Tarski Undefinability Theorem Succinctly Refuted

What is the basis for reason? And mathematics?

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PeteOlcott
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Re: Tarski Undefinability Theorem Reexamined

Post by PeteOlcott » Fri Apr 05, 2019 8:05 pm

Logik wrote:
Fri Apr 05, 2019 7:36 pm
wtf wrote:
Fri Apr 05, 2019 7:14 pm
Syntax is symbol manipulation. Semantics is meaning.
Interjection (or a rude derailment). Part of solving the symbol-grounding problem ( https://en.wikipedia.org/wiki/Symbol_grounding_problem ) is the unification of syntax and semantics.
Ah great it seems that you understand me. Tarski handled this problem by grounding and object language in a meta-language.
I show that this is unnecessary, the meta-language can ground itself directly within itself. All of semantics is simply
relations between concepts that could be expressed as relations between integers.

Gödel 1944
Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote:

By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, etc. (with a similar hierarchy for extensions), and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together.

Minimal Type Theory was designed to meet that spec:
https://www.researchgate.net/publicatio ... y_YACC_BNF

wtf
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Re: Tarski Undefinability Theorem Reexamined

Post by wtf » Fri Apr 05, 2019 8:11 pm

PeteOlcott wrote:
Fri Apr 05, 2019 7:58 pm
Not a deflection a necessary prerequisite to further communication.
Unless and and until you fully understand how semantics is expressed using syntax you don't know enough to critique me.
LOL

PeteOlcott
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Re: Tarski Undefinability Theorem Reexamined

Post by PeteOlcott » Fri Apr 05, 2019 8:20 pm

wtf wrote:
Fri Apr 05, 2019 8:11 pm
PeteOlcott wrote:
Fri Apr 05, 2019 7:58 pm
Not a deflection a necessary prerequisite to further communication.
Unless and and until you fully understand how semantics is expressed using syntax you don't know enough to critique me.
LOL
Logik wrote:
Fri Apr 05, 2019 7:36 pm
wtf wrote:
Fri Apr 05, 2019 7:14 pm
Syntax is symbol manipulation. Semantics is meaning.
Interjection (or a rude derailment). Part of solving the symbol-grounding problem ( https://en.wikipedia.org/wiki/Symbol_grounding_problem ) is the unification of syntax and semantics.
the unification of syntax and semantics, Something that you simply presume away.

Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 12:13 am

PeteOlcott wrote:
Fri Apr 05, 2019 8:20 pm
the unification of syntax and semantics, Something that you simply presume away.
Que?

I merely recognize that truth (or the meaning of truth) is semantic. First and foremost.

Everything else is mere mediums of communication and expression.

Logic is just another language.

Logik
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Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 12:19 am

PeteOlcott wrote:
Fri Apr 05, 2019 8:05 pm
Ah great it seems that you understand me. Tarski handled this problem by grounding and object language in a meta-language.
I show that this is unnecessary, the meta-language can ground itself directly within itself.
Language cannot ground itself because symbols cannot ground themselves.

A symbol departs "the ground" the moment it's uttered. Once having taken off it is grounded again when it is interpreted.

That which interprets the language is what grounds the symbol again.

The problem is that if I mean A, utter B, and you interpret that as C you have grounded my symbol incorrectly.

Encoding/decoding.

https://en.wikipedia.org/wiki/Encoding/ ... munication

Programming languages are grounded because they are deterministic. Such is the nature of computers.

PeteOlcott
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Re: Tarski Undefinability Theorem Reexamined

Post by PeteOlcott » Sat Apr 06, 2019 4:19 am

wtf wrote:
Fri Apr 05, 2019 8:11 pm
PeteOlcott wrote:
Fri Apr 05, 2019 7:58 pm
Not a deflection a necessary prerequisite to further communication.
Unless and and until you fully understand how semantics is expressed using syntax you don't know enough to critique me.
LOL
I was referring to WTF presuming it away, you seem to have correctly.
He dismissed what I said out-of-hand, I was pointing out that you did not
so two votee (you and I) to one (him).

PeteOlcott
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Re: Tarski Undefinability Theorem Reexamined

Post by PeteOlcott » Sat Apr 06, 2019 4:24 am

Logik wrote:
Sat Apr 06, 2019 12:19 am
PeteOlcott wrote:
Fri Apr 05, 2019 8:05 pm
Ah great it seems that you understand me. Tarski handled this problem by grounding and object language in a meta-language.
I show that this is unnecessary, the meta-language can ground itself directly within itself.
Language cannot ground itself because symbols cannot ground themselves.

A symbol departs "the ground" the moment it's uttered. Once having taken off it is grounded again when it is interpreted.

That which interprets the language is what grounds the symbol again.

The problem is that if I mean A, utter B, and you interpret that as C you have grounded my symbol incorrectly.

