I think we can make the positive claim that nothing like 'gods' exist

[Jarhyn]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

 

[steve_bank]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

 

[Jarhyn]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

 

[skepticalbip]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted "reasoning". Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe long before there were humans to create either language or math. Just as things had mass and weight long before humans created the units of kilograms to measure it.

 

[Jarhyn]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

The one thing in math that is "apparently random" or at least random-like seems to be the distribution of primes.

If we can provably tie those together, there is certainly no "god*", and the full determinism of the universe will have been laid out.

It goes back to what I said in the other thread on proving whether gods exist insofar as to determine IF there are fingerprints in the form of this, you need to know what it looks like without interference and for that you need to know exactly what relationship of stuff and arrangement gives rise to this progression of events.

If this progression of events is predicted to be observed as a relationship along sequential values, a holographic projection of a single field, that would settle it once and for all.

I'm not saying that it is, merely that determining what it is will determine whether or not there have been touches on it.

 

[skepticalbip]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

You still have it backwards. The universe behaves the way it does. We use math to better describe and understand it.

 

[Jarhyn]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

You still have it backwards. The universe behaves the way it does. We use math to better describe and understand it.

And what I am saying is that it might actually prove to be the other way around, that the way the universe behaves the way it does and is so perfectly describable within the axioms of math is that it MAY prove to be a simple and fixed relationship that is just a necessary corollary of those axioms which math is a product of.

 

[skepticalbip]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

You still have it backwards. The universe behaves the way it does. We use math to better describe and understand it.

And what I am saying is that it might actually prove to be the other way around, that the way the universe behaves the way it does and is so perfectly describable within the axioms of math is that it MAY prove to be a simple and fixed relationship that is just a necessary corollary of those axioms which math is a product of.

And you would be wrong. You are confusing reality and how (the method used) we understand reality.

ETA:
It just struck me. Your "reasoning" sounds much like a throwback to the Pythagoreans, an ancient Greek religious sect.

 

[steve_bank]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

The one thing in math that is "apparently random" or at least random-like seems to be the distribution of primes.

If we can provably tie those together, there is certainly no "god*", and the full determinism of the universe will have been laid out.

It goes back to what I said in the other thread on proving whether gods exist insofar as to determine IF there are fingerprints in the form of this, you need to know what it looks like without interference and for that you need to know exactly what relationship of stuff and arrangement gives rise to this progression of events.

If this progression of events is predicted to be observed as a relationship along sequential values, a holographic projection of a single field, that would settle it once and for all.

I'm not saying that it is, merely that determining what it is will determine whether or not there have been touches on it.

Math is used to quantitativlely describe physical reality, reality does not conform to math.

 

[Jarhyn]

Math is used to quantitativlely describe physical reality, reality does not conform to math.

This is a rather bold claim to make in light of the fact we don't even really know what reality is, merely that it is.

 

[excreationist]

So the Greeks believed that gods that they weren't aware of existed - and if you're not aware of something you can't properly worship it.

They clearly did not agree. If your starting assumption is that there are a great many deities, some of whom have revealed themselves to the people of other nations but not yet yourself, why wouldn't it make sense to hedge your bets and honor the unknown gods "just in case"?

I'm talking about fictional beings that could still be called gods and goddesses even if they were not worshipped....

This seems like a clear-cut appplication of Pascal's Wager.

You might be interested in this related thread:

Partly defending Pascal's Wager? (only one popular eternal hell for non-believers)

Pascal's Wager began talking about Christianity.... If you believe in Jesus/God: Jesus/God exists - go to paradise forever Jesus/God doesn't exist - time wasted, etc If you don't believe in Jesus/God: Jesus/God exists - go to hell forever Jesus/God doesn't exist - nothing A counter-argument...

iidb.org

I'm saying that it seems only Christianity is relevant to the wager....

 

[Politesse]

So the Greeks believed that gods that they weren't aware of existed - and if you're not aware of something you can't properly worship it.

They clearly did not agree. If your starting assumption is that there are a great many deities, some of whom have revealed themselves to the people of other nations but not yet yourself, why wouldn't it make sense to hedge your bets and honor the unknown gods "just in case"?

I'm talking about fictional beings that could still be called gods and goddesses even if they were not worshipped....

This seems like a clear-cut appplication of Pascal's Wager.

You might be interested in this related thread:

Partly defending Pascal's Wager? (only one popular eternal hell for non-believers)

Pascal's Wager began talking about Christianity.... If you believe in Jesus/God: Jesus/God exists - go to paradise forever Jesus/God doesn't exist - time wasted, etc If you don't believe in Jesus/God: Jesus/God exists - go to hell forever Jesus/God doesn't exist - nothing A counter-argument...

iidb.org

I'm saying that it seems only Christianity is relevant to the wager....

