Reality is the Set of All Things that Exist

Ostronomos said:

All things that exist can be considered sets due to the fact that they are entities unto themselves.

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Ostronomos said:

An equivalence relation between God and Reality suffices to demonstrate that God is real.

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Realness is a property that you must prove is preserved by an equivalence relation.

For example, I can imagine a solid torus. The solid torus is homeomorphic to a coffee cup. The coffee cup is real, but the torus is not real (I've imagined it). So you need more if you want to show that God is 'real'.

Ponder This said:

I don't think it's clear why everything is a set. How does being an entity onto itself make a thing a set?​

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No that is incorrect. There are levels of reality from basic to ultimate. God is the ultimate.

Realness is a property that you must prove is preserved by an equivalence relation.

For example, I can imagine a solid torus. The solid torus is homeomorphic to a coffee cup. The coffee cup is real, but the torus is not real (I've imagined it). So you need more if you want to show that God is 'real'.

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Realness is indeed a property that can be proven by an equivalence relation as constraints of such a relation are mathematically defined to set the standard of proof. It suffices.

Ostronomos said:

All entities are analogous to sets and their elements. If you really think about it, they are mathematically indistinguishable. Thus reality and God qualify as the universal set. This makes God objective.

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As a basis for set theory, perhaps. As a basis for reality? Unclear.

Ostronomos said:

No that is incorrect. There are levels of reality from basic to ultimate. God is the ultimate.

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You defined God as a mathematical object. We have to wonder if your definition is complete.

Ostronomos said:

Realness is indeed a property that can be proven by an equivalence relation as constraints of such a relation are mathematically defined to set the standard of proof. It suffices.

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Perhaps you missed it, but I gave a counterexample to the notion that realness is preserved by an equivalence relation. In particular, topologists define an equivalence relation on topological spaces using homeomophisms. A topological space, T, is said to be homeomorphic to a topological space, S, iff there exists a homeomorphism, h, such that h: T -> S and the inverse of h is continuous.

Using this I was able to explain that a torus which I imagine (in other words, is not real) is equivalent to a coffee cup (which is real). Thus the property of being 'real' was not preserved by the equivalence relation. In fact, there is a joke, well-known among mathematicians, that topologists don't understand the difference between a coffee cup and a donut. And this highlights the problem.

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In fact, what you did was you claimed that G ϵ R.
In other words, you supposed that God was real and thus belonged to the set of all things real.
You didn't prove God was real by defining an equivalence relation. You straight up asserted it as a fact and later said that you proved it.

Well, if it wasn't obvious that God was real, then you have to actually prove that G ϵ R instead of asserting it as a fact.

I think you need to say something like:
Suppose G ϵ R and R ϵ G.
R has the property that R = P(R) and G has the property that G = P(G).
Therefore, R ⊆ G and G ⊆ R.
Hence, G = R.

This puts it in the form of a Theorem which we can call the 'God-Reality Equivalence Theorem'.
if God is real and all of Reality is part of God, then God and Reality are equivalent*.

*equivalent as sets. So for example, God may have properties such as 'omniscience' that Reality doesn't have, and Reality may have properties that God does not have such as 'obeying the laws of physics'.

Ponder This said:

As a basis for set theory, perhaps. As a basis for reality? Unclear.



You defined God as a mathematical object. We have to wonder if your definition is complete.



Perhaps you missed it, but I gave a counterexample to the notion that realness is preserved by an equivalence relation. In particular, topologists define an equivalence relation on topological spaces using homeomophisms. A topological space, T, is said to be homeomorphic to a topological space, S, iff there exists a homeomorphism, h, such that h: T -> S and the inverse of h is continuous.

Using this I was able to explain that a torus which I imagine (in other words, is not real) is equivalent to a coffee cup (which is real). Thus the property of being 'real' was not preserved by the equivalence relation. In fact, there is a joke, well-known among mathematicians, that topologists don't understand the difference between a coffee cup and a donut. And this highlights the problem.