Encoding/decoding.

https://en.wikipedia.org/wiki/Encoding/ ... munication

Programming languages are grounded because they are deterministic. Such is the nature of computers.
When one assumes that certain symbols are tied to specific logic resolution
algorithms then symbols are merely infix notation for functions on strings.
In theory this could all be translated into Lambda Calculus equivalents.

In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings.

Logik
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Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 7:13 am

PeteOlcott wrote:
Sat Apr 06, 2019 4:24 am
When one assumes that certain symbols are tied to specific logic resolution
algorithms then symbols are merely infix notation for functions on strings.
In theory this could all be translated into Lambda Calculus equivalents.

In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings.
But you do understand that the expression/representation of strings is just language, right?

And language itself has no intrinsic meaning e.g semantics until interpreted.

wtf
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Re: Tarski Undefinability Theorem Reexamined

Post by wtf » Sat Apr 06, 2019 7:07 pm

PeteOlcott wrote:
Sat Apr 06, 2019 4:19 am
wtf wrote:
Fri Apr 05, 2019 8:11 pm
PeteOlcott wrote:
Fri Apr 05, 2019 7:58 pm
Not a deflection a necessary prerequisite to further communication.
Unless and and until you fully understand how semantics is expressed using syntax you don't know enough to critique me.
LOL
I was referring to WTF presuming it away, you seem to have correctly.
He dismissed what I said out-of-hand, I was pointing out that you did not
so two votee (you and I) to one (him).
Well Pete you've finally done it. You're talking to yourself and STILL not making sense.

wtf
Posts: 838
Joined: Tue Sep 08, 2015 11:36 pm

Re: Tarski Undefinability Theorem Reexamined

Post by wtf » Sat Apr 06, 2019 7:16 pm

Logik wrote:
Fri Apr 05, 2019 7:36 pm
My meaning is deterministic when interpreted by a physical machine called a computer. My words (bashing on a keyboard) have physical, real-world consequences (mutating memory on computers, altering voltages on routers transmitting packets etc. etc.).
I certainly agree with you that an abstract computation represented as an algorithm, has real-world consequences when implemented on a physical substrate. The Euclidean algorithm written down in a book is abstract. When I implement it on a supercomputer or a computer made out of logic gates built with dominos, the execution of that computation takes time, expends physical resources, and generates heat. [Annoying Youtube ad precedes really cool video].

But those things are not meaning. Example. I am sitting in my favorite chair reading a favorite book. The experience brings back memories of the first time I read that book, the people I knew and the experiences I was having at the time. That's meaning.

It's also true that to see what I'm reading I have an electric lamp plugged into the wall. The lamp draws electrical power from the wall socket, which is produced by the utility company. There's a physical flow of electrons.

But there is no meaning in the flow of electrons. The meaning is in my experience of reading the book.
Logik wrote:
Fri Apr 05, 2019 7:36 pm
I am intentionally pushing the buttons on my keyboard knowing that you are going to be reading this text very shortly.
Yes exactly. The electron flows enabled by the key presses are physical; but they are not the meaning. The meaning is inherent in the human intention behind the communication. You seem to be agreeing with me.
Logik wrote:
Fri Apr 05, 2019 7:36 pm
Bar for the fact that you may (mis?)interpret what I am saying I would be willing to argue for a position that computers ground symbols.
No, your own example shows that's wrong. The meaning is not in the electron flows. The meaning is in the human interpretation and motivation that causes you to press those particular keys, and that causes me to read and desire to respond.

Bit flipping has no meaning. Bits are flipped in a video game or a heart pacemaker. The bits don't care, the electrons don't care. Only the humans care. Living creatures impart meaning to the bit flipping. Which your own example seems to support.

Your laptop doesn't care that its circuits are used to watch cartoons or write the great American novel. It's you who cares. Syntax and bit flipping have no meaning. The meaning is supplied by humans.

A physical computation generates heat. I hope you are not arguing that the heat is the meaning of the computation. It's not. The meaning of the computation is supplied by humans.

Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 7:45 pm

wtf wrote:
Sat Apr 06, 2019 7:16 pm
But those things are not meaning. Example. I am sitting in my favorite chair reading a favorite book. The experience brings back memories of the first time I read that book, the people I knew and the experiences I was having at the time. That's meaning.
Memory recall is meaning? We can do that in algorithms.
wtf wrote:
Sat Apr 06, 2019 7:16 pm
But there is no meaning in the flow of electrons. The meaning is in my experience of reading the book.
Or the consequence of you reading the book. Reading triggers memory recall.
wtf wrote:
Sat Apr 06, 2019 7:16 pm
Yes exactly. The electron flows enabled by the key presses are physical; but they are not the meaning. The meaning is inherent in the human intention behind the communication. You seem to be agreeing with me.
In a way - yes. I am agreeing, but I don' want to discuss it too broadly as broad concepts are difficult to pin down.

