The connection between free will and the religious multiverse

Discuss philosophical questions regarding theism (and atheism), and discuss religion as it relates to philosophy. This includes any philosophical discussions that happen to be about god, gods, or a 'higher power' or the belief of them. This also generally includes philosophical topics about organized or ritualistic mysticism or about organized, common or ritualistic beliefs in the existence of supernatural phenomenon.
heracleitos
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The connection between free will and the religious multiverse

Post by heracleitos »

For the sake of the argument, I will first propose a definition for the term "free will". In this definition, free will also exists in mathematical universes.

If a logic sentence is true but not possibly provable from its construction theory, then it is not preprogrammed ("predetermined") by such system. In mathematics, these logic sentences are termed "Godelian".

Godel's first incompleteness theorem establishes the precise conditions that the construction of the system must satisfy for its corresponding universe ("model") to contain true Godelian sentences.

We also assume that the physical universe satisfies the elusive Theory of Everything, i.e. the otherwise unknown construction theory of the physical universe.

If a person truly has free will, then his impact on the physical universe is a collection of Godelian true logic sentences that cannot be predicted nor proven from the Theory of Everything.

In arithmetic theory, the existence of a Godelian sentence automatically implies the existence of nonstandard universes of natural numbers.

Wikipedia on nonstandard models of arithmetic:
In mathematical logic, a non-standard universe ("model") of arithmetic theory is a universe that contains non-standard numbers.

There are several methods that can be used to prove the existence of non-standard models of arithmetic.

From the incompleteness theorems.

Gödel's incompleteness theorems also imply the existence of non-standard models of arithmetic. The incompleteness theorems show that a particular sentence G, the Gödel sentence of Peano arithmetic, is neither provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic. However, G is true in the standard model of arithmetic, and therefore any model in which G is false must be a non-standard model.
Similarly, if human free will exists, i.e. if there are Godelian sentences in the physical universe, then just like in Arithmetic Theory, it necessarily implies the existence of nonstandard physical universes.

Therefore, what religion calls heaven and hell, i.e. the religious multiverse, necessarily coexist with free will. They both exist, or they both do not exist.
Sunday66
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Re: The connection between free will and the religious multiverse

Post by Sunday66 »

heracleitos wrote: April 14th, 2022, 10:05 pm For the sake of the argument, I will first propose a definition for the term "free will". In this definition, free will also exists in mathematical universes.

If a logic sentence is true but not possibly provable from its construction theory, then it is not preprogrammed ("predetermined") by such system. In mathematics, these logic sentences are termed "Godelian".

Godel's first incompleteness theorem establishes the precise conditions that the construction of the system must satisfy for its corresponding universe ("model") to contain true Godelian sentences.

We also assume that the physical universe satisfies the elusive Theory of Everything, i.e. the otherwise unknown construction theory of the physical universe.

If a person truly has free will, then his impact on the physical universe is a collection of Godelian true logic sentences that cannot be predicted nor proven from the Theory of Everything.

In arithmetic theory, the existence of a Godelian sentence automatically implies the existence of nonstandard universes of natural numbers.

Wikipedia on nonstandard models of arithmetic:
In mathematical logic, a non-standard universe ("model") of arithmetic theory is a universe that contains non-standard numbers.

There are several methods that can be used to prove the existence of non-standard models of arithmetic.

From the incompleteness theorems.

Gödel's incompleteness theorems also imply the existence of non-standard models of arithmetic. The incompleteness theorems show that a particular sentence G, the Gödel sentence of Peano arithmetic, is neither provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic. However, G is true in the standard model of arithmetic, and therefore any model in which G is false must be a non-standard model.
Similarly, if human free will exists, i.e. if there are Godelian sentences in the physical universe, then just like in Arithmetic Theory, it necessarily implies the existence of nonstandard physical universes.

Therefore, what religion calls heaven and hell, i.e. the religious multiverse, necessarily coexist with free will. They both exist, or they both do not exist.
Maybe you explained it, but I did not understand. What is a religious multiverse?
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sunday66 wrote: April 14th, 2022, 10:56 pm Maybe you explained it, but I did not understand. What is a religious multiverse?
The religious multiverse are the nonstandard physical universes of heaven and hell (along with the standard physical universe in which we live).

So, the idea is that the existence of free will in the standard universe implies the existence of nonstandard universes.

Well, such multiverse structure certainly exists for the natural numbers, because free will provably exists in the standard universe of natural numbers.
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Sculptor1
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Re: The connection between free will and the religious multiverse

Post by Sculptor1 »

Wow!

A connection between two things that do not even exist!

Such a massive scope for verbal masturbation was never before invented.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sculptor1 wrote: April 17th, 2022, 9:26 am Wow!

A connection between two things that do not even exist!