Why? Polytheists also know how to gamble. Indeed, you could argue they know how to do it better. The consequences of upsetting Athene are no less severe than those of upsetting YHWH, they're just different. She won't burn your soul in an eternal hell, but she will happily destroy your life, your country, or worst of all (from an ancient patrilineal society's point of view) your family line. Eternal suffering is an unpleasant thought, but from the ancient Hellenistic perspective, an unavoidable one. Toadying up to the gods helped the living, but it did nothing for the dead. Only a brave few achieved Elysium, and they had to have divine blood to get in. Nobles had a slim chance, but commoners were f*cked. One thing that probably made Christianity more popular. Your average slave doesn't care much about the fates of nations, but an escape from Hades is worth... dying for.

 

[steve_bank]

The question is about scientific theories that can prove a god can not exist.

When I see one, I'll let you know.

Well, there is the hypothetical of whether the universe is some interaction of iteration along properties that exist within the number line, such as "the universe is really just a massive prime filter", which would conveniently account for why certain things seem random, and why some are statistically assured.

In such a cosmology, there can be no 'god' by the definition of "creator entity" because it is merely "a property observed as you count numbers from 1 to infinity", which itself encodes math because it's all just properties of a trivial mathematical relationship, and would be observed in any reality capable of hosting such large numbers and operating on them to describe the relationships that exist between them.

Who's speculation? An finitely divisible number line is a useful mathematical abstraction. It is not reality. Same with Eucliden Geometry. It is based on a point being infinity small and massless, and a line being comprised of an infinte number of points infinitely divisible.

You are philosophizing, not invoking science.

No, I'm saying IFF the universe can be proved to be nothing but a necessary interaction observable along the number line, then there cannot be no "god*", it is just an inevitability in any system that expresses "count".

*Of the "created and interacts with" variety.

Philosophizing, not science. Sounds more like the form of a theist proof that god exists.

Given Newtons laws of motion god can not exist because...
Givem equiipartition of energy god can not exist because...
Because of time dilation god can no exist because...

Now man I'm saying "if we figure out that the universe is just some inevitability of math, then that's all the universe is and "God*" has no place in it."

That is rather twisted reasoning. Math is just a logical language that aids us in understanding, not a physical creative force. There was a universe before there were humans to create either language or math.

Yet the universe still universally behaves in ways describable by math, all except for a virtual particle field that seems "random".

You still have it backwards. The universe behaves the way it does. We use math to better describe and understand it.

And what I am saying is that it might actually prove to be the other way around, that the way the universe behaves the way it does and is so perfectly describable within the axioms of math is that it MAY prove to be a simple and fixed relationship that is just a necessary corollary of those axioms which math is a product of.

And it might be found the moon is filled with mozzereall chese and peperoini.

Math is used to quantitativlely describe physical reality, reality does not conform to math.

This is a rather bold claim to make in light of the fact we don't even really know what reality is, merely that it is.

Pop philosophy.

Math is used to quantitatively model observation, if that sounds better to you.

The point is math is not rerality, words are not reality. The saying is 'the map is not the countryside. Using number lines to prove something physical is infinite makes no sense. Someone on the science forum argued that an infinite number line proved life after death.

You are arguing philosophy on q science topic. Non Sequitur.

What is reality is a nonsense question, unanswerable. Science models reality.

BTW, bold is my middle name.....

 

[bilby]

Your "reasoning" sounds much like a throwback to the Pythagoreans, an ancient Greek religious sect.

Those guys always seemed to have an angle...

 

[skepticalbip]

Your "reasoning" sounds much like a throwback to the Pythagoreans, an ancient Greek religious sect.

Those guys always seemed to have an angle...

This site really needs to add a "groan" emoji.

 

[T.G.G. Moogly]

And it might be found the moon is filled with mozzereall chese and peperoini.

And of course even if it is proven to be pepperoni and mozzy it will still act and feel like the moon. Very mysterious. We must uncover the mystery of how this happens. Woooooo.....

 

[atrib]

Math is used to quantitativlely describe physical reality, reality does not conform to math.

Better stated as: "math is is used to quantitatively describe certain emergent characteristics of reality". What we observe with our senses, or instruments that serves as extensions of our senses, is an interpretation of reality, not reality itself. We cannot see the underlying universal quantum field, we can only observe certain emergent phenomena that derive from this field.

 

[steve_bank]

Math is used to quantitativlely describe physical reality, reality does not conform to math.

Better stated as: "math is is used to quantitatively describe certain emergent characteristics of reality". What we observe with our senses, or instruments that serves as extensions of our senses, is an interpretation of reality, not reality itself. We cannot see the underlying universal quantum field, we can only observe certain emergent phenomena that derive from this field.

