Violins of nothing

[Aloysium]

I still don’t understand how this is at all relevant. Sure, relationships exist. But you need objects in order to have relationships between objects. God has to create objects. I have pointed out problems in the concept of creating objects ex nihilo.

Nothing exists outside a relationship with something else.
This is obviously true in ourselves as material beings, transforming complex forms of matter into our own material substance, and in our perceptions and cognition.
But even in our understanding of matter itself, we conceptualize how

• atoms exist as the overarching relationship between subatomic constituents,
• molecules, increasingly complex relationships between atoms, which then
• come together within the relationship we know to be a living organism.
  All this coming into being within the the wholeness that is the relationship between God and His creation.

You mention objects. What do you think they are?

 

[thinkandmull]

Saying the world came by God and of from God surely puts “something from nothing” in a different perspective. So only a power, all great, can do this huh?

 

[yppop]

I still don’t understand how this is at all relevant. Sure, relationships exist. But you need objects in order to have relationships between objects. God has to create objects. I have pointed out problems in the concept of creating objects ex nihilo.

JK
The apparent dilemma between God’s omnipresence and “creation ex nihilo” is resolved with an understanding of the nature of infinity. In transfinite number theory, aleph(0) represents the infinitude of rational numbers and aleph(1) represents the infinitude of real numbers. The rational numbers are included in the real numbers.

Cantor has shown that each and every point in three dimensional space can be represented by a number on the real number line. The real numbers are dimensionally infinite and infinitely divisible, which means there are an infinitude of real numbers in any segment of the real number line however small you care to make it. Since the real numbers represent continuous space, in any three dimensional volume, however small, there will be an infinitude of points.

On the other hand, the rational numbers are denumerable, meaning they can be counted, and there are gaps between each and every rational number and its neighbors on the real number line. Rational numbers are infinite in dimensionality but are not infinitely divisible. Rational numbers represent discrete space.

Consider this relationship from transfinite theory: aleph(1) - aleph(0) = aleph(1)

This means that we can remove all the rational numbers from the real number line and hence all the points of discrete space from continuous space without change or diminishment to continuous space. Discrete space is imbedded in continuous space. Continuous space is omnipresent, discrete space is not.

I contend that it is discrete space that gives dimensionality to the universe. Since discrete space is composed of objects without dimension, namely points, and the universe is finite, I contend that the number of discrete points required to construct the universe and everything within is also finite. Any object with zero dimension, such as a point, when multiplied by a finite number, however large, still has zero dimension.

Consequently, there is an infinitude of continuous space designated as aleph(1) that cannot be diminished, and hence remains everywhere present in every infinite dimension (omnipresent) from which a finite volume of discrete space designated as aleph(0) has been separated (the singularity),

Hence: " aleph(0) - aleph(0) = aleph(1) " means the universe has been mathematically created from 0 = nothing (creation ex nihilo). And God has created the universe from nothing and still remains omnipresent.

If a finite and simple mind like mine can figure out how this dilemma, imagine what an infinite, omniscient, and omnipotent God can do.
Yppop

 

[JapaneseKappa]

JK
The apparent dilemma between God’s omnipresence and “creation ex nihilo” is resolved with an understanding of the nature of infinity. In transfinite number theory, aleph(0) represents the infinitude of rational numbers and aleph(1) represents the infinitude of real numbers. The rational numbers are included in the real numbers.

Cantor has shown that each and every point in three dimensional space can be represented by a number on the real number line. The real numbers are dimensionally infinite and infinitely divisible, which means there are an infinitude of real numbers in any segment of the real number line however small you care to make it. Since the real numbers represent continuous space, in any three dimensional volume, however small, there will be an infinitude of points.

On the other hand, the rational numbers are denumerable, meaning they can be counted, and there are gaps between each and every rational number and its neighbors on the real number line. Rational numbers are infinite in dimensionality but are not infinitely divisible. Rational numbers represent discrete space.

Consider this relationship from transfinite theory: aleph(1) - aleph(0) = aleph(1)

This means that we can remove all the rational numbers from the real number line and hence all the points of discrete space from continuous space without change or diminishment to continuous space. Discrete space is imbedded in continuous space. Continuous space is omnipresent, discrete space is not.

I contend that it is discrete space that gives dimensionality to the universe. Since discrete space is composed of objects without dimension, namely points, and the universe is finite, I contend that the number of discrete points required to construct the universe and everything within is also finite. Any object with zero dimension, such as a point, when multiplied by a finite number, however large, still has zero dimension.

