" precession of the orbit of Mercury.
Even now, many if not most scientists still don't see Newton's theory as wrong despite the evidence.
EB

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