Godel's Argument For God is Not Realistic

[godelian]

In addition of my critique of the failure of Godel's argument, here is one with reference to Kant:

No, Kant is out of the game now. His arguments can no longer participate because they are not specifically directed at Gödel's axioms. Furthermore, Kant's main argument, i.e. the purported undefinability of existence, is simply unsubstantiated.

The entire domain has now been annexed by mathematics, while Kant's views are mathematically objectionable.

Gödel was indeed able to prove that the existence of something, which he defined as divine, necessarily follows from certain assumptions. But whether these assumptions are justified can be called into doubt.

Well, that is the nature of the game. So, at least this author is seemingly willing to accept to play by the rules of the game:

If you want to criticize a mathematically unobjectionable proof, then you must direct all criticism at its axioms.

For example, if I assume that all cats are tricolored and know that tricolored cats are almost always female, then I can conclude: almost all cats are female. Even if the logical reasoning is correct, this of course does not hold. For the very assumption that all cats are tricolored is false.

Here the author is already in violation of the rules. You cannot use mathematics to prove anything about the physical universe. There is no axiomatic foundation available for that. So, if I assume that all cats are tricolored can never be a valid axiom because cats are not abstract, Platonic objects. They are part of the physical universe. Therefore, they cannot be axiomatized.

From a mathematical point of view, however, these thought experiments became really serious only through Gödel’s efforts.
As it turns out, Gödel’s logical inferences are all correct—even computers have been able to prove that.

Yes, Gödel's proof is mathematically unobjectionable. Hence, he needs to criticize its axioms and nothing else.

This does not settle the final question of the existence of one (or more) divine beings.

The author vaguely discusses the axioms but he actually does not manage to criticize them. In fact, he doesn't even really try. Therefore, his conclusion does not follow from anything, really.

Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting.

This conclusion also does not follow from anything that he has discussed. Seriously, this author is just another intellectually dishonest mainstream media word-salad charlatan.

Has mathematics now finally disproved the claims of all atheists?
As you probably already suspect, it has not.

Wait a minute! Atheists do not even have a mathematically unobjectionable claim. Hence, there is nothing that Gödel would need to "disprove". It is Gödel who has produced mathematically unobjectionable work and not the atheists. The rules of the game say that atheists must now successfully criticize Gödel's axioms. Where exactly can we find their mathematically legitimate criticism?

[Skepdick]

It is not AI's problem.
I asked AI re 'numbers-by-themselves' so it answer in terms of 'number'.

When I stated 'numbers-by-themselves' my intention was with reference to numerals or digits.
'numbers-by-themselves' i.e. without reference to any conceptual system, e.g. mathematics, music, etc.

You continue to be confused.

The term "2" is not the number 2.
The number 2 itself doesn't exist except within a conceptual system which brings it into existence.

[Veritas Aequitas]

In addition of my critique of the failure of Godel's argument, here is one with reference to Kant:

No, Kant is out of the game now. His arguments can no longer participate because they are not specifically directed at Gödel's axioms. Furthermore, Kant's main argument, i.e. the purported undefinability of existence, is simply unsubstantiated.

The entire domain has now been annexed by mathematics, while Kant's views are mathematically objectionable.

Gödel was indeed able to prove that the existence of something, which he defined as divine, necessarily follows from certain assumptions. But whether these assumptions are justified can be called into doubt.

Well, that is the nature of the game. So, at least this author is seemingly willing to accept to play by the rules of the game:

If you want to criticize a mathematically unobjectionable proof, then you must direct all criticism at its axioms.

For example, if I assume that all cats are tricolored and know that tricolored cats are almost always female, then I can conclude: almost all cats are female. Even if the logical reasoning is correct, this of course does not hold. For the very assumption that all cats are tricolored is false.

Here the author is already in violation of the rules. You cannot use mathematics to prove anything about the physical universe. There is no axiomatic foundation available for that. So, if I assume that all cats are tricolored can never be a valid axiom because cats are not abstract, Platonic objects. They are part of the physical universe. Therefore, they cannot be axiomatized.