Consequently, there is an infinitude of continuous space designated as aleph(1) that cannot be diminished, and hence remains everywhere present in every infinite dimension (omnipresent) from which a finite volume of discrete space designated as aleph(0) has been separated (the singularity),

Hence: " aleph(0) - aleph(0) = aleph(1) " means the universe has been mathematically created from 0 = nothing (creation ex nihilo). And God has created the universe from nothing and still remains omnipresent.

If a finite and simple mind like mine can figure out how this dilemma, imagine what an infinite, omniscient, and omnipotent God can do.
Yppop

This sounds like the sort of thing you might hear in a freshman philosophy class after requiring the students to read the wikipedia page on the concept of cardinality. There is a lot more philosophical speculation than understanding of mathematics.

My argument has basically been that if you let ℝ be God and ℚ be us, ℚ⊆ℝ

You’re sort of saying that God is actually the set difference ℝ\ℚ. But while ℝ\ℚ has the same cardinality as ℝ, it is certainly doesn’t have the same elements. And so my original point is still somewhat relevant. Can you meaningfully define ℝ\ℚ if ℚ doesn’t exist? Or, alternatively, if there are a set of points that God is defined not to be, then in what sense did he create those points?

In my mind, God would not have created the points which are defined to not be in God, but rather those points would exist by virtue of the definition of God (i.e. necessarily.)

I think the much simpler hypothesis would be to think of God as originally ℝ, but at some point defined ℚ as us, and so we were created out of God.

 

[Aloysium]

. . . it is discrete space that gives dimensionality to the universe. Since discrete space is composed of objects without dimension, namely points, and the universe is finite, I contend that the number of discrete points required to construct the universe and everything within is also finite. Any object with zero dimension, such as a point, when multiplied by a finite number, however large, still has zero dimension.

Consequently, there is an infinitude.of continuous space designated as aleph(1) that cannot be diminished, and hence remains everywhere present in every infinite dimension (omnipresent) from which a finite volume of discrete space designated as aleph(0) has been separated (the singularity),

Hence: " aleph(0) - aleph(0) = aleph(1) " means the universe has been mathematically created from 0 = nothing (creation ex nihilo). And God has created the universe from nothing and still remains omnipresent. . .

The mathematics might more represent an underlying (un)structure from which creation emerges.
It is not God.
It is not actually nothing either, as the foundation of and the overarching reality containing all things.

 

[yppop]

This sounds like the sort of thing you might hear in a freshman philosophy class after requiring the students to read the wikipedia page on the concept of cardinality. There is a lot more philosophical speculation than understanding of mathematics.

What is this? Are you seriously implying that I am immature (freshman philosophy)?; uneducated (wikipedia)?; and lacking mathematical knowledge (philosophical speculation)?
If you read my bio I think I deserve more respect than that. Or are you merely trying to divert my attention from the fact that it appears that you don’t understand my argument

My argument has basically been that if you let ℝ be God and ℚ be us, ℚ⊆ℝ

I believe you are playing with finite sets here. I am playing with infinite sets.

You’re sort of saying that God is actually the set difference ℝ\ℚ.

What does “sort of saying” mean? I never said anything of the sort. I don’t know what God is. I am merely arguing that if we can use transfinite numbers as a possible way of showing the compatibility of “omnipresence” and “creatio ex nihilo”, then surely God can do it.

But while ℝ\ℚ has the same cardinality as ℝ, it is certainly doesn’t have the same elements. And so my original point is still somewhat relevant. Can you meaningfully define ℝ\ℚ if ℚ doesn’t exist? Or, alternatively, if there are a set of points that God is defined not to be, then in what sense did he create those points?

R\Q is not a set; it merely indicates that what is in R is not in Q. When discussing infinite sets, as I am in my post, the cardinality of infinite R is aleph(1) and the cardinality of Q is aleph(0) and aleph(1) - aleph(0) = aleph (1) no matter what the elements are. The cardinality of a set is not associated with the nature of the elements whether they are dogs or numbers. {Fido, Lassie, and Snoopy} = {5,11,17} = cardinality 3. I know this may seem intuitively mind boggling but after the rational numbers are removed from the real number line there is still the same number, aleph(1), remaining in aleph (1) in spite of my typo aleph(0) - aleph(0) - aleph(1) in my second last paragraph.