Such a massive scope for verbal masturbation was never before invented.
Free will could exist. That is actually a real possibility!

Seriously, who says that the Theory of Everything does not contain a copy of the relevant fragment (Robinson's Q) of Arithmetic Theory?

Can you guarantee that? How?

By the way, Stephen Hawking, for example, clarified in his lecture "Gödel and the End of Physics" that he also believed that the Theory of Everything is fundamentally incomplete:
In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models. That is, a model can be arbitrarily detailed, and can contain an arbitrary amount of information, without affecting the universes they describe. But we are not angels, who view the universe from the outside. Instead, we and our models, are both part of the universe we are describing. Thus a physical theory, is self referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent, or incomplete. The theories we have so far, are both inconsistent, and incomplete.
Hawking also believed that the core problem is caused by our own presence in the physical universe. However, as I mentioned previously, the problem only occurs if we truly have free will. The mere self-referentiality that Hawking mentions, is actually not enough. We must also be incorrigibly loose cannons!
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The Beast
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Re: The connection between free will and the religious multiverse

Post by The Beast »

In such systems (incomplete) I might design a dimension called the Godelia. This is the dimension of imperfection. That is of an arbitrary whatever. Whatever is the arbitrary unit. In unstable systems or “Gedelian” The Godelia will insert whatever as needed. In closed systems, the Godelia will try to insert reorganization or add new dimensions. A particular whatever in a new dimension. In another whatever dimension I might create exotic matter. This exotic matter might be connected to a whatever cloud I created by tweaking known channels. The Godelia cloud. Then, by definition, closed systems and open systems are not perfect. This is due to the Godelia effect. This way “everything” is congruent with free will and reality. Creating exotic matter is not a new thing as demonstrated by the “cat state” of known standard matter.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Hey, this is a real math phenomenon!

The natural numbers are not just a single universe ("model"). It is a multiverse, which has additional non-standard universes ("models").
Wikipedia on non-standard models of arithmetic wrote: In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934).
In fact, you can detect from within the standard universe of natural numbers that these non-standard universes of natural numbers must exist.

Just like most theories expressed in the language of first-order logic, arithmetic theory simply fails to commit its non-logical symbols to a unique (intended) interpretation. When this happens, you get an entire multiverse instead of a single universe.
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Sculptor1
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Re: The connection between free will and the religious multiverse

Post by Sculptor1 »

heracleitos wrote: April 17th, 2022, 9:49 am
Sculptor1 wrote: April 17th, 2022, 9:26 am Wow!

A connection between two things that do not even exist!

Such a massive scope for verbal masturbation was never before invented.
Free will could exist. That is actually a real possibility!

Seriously, who says that the Theory of Everything does not contain a copy of the relevant fragment (Robinson's Q) of Arithmetic Theory?

Can you guarantee that? How?

By the way, Stephen Hawking, for example, clarified in his lecture "Gödel and the End of Physics" that he also believed that the Theory of Everything is fundamentally incomplete:
In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models. That is, a model can be arbitrarily detailed, and can contain an arbitrary amount of information, without affecting the universes they describe. But we are not angels, who view the universe from the outside. Instead, we and our models, are both part of the universe we are describing. Thus a physical theory, is self referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent, or incomplete. The theories we have so far, are both inconsistent, and incomplete.
Hawking also believed that the core problem is caused by our own presence in the physical universe. However, as I mentioned previously, the problem only occurs if we truly have free will. The mere self-referentiality that Hawking mentions, is actually not enough. We must also be incorrigibly loose cannons!
QED my last sentence.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sculptor1 wrote: April 17th, 2022, 12:14 pm QED my last sentence.
I think that the problem is that the concept of nonstandard natural numbers may sound a bit complex, but I assure you that it is not.

If you try to define the natural numbers, i.e. 0, 1, 2, 3, ..., you cannot achieve that in first-order logic without simultaneously defining lots of other, so-called nonstandard natural numbers.

If you understand why this problem occurs with numbers, you will quickly realize that this problem also affects the physical universe, the definition of which may very well specify the existence of nonstandard physical universes.

The result of defining anything in logic almost never leads to a single-universe interpretation but to a multiverse one.

At first glance, it may look like a definition will lead to just the intended interpretation, but that almost never happens.

This problem was first discovered by Thoralf Skolem in 1934 for the natural numbers but it also occurs in ZFC set theory, and in fact, almost everywhere in mathematics where definitions are nontrivial.