In context of making symbols meaningful, and in context where intention is meaning the algorithms I write capture my intention and therefore my meaning.

I automate parts of myself. Those algorithms act on my behalf - they capture some of my agency.
wtf wrote:
Sat Apr 06, 2019 7:16 pm
No, your own example shows that's wrong. The meaning is not in the electron flows. The meaning is in the human interpretation and motivation that causes you to press those particular keys, and that causes me to read and desire to respond.
The meaning is in my intention to move information from my head to yours halfway around the world in 0.300 seconds.

Symbols are the medium, but they key property of computer substrate is the determinism.

The consequence of the symbol is consistently interpreted by the computer. Even if not so by the human.
wtf wrote:
Sat Apr 06, 2019 7:16 pm
Bit flipping has no meaning. Bits are flipped in a video game or a heart pacemaker. The bits don't care, the electrons don't care. Only the humans care. Living creatures impart meaning to the bit flipping. Which your own example seems to support.
Counter-example. If humans attach meaning to desirable outcomes then making a machine achieve said desirable outcome on my behalf is meaningful.

It means something to have my house clean - I got a Roomba. It cleans my house for me.
wtf wrote:
Sat Apr 06, 2019 7:16 pm
A physical computation generates heat. I hope you are not arguing that the heat is the meaning of the computation. It's not. The meaning of the computation is supplied by humans.
I don't think it's that simple.

I want to make my wife happy. I know she likes song X. My intention (which is meaningful) is transferred to a computer.

Computer causes joy vicariously by translating intention into action and vicariously causing memory recall.


To simply the taxonomy - meaning needs not be only about the past. It can be about the future also. Dreams/desires.

And if you want to be pedantic - you like experiencing old memories. But your experience happens post hoc your desire.
I want to experience old memories - therefore I will read this book. Cause -> effect.

Meaning is a consequence.

wtf
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Re: Tarski Undefinability Theorem Reexamined

Post by wtf » Sat Apr 06, 2019 7:59 pm

Logik wrote:
Sat Apr 06, 2019 7:45 pm
Memory recall is meaning? We can do that in algorithms.
That's so disingenuous I didn't read further.

The meaning is in the feelings and subjective experiences evoked by memory. If you don't understand this you are out of touch with your own experience of being alive. Either that or just practicing your sophistry.

Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 8:05 pm

wtf wrote:
Sat Apr 06, 2019 7:59 pm
Logik wrote:
Sat Apr 06, 2019 7:45 pm
Memory recall is meaning? We can do that in algorithms.
That's so disingenuous I didn't read further.

The meaning is in the feelings and subjective experiences evoked by memory. If you don't understand this you are out of touch with your own experience of being alive. Either that or just practicing your sophistry.
Sure, and feelings/experiences are just information. Reliving the past. Replaying the video in your head.

I understand it just find and I've integrated it into my own system for processing my own emotions.

I just don't like sacred cows. Not even the sacred cows that there's something magical going on in my head that is called "meaning". It's just physics.

I don't have to ascribe it to magic to be in touch with myself and to love the experience of being.
Perhaps you lack a conceptual model of "self" for effective meta-cognition?

Quite the opposite of sophistry. Science. I use this model to predict self and others in social settings. Works just fine.

wtf
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Re: Tarski Undefinability Theorem Reexamined

Post by wtf » Sat Apr 06, 2019 8:09 pm

Logik wrote:
Sat Apr 06, 2019 8:05 pm

I just don't like sacred cows. Not even the sacred cows that there's something magical going on in my head. It's just physics.
You're being disingenuous again. Is that all you've got? Can't you challenge yourself to do better?

I did not say there's anything magical going on, and I defy you to show that I did.

I did not deny that it's "just physics," and I defy you to dhow that I did.

You're just lying about what I said because your argument is weak.

It could all be "just physics" but definitely not "just computation." Huge difference. But why do you care? You're no longer trying to have an intelligent conversation. Your points are weak and you're reduced to lying about what I said.

Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

Post by Logik » Sat Apr 06, 2019 8:15 pm

wtf wrote:
Sat Apr 06, 2019 8:09 pm
Logik wrote:
Sat Apr 06, 2019 8:05 pm

I just don't like sacred cows. Not even the sacred cows that there's something magical going on in my head. It's just physics.
You're being disingenuous again. Is that all you've got? Can't you challenge yourself to do better?
No, I am not being disingenuous. And I have no interest continuing a conversation with somebody who's going to second-guess my meaning.

I have no idea how to do any "better" than physics.

Models of reality is all we have. Models of our own mind is all we have. My meta-cognition (self-awareness) is based on a computational framework. You pointed out that ultra-finitism is attempting to be consistent with this reality - hence: one framework for everything.

Model-dependent realism.

All models are wrong - some are useful. If models with predictive utility are "sophistry" well - I can't stop you from inventing whatever taxonomy works for you...

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