YPPOP

 

[JapaneseKappa]

What is this? Are you seriously implying that I am immature (freshman philosophy)?; uneducated (wikipedia)?; and lacking mathematical knowledge (philosophical speculation)?
If you read my bio I think I deserve more respect than that. Or are you merely trying to divert my attention from the fact that it appears that you don’t understand my argument

I believe you are playing with finite sets here. I am playing with infinite sets.

So you are capable of saying the words “The real numbers are dimensionally infinite and infinitely divisible…On the other hand, the rational numbers are denumerable” but you are not capable of recognizing the normal math symbols for the real numbers or rational numbers? I’m not sure how you can think I’m “playing with finite sets” when you yourself referenced the same sets in your post to explain the difference in your alephs.

What does “sort of saying” mean? I never said anything of the sort. I don’t know what God is. I am merely arguing that if we can use transfinite numbers as a possible way of showing the compatibility of “omnipresence” and “creatio ex nihilo”, then surely God can do it.

I said “sort of” because I didn’t think you were actually saying God was exactly the same thing as the rational numbers. But it certainly seemed like you were using the rational numbers as an analogy to understand God when you said “Consequently, there is an infinitude of continuous space designated as aleph(1) that cannot be diminished, and hence remains everywhere present in every infinite dimension (omnipresent) from… aleph(0)”

R\Q is not a set; it merely indicates that what is in R is not in Q. When discussing infinite sets, as I am in my post, the cardinality of infinite R is aleph(1) and the cardinality of Q is aleph(0) and aleph(1) - aleph(0) = aleph (1) no matter what the elements are.

I’m pretty sure that anyone whose math knowledge is deserving of respect would know that the result of a set subtraction is in fact a set. I drew attention to the fact that ℚ is not a subset of ℝ\ℚ to address your “omnipresence” quip. Even though ℝ\ℚ is still uncountably infinite, it no longer contains ℚ.

 

[yppop]

Kappa,

1. The set of points in an infinitude of 3-dimensional continuous space has the same cardinality as R, the set of real numbers, namely aleph(1)
2. Continuous space is infinitely divisible and infinite in extent, i.e., it is densely present everywhere.
3. An infinite volume of continuous space is by definition omnipresence.
4. The set of points in an infinitude of 3-dimensional discrete space has the same cardinality as Q, the set of rational numbers, aleph(0).
5. "aleph(1) - aleph(0) = aleph(1)" is to say that: "aleph(1) - 0 = aleph(1)"
6. In the world of real number infinitudes, aleph(0) is, by definition, nothing.

I know you don’t understand my argument because you obviously missed the most important contention found in my original post.

From my post 43

“I contend that it is discrete space that gives dimensionality to the universe. Since discrete space is composed of objects without dimension, namely points, and the universe is finite, I contend that the number of discrete points required to construct the universe and everything within is also finite. Any object with zero dimension, such as a point, when multiplied by a finite number, however large, still has zero dimension.”

I use aleph(1) to demonstrate omnipresence and aleph(0) to represent nihilo the above paragraph is my approach to the “creation” part of “creatio ex nihilo”.

If you can’t disprove any of the 6 numbered statements above directly without diversion then I will allow you a final personal attack without recrimination. I assume you are a young man or woman (your anonymity doesn’t allow anything else) and have the personal need of the immature mind for personal attack and diversion. You could debunk this assumption by telling me how old you are and what kind of education you have.

Yppop

PS - From my bio you should figure out that Yppop is Poppy spelled backwards and being a grandfather was one of my aspirations, greatly achieved . What does a “JapaneseKappa” aspire to?

 

[thinkandmull]

soryy yppop, but this discussion has descended into nonsense. Mathematical formulaes have nothing to do with understanding “something from nothing”

 

[Aloysium]

0 is not nothing; it is no-thing.
Nothing would be something like the non-existence of mathematics.
God created the No-thing underlying the universe (energy let’s call it) which was added to in the creation of each hierarchical level leading to mankind.

:twocents:

 

[thinkandmull]

If nothing is like a basis or entity, why can’t things pop out of it on their own?

 

[Aloysium]

Even from an unformed substrate of being already in existence, there has to be a cause for something to appear.
Very, very, very tiny things may come in and out of existence, but that would reflect the properties of the medium in which it occurs.

:twocents:

 

[Peter_Plato]

If nothing is like a basis or entity, why can’t things pop out of it on their own?