The intended interpretation ("model") of science is the physical universe:
Wikipedia on "interpretation" wrote: Most formal systems have many more models than they were intended to have (the existence of non-standard models is an example). When we speak about 'models' in empirical sciences, we mean, if we want reality to be a model of our science, to speak about an intended model.
It is quite unlikely that the physical universe is the only interpretation ("model") of its theory (of which science is an approximation). It is the multiverse that is the default structure for interpretation and not the single universe.
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Sculptor1
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Re: The connection between free will and the religious multiverse

Post by Sculptor1 »

heracleitos wrote: April 17th, 2022, 8:54 pm
Sculptor1 wrote: April 17th, 2022, 12:14 pm QED my last sentence.
I think that the problem is that the concept of nonstandard natural numbers may sound a bit complex, but I assure you that it is not.
This is not an apt response.

If you try to define the natural numbers, i.e. 0, 1, 2, 3, ..., you cannot achieve that in first-order logic without simultaneously defining lots of other, so-called nonstandard natural numbers.

If you understand why this problem occurs with numbers, you will quickly realize that this problem also affects the physical universe, the definition of which may very well specify the existence of nonstandard physical universes.

The result of defining anything in logic almost never leads to a single-universe interpretation but to a multiverse one.

At first glance, it may look like a definition will lead to just the intended interpretation, but that almost never happens.

This problem was first discovered by Thoralf Skolem in 1934 for the natural numbers but it also occurs in ZFC set theory, and in fact, almost everywhere in mathematics where definitions are nontrivial.

The intended interpretation ("model") of science is the physical universe:
Wikipedia on "interpretation" wrote: Most formal systems have many more models than they were intended to have (the existence of non-standard models is an example). When we speak about 'models' in empirical sciences, we mean, if we want reality to be a model of our science, to speak about an intended model.
It is quite unlikely that the physical universe is the only interpretation ("model") of its theory (of which science is an approximation). It is the multiverse that is the default structure for interpretation and not the single universe.
Are you responding to a different person's post?? Because this does not reflect upon anything I said.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sculptor1 wrote: April 18th, 2022, 7:14 am This is not an apt response.
The problem is undoubtedly the many references to model theory in my answer.
Wikipedia on "model theory" wrote: In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold).[1] The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.
Model theory mostly revolves around the problem that:

The complete solution is almost always a multiverse and not a single universe.

In my opinion, model theory is truly the admiral ship of metamathematics. Even though it is still real math, it reads much more like philosophy:
Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. This has prompted the comment that "if proof theory is about the sacred, then model theory is about the profane".[3]
Model theory is actually much better than most other philosophy-like subjects. In the end, unlike many areas in other philosophy-like disciplines, model theory still has a legitimate and consistent structure.

Model theory may at times be a bit "hard" but it is definitely worth it!
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Sculptor1
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Re: The connection between free will and the religious multiverse

Post by Sculptor1 »

heracleitos wrote: April 18th, 2022, 9:56 pm
Sculptor1 wrote: April 18th, 2022, 7:14 am This is not an apt response.
The problem is undoubtedly the many references to model theory in my answer.
Wikipedia on "model theory" wrote: In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold).[1] The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.
Model theory mostly revolves around the problem that:

The complete solution is almost always a multiverse and not a single universe.

In my opinion, model theory is truly the admiral ship of metamathematics. Even though it is still real math, it reads much more like philosophy:
Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. This has prompted the comment that "if proof theory is about the sacred, then model theory is about the profane".[3]
Model theory is actually much better than most other philosophy-like subjects. In the end, unlike many areas in other philosophy-like disciplines, model theory still has a legitimate and consistent structure.

Model theory may at times be a bit "hard" but it is definitely worth it!
It may well be but it is not relevant here.
Are you responding to a different person's post?? Because this does not reflect upon anything I said.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sculptor1 wrote: April 19th, 2022, 5:17 am It may well be but it is not relevant here.
Well, I keep getting irrelevant posts in response to mine, likeost of yours.

Discussing the connection between a multiverse and the existence of Godelian sentences in one of its universes is obvious to someone familiar with model theory. It is clearly not obvious to you.

So, I certainly do understand what the real problem is.
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Sculptor1
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Re: The connection between free will and the religious multiverse

Post by Sculptor1 »

heracleitos wrote: April 19th, 2022, 6:27 am
Sculptor1 wrote: April 19th, 2022, 5:17 am It may well be but it is not relevant here.
Well, I keep getting irrelevant posts in response to mine, likeost of yours.

Discussing the connection between a multiverse and the existence of Godelian sentences in one of its universes is obvious to someone familiar with model theory. It is clearly not obvious to you.

So, I certainly do understand what the real problem is.

I see. As with the other thread I think it time to end the conversation.
heracleitos
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Re: The connection between free will and the religious multiverse

Post by heracleitos »

Sculptor1 wrote: April 19th, 2022, 8:26 am I see. As with the other thread I think it time to end the conversation.
Agreed. As the OP of this thread, I would certainly be more than happy to talk with other people about the subject. Model theory has quite a bit of impact on metaphysics. If other people are open to that, let them feel free be my guest in this thread!
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