…

In fact, what you did was you claimed that G ϵ R.
In other words, you supposed that God was real and thus belonged to the set of all things real.
You didn't prove God was real by defining an equivalence relation. You straight up asserted it as a fact and later said that you proved it.

Well, if it wasn't obvious that God was real, then you have to actually prove that G ϵ R instead of asserting it as a fact.

I think you need to say something like:
Suppose G ϵ R and R ϵ G.
R has the property that R = P(R) and G has the property that G = P(G).
Therefore, R ⊆ G and G ⊆ R.
Hence, G = R.

This puts it in the form of a Theorem which we can call the 'God-Reality Equivalence Theorem'.
if God is real and all of Reality is part of God, then God and Reality are equivalent*.

*equivalent as sets. So for example, God may have properties such as 'omniscience' that Reality doesn't have, and Reality may have properties that God does not have such as 'obeying the laws of physics'.

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Thank you for clearing that up. On your last point, reality is a property or element of God and God is a property or element of reality. Bertrand Russell claimed something similar to this argument. He called necessary existence or reality a positive property. And that god possesses all positive properties. If this is true then God obeys the laws of Physics along with reality and reality has attributes like omniscience along with God, since they're equivalent.

Thank you.

Ostronomos said:

Thank you for clearing that up. On your last point, reality is a property or element of God and God is a property or element of reality. Bertrand Russell claimed something similar to this argument. He called necessary existence or reality a positive property. And that god possesses all positive properties. If this is true then God obeys the laws of Physics along with reality and reality has attributes like omniscience along with God, since they're equivalent.

Thank you.

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I'm having trouble following your logic here.
You say 'property or element of'. Do you mean that 'property of' and 'element of' are interchangeable phrases?

At any rate, I do not understand why the properties of a thing would be considered to be elements of it.

For example, a set can have other properties besides being a set such as being a poset and that the same set may have two or more distinct posets defined for it. It's also possible to perform various operations on a set to create a group, or field, or ring. Equivalence Relation is really not saying very much, otherwise everyone would think donuts and coffee cups are the same thing.

Something like 'obeying the laws of physics' is really much more than set equivalence. It's not clear that there is only one set of 'laws of physics' that would apply to the set of things comprising reality. There could be other sets of laws physics that could've applied to reality (in theory we only abide by our current set of laws of physics because off how our particular Big Bang worked out).

So it really isn't clear to me how you've argued for anything more than set equivalence. If you mean that God and Reality are equivalent in an even deeper way than their elements would indicate, then I think you need to more clearly define in what way that is. Is Reality as a topological space homeomorphic to God? But then, how do you define God as a topological space in the first place? I wonder if it even makes sense to describe God in that fashion.

Ponder This said:

I'm having trouble following your logic here.
You say 'property or element of'. Do you mean that 'property of' and 'element of' are interchangeable phrases?

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Yes.

At any rate, I do not understand why the properties of a thing would be considered to be elements of it.

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Any part of something can be likened to an element of it.

For example, a set can have other properties besides being a set such as being a poset and that the same set may have two or more distinct posets defined for it. It's also possible to perform various operations on a set to create a group, or field, or ring. Equivalence Relation is really not saying very much, otherwise everyone would think donuts and coffee cups are the same thing.

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The coffee cup and the donut may be topologically equivalent but their shapes are distinguishable.

Something like 'obeying the laws of physics' is really much more than set equivalence. It's not clear that there is only one set of 'laws of physics' that would apply to the set of things comprising reality. There could be other sets of laws physics that could've applied to reality (in theory we only abide by our current set of laws of physics because off how our particular Big Bang worked out).

So it really isn't clear to me how you've argued for anything more than set equivalence. If you mean that God and Reality are equivalent in an even deeper way than their elements would indicate, then I think you need to more clearly define in what way that is. Is Reality as a topological space homeomorphic to God? But then, how do you define God as a topological space in the first place? I wonder if it even makes sense to describe God in that fashion.

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It does make sense to describe God as ultimate reality. Hence ultimate reality is a topological space homeomorphic to God. But not only that, minds process information and ultimate reality is the mind of God. And ultimate reality is isomorphic to a description. The describer is God.