On AT (Aristotelian-Thomistic) metaphysics, things can only exist actually if they have the potential to exist. No-thing would be something like the non-existence of things that could exist. In other words, creation ex nihilo or “from nothing” would mean something like actualizing the existence of things which could exist potentially. Arising ex nihilo means coming from the nothing which is the potentiality of things that can be actualized.

God, as Actualizer, brings things which potentially are (but in actuality are not) into existence. These entities exist only in virtue of their potential to exist being actualized in fact. In effect, they are nothing until actualized, at which point they come into existence “from nothing” (ex nihilo.)

The other point to be made relates to the manner in which things exist. Contingent things are not ens ex se (out of their own being) but, rather, they are ***ens ab alio ***(have being in something else.)

It has been argued in this thread (by some) that things cannot come from nothing but must, therefore, be made out of the Being of God. That need not be true because the third possibility is that contingent things may be ontologically grounded in a kind of existential “medium” (space-time) which enables the potential existence of material entities by essentially delimiting their mode of existence. The manner in which they exist is not in God, not Ipsum Esse Subsistens, but being grounded in contingency or potentiality (ens ab alio.)

 

[JapaneseKappa]

1. An infinite volume of continuous space is by definition omnipresence.

That is a really weird definition of omnipresence. I imagine a second set of three dimensions which does not intersect our own. How can our three dimensional space be omnipresent if it is not present in these new dimensions?

1. The set of points in an infinitude of 3-dimensional discrete space has the same cardinality as Q, the set of rational numbers, aleph(0).
2. "aleph(1) - aleph(0) = aleph(1)" is to say that: "aleph(1) - 0 = aleph(1)"
3. In the world of real number infinitudes, aleph(0) is, by definition, nothing.

This seems to me to be an abuse of your own notation. aleph(0) does not (or at least should not) mean “some quantity aleph times 0.” Or, perhaps, you think subtraction works the same way with transfinites as with finite numbers?

en.wikipedia.org/wiki/Cardinal_number#Subtraction
“Assuming the axiom of choice and, given an infinite cardinal σ and a cardinal μ, there exists a cardinal κ such that μ + κ = σ if and only if μ ≤ σ. It will be unique (and equal to σ) if and only if μ < σ.”

In other words, since in your example μ = σ, the κ which satisfies the equation μ + κ = σ is not unique. Therefore, just because you can find some κ1 and κ2 which satisfy the equation, it does not follow that κ1=κ2. In other words, aleph(0) is not magically equal 0 as soon as aleph(1) walks in the room. If we could, then we could trivially prove that 1=2=3=4=5=… which is a clear contradiction.

I use aleph(1) to demonstrate omnipresence and aleph(0) to represent nihilo the above paragraph is my approach to the “creation” part of “creatio ex nihilo”.

If you can’t disprove any of the 6 numbered statements above directly without diversion then I will allow you a final personal attack without recrimination. I assume you are a young man or woman (your anonymity doesn’t allow anything else) and have the personal need of the immature mind for personal attack and diversion. You could debunk this assumption by telling me how old you are and what kind of education you have.

PS - From my bio you should figure out that Yppop is Poppy spelled backwards and being a grandfather was one of my aspirations, greatly achieved . What does a “JapaneseKappa” aspire to?

I aspire to gain power by taking people’s shirikodama.

Your analogy has several problems with it’s mathematical basis, but there are even bigger-picture problems with it. My original point, which prompted your mathmatical hand-waving was that “in the beginning” there is no way to “get outside” God that would allow him to create ex nihilo. Your response seemed to be “well, if God is like the real numbers, and we are like some finite set of rational numbers, then compared to God our cardinality is basically 0.” But now I think you were not even saying that, you might have been saying that some sort of 3-coordinate space existed “in the beginning” but wasn’t part of God. The problem here is that either God created the 3 coordinate space ex nihilo (in which case you’re trying to avoid the problem I raised by hiding the ex nihilo creation) or the 3 coordinate space is some sort of second uncaused cause.

In any case, if we go with my initial interpretation (that the real numbers are like God and we are like some finite set of rational numbers) then we have always been a subset, or part, of God. If God at some point designated our particular set as special, he didn’t do so ex nihilo, but rather ex-himself.

 

[JapaneseKappa]

It has been argued in this thread (by some) that things cannot come from nothing but must, therefore, be made out of the Being of God. That need not be true because the third possibility is that contingent things may be ontologically grounded in a kind of existential “medium” (space-time) which enables the potential existence of material entities by essentially delimiting their mode of existence. The manner in which they exist is not in God, not Ipsum Esse Subsistens, but being grounded in contingency or potentiality (ens ab alio.)