From a mathematical point of view, however, these thought experiments became really serious only through Gödel’s efforts.
As it turns out, Gödel’s logical inferences are all correct—even computers have been able to prove that.

Yes, Gödel's proof is mathematically unobjectionable. Hence, he needs to criticize its axioms and nothing else.

This does not settle the final question of the existence of one (or more) divine beings.

The author vaguely discusses the axioms but he actually does not manage to criticize them. In fact, he doesn't even really try. Therefore, his conclusion does not follow from anything, really.

Whether mathematics is really the right way to answer this question is itself questionable—even if thinking about it is quite exciting.

This conclusion also does not follow from anything that he has discussed. Seriously, this author is just another intellectually dishonest mainstream media word-salad charlatan.

Has mathematics now finally disproved the claims of all atheists?
As you probably already suspect, it has not.

Wait a minute! Atheists do not even have a mathematically unobjectionable claim. Hence, there is nothing that Gödel would need to "disprove". It is Gödel who has produced mathematically unobjectionable work and not the atheists. The rules of the game say that atheists must now successfully criticize Gödel's axioms. Where exactly can we find their mathematically legitimate criticism?

see:
Philosophy overrides Science and Mathematics
see: viewtopic.php?p=707220#p707220

Kant is using philosophy to show Godel's argument while valid within the mathematic system, it is not sound in terms of reality.

[godelian]

Philosophy overrides Science and Mathematics

You wish!

Philosophy can never overrule mathematically unobjectionable proof.
Philosophy can never overrule experimental test results. Only a counterexample test result can achieve that.

[Veritas Aequitas]

Philosophy overrides Science and Mathematics

You wish!

Philosophy can never overrule mathematically unobjectionable proof.
Philosophy can never overrule experimental test results. Only a counterexample test result can achieve that.

Note my generic definition of philosophy here;
viewtopic.php?f=5&t=28792

A counter example is fundamentally a philosophical element.

What is crucial with philosophy is the use of critical thinking to assess where mathematics stands.

When you insists that Godel's argument is absolute, it cannot be mathematical but you are extending to and invoking philosophy-proper to justify your case but your conclusion is wrong is this case.

[godelian]

A counter example is fundamentally a philosophical element.

No, it is an experimental test result. It comes out of a laboratory.

What is crucial with philosophy is the use of critical thinking to assess where mathematics stands.

The term "critical thinking" is mostly used as an intellectually dishonest tool to encourage people to criticize views that go counter the mainstream propaganda while lauding views that are favorable to it. It is, for example, a very important term in the vocabulary of the Chinese Communist Party.

It is what George Orwell, in "Politics and the English language", calls a "meaningless word" in the same vein as "democracy" or "rule of law". It is mostly meant to activate the bullshit detector.

When you insists that Godel's argument is absolute

You did not quote me there. This is rather some kind of strawman.

it cannot be mathematical but you are extending to and invoking philosophy-proper to justify your case but your conclusion is wrong is this case.

That is just a word salad. One problem with philosophy, is that it easily lends itself to sophistry. This was already a serious problem in ancient Athens, and the problem actually never got solved.

[Veritas Aequitas]

This video give very serious objections to Godel Argument;

Objections to Godel's Ontological Argument
https://www.youtube.com/watch?v=XfXAs66GW70

[Veritas Aequitas]

A counter example is fundamentally a philosophical element.

No, it is an experimental test result. It comes out of a laboratory.

What is crucial with philosophy is the use of critical thinking to assess where mathematics stands.

The term "critical thinking" is mostly used as an intellectually dishonest tool to encourage people to criticize views that go counter the mainstream propaganda while lauding views that are favorable to it. It is, for example, a very important term in the vocabulary of the Chinese Communist Party.

It is what George Orwell, in "Politics and the English language", calls a "meaningless word" in the same vein as "democracy" or "rule of law". It is mostly meant to activate the bullshit detector.

When you insists that Godel's argument is absolute

You did not quote me there. This is rather some kind of strawman.

it cannot be mathematical but you are extending to and invoking philosophy-proper to justify your case but your conclusion is wrong is this case.

That is just a word salad. One problem with philosophy, is that it easily lends itself to sophistry. This was already a serious problem in ancient Athens, and the problem actually never got solved.