Emergent can have a substantive meaning, it is also used to infer something arsing without causality. A refutation of physical reductionism. Properties exist in a system not traceable to a system cause. It was used on science threads to make a case for the paranormal.

We obviously quantify what we observe and what we can infer. As I have said several times it is hubris to assumewe know or can know everything. That being said, that can not be used to justify assertions with no evidence, like telepathy or mind body duality.

Math is a map, and the map is not the countryside.

 

[Jarhyn]

Math is used to quantitativlely describe physical reality, reality does not conform to math.

Better stated as: "math is is used to quantitatively describe certain emergent characteristics of reality". What we observe with our senses, or instruments that serves as extensions of our senses, is an interpretation of reality, not reality itself. We cannot see the underlying universal quantum field, we can only observe certain emergent phenomena that derive from this field.

Emergent can have a substantive meaning, it is also used to infer something arsing without causality. A refutation of physical reductionism. Properties exist in a system not traceable to a system cause. It was used on science threads to make a case for the paranormal.

We obviously quantify what we observe and what we can infer. As I have said several times it is hubris to assumewe know or can know everything. That being said, that can not be used to justify assertions with no evidence, like telepathy or mind body duality.

Math is a map, and the map is not the countryside.

Let's take for observation a universe defined of smallest meaningful changes on a binary field on the basis of some complex but ultimately describable form of interaction. This system could not function in the way it does, it could not be the universe it was, were it not necessarily describable and bound to the properties demanded by the axioms of math.

It is in fact subordinated to the same fundamental concepts of "set" and "class" as all "things" fundamentally are.

Nothing in that universe, described in all ways as it is even in the absurd elements, can violate the laws of mathematics on a fundamental level.

Even such odd behaviors as (make thing: -1 bar) (melt thing: +1.5bar) are fundamentally modeled by and reliant on a mathematically describable relationship and algorithmic behavior, a well defined interaction on a set by algorithm.

The "map" is a countryside when the countryside itself is the "map".

 

[atrib]

Math is used to quantitativlely describe physical reality, reality does not conform to math.

Better stated as: "math is is used to quantitatively describe certain emergent characteristics of reality". What we observe with our senses, or instruments that serves as extensions of our senses, is an interpretation of reality, not reality itself. We cannot see the underlying universal quantum field, we can only observe certain emergent phenomena that derive from this field.

Emergent can have a substantive meaning, it is also used to infer something arsing without causality. A refutation of physical reductionism. Properties exist in a system not traceable to a system cause. It was used on science threads to make a case for the paranormal.

We obviously quantify what we observe and what we can infer. As I have said several times it is hubris to assumewe know or can know everything. That being said, that can not be used to justify assertions with no evidence, like telepathy or mind body duality.

Math is a map, and the map is not the countryside.

Let's take for observation a universe defined of smallest meaningful changes

How is "meaningful" defined? Is a change in the state of one degree of freedom at one point "meaningful"?

on a binary field on the basis of some complex but ultimately describable form of interaction.

OK. But what do we gain from this observation? Is our universe (the one we live in) completely describable, i.e. fully determinate? And why does the field have to be binary/discretized? The beauty of a field is that it is continuous, and can be modeled/described using a continuous function instead of discrete values.

This system could not function in the way it does, it could not be the universe it was, were it not necessarily describable and bound to the properties demanded by the axioms of math.

Math is a tool invented by humans to help us quantify observations. The universe we live in does what it does, irrespective of whether we have constructed or can construct mathematical models to describe its behavior. Again, I don't understand what your hypothetical universe example is supposed to illustrate.

It is in fact subordinated to the same fundamental concepts of "set" and "class" as all "things" fundamentally are.

What does this mean?

Nothing in that universe, described in all ways as it is even in the absurd elements, can violate the laws of mathematics on a fundamental level.

Perhaps your hypothetical universe cannot, if you have built it that way. What does this have to do with the universe we actually live in?

Even such odd behaviors as (make thing: -1 bar) (melt thing: +1.5bar) are fundamentally modeled by and reliant on a mathematically describable relationship and algorithmic behavior, a well defined interaction on a set by algorithm.

The "map" is a countryside when the countryside itself is the "map".

You have failed to make your point. I agree with Steve, math provides tools that help us predict/map out the state of the universe, but the models are merely crude approximations - they are not reality itself. The map is, by practical necessity, a much smaller and more conveniently accessed device that can be folded and stored in the pocket when not in use, unlike the actual countryside that the map represents.

Unless you are asserting that the universe is a simulation/model constructed by an entity outside its boundaries. In that case, the countryside itself may be the map to a bigger reality. But we have no evidence to tell us that such is the case.