But it would then be fine to argue that space-time itself was made out of the being of God?

 

[Peter_Plato]

But it would then be fine to argue that space-time itself was made out of the being of God?

Space-time does not exist a se, ergo it cannot be “made out of the Being of God” who is Ipsum Esse Subsistens.

 

[JapaneseKappa]

Space-time does not exist a se, ergo it cannot be “made out of the Being of God” who is Ipsum Esse Subsistens.

1: How do you know space-time itself does not exist a se?
2: What is the “existential medium” in which space-time itself is grounded, and where did it come from?

That need not be true because the third possibility is that contingent things may be ontologically grounded in a kind of existential “medium” (space-time) which enables thepotential existence of material entities by essentially delimiting their mode of existence."

 

[Peter_Plato]

1: How do you know space-time itself does not exist a se?

Standard inflationary cosmology. Space-time continuum came into existence 13.7 billion years ago.

2: What is the “existential medium” in which space-time itself is grounded, and where did it come from?

No, space-time IS the existential medium which grounds material existents.

 

[JapaneseKappa]

Standard inflationary cosmology. Space-time continuum came into existence 13.7 billion years ago.

But this is the sort of “coming into existence” that people like Hawking famously claim is possible. They are not so much asserting that something can come from a philosophical nothing as they are asserting that our space-time continuum is itself embedded in something else which allows space-time continuums to spontaneously sprout.

No, space-time IS the existential medium which grounds material existents.

But it does exist, right? Your contention was, quote, " That need not be true because the third possibility is contingent things may be ontologically grounded in a kind of existential “medium”" Therefore, if space-time is a thing that exists and it is contingent, that it must therefore be “grounded in a kind of existential medium.” Otherwise it needs to be true that, as you put it:

“It has been argued in this thread (by some) that things cannot come from nothing but must, therefore, be made out of the Being of God.”

 

[Peter_Plato]

But this is the sort of “coming into existence” that people like Hawking famously claim is possible. They are not so much asserting that something can come from a philosophical nothing as they are asserting that our space-time continuum is itself embedded in something else which allows space-time continuums to spontaneously sprout.

That would lead to either:

1. An infinite regress of continuums grounded in continuums grounded in continuums, ad infinitum, or
2. An Arisotelian-Thomistic (AT) Uncaused Cause (Ipsum Esse Subsistens) which exists a se and which self-explains its own existence and does not require a ground of being beyond itself.

The problem with Hawking’s “something else” (quantum vacuum?) to ground space-time is that he is merely off-loading the explanatory principle onto some unspecified ground from which things “spontaneously sprout” so as to waylay the need to explain what this mysterious existential ground could possibly be.

Even if he is correct that this “something else” exists he still hasn’t shown how it explains what does exist. AT metaphysics makes the claim that at some point a sufficiently explanatory ground MUST exist - the regress cannot go on indefinitely or nothing is ultimately explained.

But it does exist, right? Your contention was, quote, " That need not be true because the third possibility is contingent things may be ontologically grounded in a kind of existential “medium”" Therefore, if space-time is a thing that exists and it is contingent, that it must therefore be “grounded in a kind of existential medium.” Otherwise it needs to be true that, as you put it:

“It has been argued in this thread (by some) that things cannot come from nothing but must, therefore, be made out of the Being of God.”

By "existential medium” I mean a kind of “mode” of existence according to which individual entities subsist on their own terms. Physical entities exist within space-time-matter-energy as the mode according to which they exist. They exist as material beings within space-time as their medium.

To try to “ground” material entities in God as their “ground of being” is much like attempting to ground ideas/dreams/qualia in the material world as if these things exist as physical entities. They simply don’t.

The analog could be something like ideas/dreams/qualia are to the material world as physical entities are to God. God, then is “super-real” relative to material creation in the analogous sense that physical entities in the material world appear “super-real” compared to dreams/ideas/qualia.

We would not claim material things are made “out of the being of God” any more than we would claim dreams or ideas are made "out of the being of matter.”

This would not prevent differing ontological realities from “instantiating" in some sense within other levels of reality.

Another example: we would not say that numbers exist “materially” even though material entities in some sense “correspond” to or exhibit mathematical existents. We surely would say numbers are “made out of” the being of matter, would we?