You are very lost.

Counter example: an example that refutes or disproves a proposition or theory
The process of countering a propose theory with an example is a philosophical exercise.
It need not be mathematical alone;

The Swiss model serves as a noteworthy counterexample to the American system, where methadone and other medications used to treat opioid addiction are guarded by a maze of laws and regulations and typically viewed with skepticism or judgment.
—Lev Facher, STAT, 26 Mar. 2024
That civilization provides both a counterexample to the notion of man’s impermanence — and a warning.
—Jack Butler, National Review, 31 Dec. 2023

Your understanding of 'critical thinking' in confining it to communism is so shallow;

Critical thinking is the analysis of available facts, evidence, observations, and arguments in order to form a judgement by the application of rational, skeptical, and unbiased analyses and evaluation.[1]
The application of critical thinking includes self-directed, self-disciplined, self-monitored, and self-corrective habits of the mind,[2] thus a critical thinker is a person who practices the skills of critical thinking or has been trained and educated in its disciplines.[3]
Philosopher Richard W. Paul said that the mind of a critical thinker engages the person's intellectual abilities and personality traits.[4]
Critical thinking presupposes assent to rigorous standards of excellence and mindful command of their use in effective communication and problem solving, and a commitment to overcome egocentrism and sociocentrism

Communism do not promote the above critical thinking.
In addition, you did not provide references and evidence to support your claim.

You also have a very contorted view of what is philosophy despite me giving you what philosophy proper is.
Philosophy basically [at the least] is the love of wisdom, there is no way sophistry [negative sense] can come into the picture.

At present, the term philosophy has been bastardized especially in academic philosophy, but that is not philosophy proper.

[Skepdick]

Your understanding of 'critical thinking' in confining it to communism is so shallow;

So lets remove all confinements.

Is critique of critical thinking itself critical thinking or not?

What sort of thinking is non-critical thinking?
Is critical thinking better than non-critical thinking; or is non-critical thinking better than critical thinking?

[godelian]

The process of countering a propose theory with an example is a philosophical exercise.
It need not be mathematical alone;

I was referring to a counterexample in science.

A scientific theory is supported by a report with experimental test results.

So, you tried to make water boil a few hundred times and you observe and write down that the temperature was 100 °C. You publish this data set and ask for feedback from other scientist across the globe who have invested in a state-of-the-art water-boiling accelerator.

A few days later, a scientist in Paraguay sends a message to the mailing list, reporting that he has been able to pull off the feat of making water boil at 110 °C by throwing salt into the accelerator. Can anybody confirm this spectacular breakthrough because there is a Nobel prize at stake now!

This is the falsifying counterexample in science. It is not philosophical. It is an experimental test result.

Communism do not promote the above critical thinking.
In addition, you did not provide references and evidence to support your claim.

Nobody who uses the term "critical thinking" seeks to promote it. The use of this term is always meant to achieve exactly the opposite.

The communist party sought to encourage critical thinking of the capitalist system and its exploitation of the worker class, and to promote the natural discovery of the solution, i.e. the revolution of the proletariat. If you failed to be critical of the bourgeoisie, then you were deemed intellectually inept or a class traitor, or even a kulak capitalist yourself, and therefore an enemy of the people.

Do you disagree with me that the above sounds very critical? Isn't it a jewel of critical thinking?

Communism is very critical! Communists analyze and investigate and deeply think! I don't know of anyone who is more deserving of the title, "Greatest critical stinker" than our great leader Joseph Stalin!

You also have a very contorted view of what is philosophy despite me giving you what philosophy proper is.
Philosophy basically [at the least] is the love of wisdom, there is no way sophistry [negative sense] can come into the picture.

At present, the term philosophy has been bastardized especially in academic philosophy, but that is not philosophy proper.

I use a trivially simple definition for the term "philosophy".

A statement about physical-world facts is NOT philosophy. A statement is philosophical if it is a statement about other statements.