Ostronomos said:

Any part of something can be likened to an element of it.

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Well, that is simply not true (from a mathematical perspective).
You see in mathematics, we are very precise about how we define things and what things actually mean.
There is no room for an equivocation fallacy in mathematics where we wave our hands and say something is sort of like something, therefore they are the 'same'.

Ponder This said:

Well, that is simply not true (from a mathematical perspective).
You see in mathematics, we are very precise about how we define things and what things actually mean.
There is no room for an equivocation fallacy in mathematics where we wave our hands and say something is sort of like something, therefore they are the 'same'.

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But that is the formal definition of element. A part of something. Sets are defined by their elements or parts. Are you claiming I am using this wrongly?

Ostronomos said:

But that is the formal definition of element. A part of something. Sets are defined by their elements or parts. Are you claiming I am using this wrongly?

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That is not the definition of 'property' which is 'attribute, quality or characteristic'.
So yes, you've used this wrongly.

And, in fact, I pointed out that sometimes a thing is defined as a set with additional properties. For example, there can be multiple partial orderings on a given set. Even though the sets are the same, the partial orderings are not. Therefore, they are not the same.

Let A = {a, b, c, d}
Define the partial ordering P defined on A by a<b<c<d.
Define the partial ordering Q defined on A by b<c<d<a
Define the partial ordering R defined on A by c<d<a<b

Nor is an equivalence relation sufficient for sameness as I pointed out how coffee cups and donuts can be in the same equivalence class (allowing them to share some characteristics). Yet obviously coffee cups and donuts have different properties and are not the same thing.

If you want to show that God and Reality are the same in a deeper way, then you need to explain how the properties of God and Reality are preserved.

Ponder This,

Sorry for the late reply. I was mentally incubating on a series of thoughtful replies to you.

Here is what I have so far.

Reality is an algebraic structure that is isomorphic to a description, where God is the describer. In Quantum Mechanics, the system in which the description is contained is known as the wavefunction, specifically the universal wavefunction. It carries the description of the universe. The describer is identified with the description and hence they are inseparable. This is why God cannot be distinguished from the background reality, because they are isomorphic and this makes Him infinite since reality is conceivably infinite: aleph_0 + aleph_0 = aleph_0. (Infinity is impossible to count for mere mortals). This makes both God and reality, hard to see. Reality is also comparable to the Quantum world at the fundamental level. This is where God resides. This explains why it is so hard to see God resulting in a lack of objective evidence. If the evolving universe is the mind of God, then it may be said that free will allows for a divergence from the universe's ultimate benevolent self-designing tendency.

Ponder This,

I was reminded of this thread today and I was hoping someone could add to my last statement.

This is proof that we are living in a simulation by the way. I rest my case. I came up with this while high.

Descriptions of reality are reality, so reality contains all descriptions of itself as part of itself, including every description of every description of reality, including every description of every description of every description of...

What's your opinion on recursively infinite sets of sets that contain themselves?

Kooky said:

Descriptions of reality are reality, so reality contains all descriptions of itself as part of itself, including every description of every description of reality, including every description of every description of every description of...

What's your opinion on recursively infinite sets of sets that contain themselves?

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It would seem that physical infinities may be an absurdity, however nothingness is an exception. If existence and non-existence are one then an infinite amount of matter can exist within an infinite amount of space (note I said space and not spacetime). But there is the widely accepted view that our physical universe was born out of nothingness (an 'it', which is synonymous with pure potential becoming actualized). However I do not accept the idea of an infinite universe but a conspansive one that remains the same size while it creates its spacetime from within. Conspansion implies that while the universe appears to expand from the materialist perspective it will appear to contract from the cosmic perspective. This is also held by blue collar cosmologist Christopher Langan. This idea is consistent with self-containment.

Reality is thus defined in such a way in which sets correspond to their self-peceptual elements.

Edit: Thus we have a new theory of reality in which sets correspond to their self-perceptual elements.