It is raining. --> not philosophical
It won't make any difference that you say that it is raining. --> philosophical

In that sense, mathematics is a subdivision in philosophy. A mathematical object, such as a number, a set, a type, a function, or a combinator, is always a statement and not a physical-world fact. Mathematics is always a statement about mathematical objects. As soon as the philosophical statement is axiomatic, it is also mathematically unobjectionable.

Every philosophical statement that respects the requirements of the axiomatic method is mathematical.

[Skepdick]

A statement about physical-world facts is NOT philosophy. A statement is philosophical if it is a statement about other statements.

.
The above statement was physically communicated from your mind into the database of this forum.
It is further communicated to my computer and physically rendered on my screen.
From there it's physically processed by my retinas and my brain.

It's true that I am making a statement about physical-world facts as stored in the forum's database; and as rendered on my screen. Therefore it's NOT philosophy.

But it's also true that my statement is a statement about another statement. Therefore it's philosophy.

So it's true that it's philosophy AND it's true that it's NOT philosophy.

A true contradiction, indeed. Thus witnessing the negation of the LNC.

Axiom rejected.

Proof terminates. Q.E.D

[godelian]

A statement about physical-world facts is NOT philosophy. A statement is philosophical if it is a statement about other statements.

.
The above statement was physically communicated from your mind into the database of this forum.
It is further communicated to my computer and physically rendered on my screen.
From there it's physically processed by my retinas and my brain.

It's true that I am making a statement about physical-world facts as stored in the forum's database; and as rendered on my screen. Therefore it's NOT philosophy.

But it's also true that my statement is a statement about another statement. Therefore it's philosophy.

So it's true that it's philosophy AND it's true that it's NOT philosophy.

A true contradiction, indeed. Thus witnessing the negation of the LNC.

Axiom rejected.

Proof terminates. Q.E.D

The map is not the territory. The physical incarnation of a message is not the message.

The symbol "1" that you can see on your screen is not the mathematical object 1. Both "1" and "one" are merely representations of the mathematical object.

One major property of a statement is that it is at best unique up to isomorphism.

What is physically sitting in forum's database is itself not a message but a collection of magnetized disk sectors. It is not the message itself.

[Skepdick]

The map is not the territory. The physical incarnation of a message is not the message.

So the above sentence is NOT the message. I've received nothing more from you than the above.

So how come I am receiving a message?

The symbol "1" that you can see on your screen is not the mathematical object 1. Both "1" and "one" are merely representations of the mathematical object.

So when you communicate "1" your message isn't communicating the mathematical object. The number 1?
What are you messaging/communicating then?

One major property of a statement is that it is at best unique up to isomorphism.

What's "isomorphism" unique up to isomorphism with?

What is physically sitting in forum's database is itself not a message but a collection of magnetized disk sectors. It is not the message itself.

So how are we communicating back and forth?

Where is "the message itself" and how does it keep moving from your head into my head and back?

How are you transmitting it if not using these symbols?

[godelian]

So the above sentence is NOT the message. I've received nothing more from you than the above.

It is a representation of the message.

So when you communicate "1" your message isn't communicating the mathematical object. The number 1?
What are you messaging/communicating then?

You can only communicate a representation of the message.

What's "isomorphism" unique up to isomorphism with?

Every translation of it. In Greek: ισομορφισμός. You can translate it into Greek, make it plural in Greek, and then translate it back into English. You will end up with "isomorphisms".

You may turn it into voice file, pluralize it while in the voice format, and from there get it back as a plural in writing too.

Where is "the message itself" and how does it keep moving from your head into my head and back?

It almost surely has a representation in the mind too, but that representation is unknown.

How are you transmitting it if not using these symbols?

As voice waves by pronouncing the message. In Hindi or Arabic. And so on. You can use Cyrillic and send the word "isomorphism" in Russian as "изоморфизм" or in Bulgarian as "изоморфизъм". These are other symbols. It is still the same message. Messages cannot control the number of their representations.

[godelian]

Where is "the message itself"

It is a Platonic abstraction. You can only view its many representations. You cannot see the thing by itself. For mathematical objects, you can use arithmetic theory as a view, and then some part of their universe will show up as numbers. If you use set theory, the same things will show up as sets. There are probably other views that you can use.