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# This has always bugged me (eternal, finite universe, plenum)

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I understand that their are no actual infinities. The infinite in mathematics is just a potentiality. I understand that the universe has to be eternal, meaning outside of time or always existing, because the opposite, that it was "created" is nonsense and violates A is A, etc. Same thing with its finiteness, there can't exist an actual infinite amount of things.

I don't understand, however, why the universe has to be a plenum, that every nook and cranny has to be "filled" with existents. I just don't see why that is necessary, from how I believe LP explained it, that to say their is "empty space" is to say that nothing exists. I don't see it that way, when saying no thing (i.e. nothing) occupies a volume you are not saying that a unit(s) of nothingness exist in that volume, you are just saying that at that given point in time, no actual existents are occupying it, and that can change, some thing can move into it.

The universe being a plenum, to me brings up a very complicated problem, namely that question that is always brought up, what is outside of it. What happens when you approach the "edge", because the universe is finite. Then LP will of course reply with, well you can't ask that, that question is invalid, etc. I think he or some Objectivist said the universe will have a way to make it so you can't reach the edge, which I thought was a bit outside the purview of metaphysics, describing how the universe works physically.

A finite and non-plenum universe would have no edge, it would be just a bunch a finite matter interacting within a void. And that void would stretch out infinitely in all directions, infinite because the infinite can be applied to a non-entity, really just a concept used in relationships of existents, "space".

That was my tirade on a plenum.

Now back to eternality, and finiteness, from the beginning.

But when picturing this it seems somewhat odd, or you can't really wrap your head around it. Wouldn't an eternal universe have an infinite amount of events, happening within it. Doesn't that violate A is A?

I guess there isn't really anything wrong with the finite part, it would seem a bit odd though when thinking about it in both a non-plenum or plenum universe. The non-plenum being the fact that if you "left" the universe, there being no edge, just leaving the vicinity of all those other existents, and kept looking back at it the scale of the universe would look pretty small a ways out there. And I think I explained earlier the weirdness of the plenum finiteness, there being an edge, what is outside, and so forth.

If anyone can share their thoughts on the subject that would be great.

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I don't understand, however, why the universe has to be a plenum, that every nook and cranny has to be "filled" with existents. I just don't see why that is necessary, from how I believe LP explained it, that to say their is "empty space" is to say that nothing exists. I don't see it that way, when saying no thing (i.e. nothing) occupies a volume you are not saying that a unit(s) of nothingness exist in that volume, you are just saying that at that given point in time, no actual existents are occupying it, and that can change, some thing can move into it.

The universe being a plenum, to me brings up a very complicated problem, namely that question that is always brought up, what is outside of it. What happens when you approach the "edge", because the universe is finite. Then LP will of course reply with, well you can't ask that, that question is invalid, etc. I think he or some Objectivist said the universe will have a way to make it so you can't reach the edge, which I thought was a bit outside the purview of metaphysics, describing how the universe works physically.

A finite and non-plenum universe would have no edge, it would be just a bunch a finite matter interacting within a void. And that void would stretch out infinitely in all directions, infinite because the infinite can be applied to a non-entity, really just a concept used in relationships of existents, "space".

That was my tirade on a plenum.

Now back to eternality, and finiteness, from the beginning.

But when picturing this it seems somewhat odd, or you can't really wrap your head around it. Wouldn't an eternal universe have an infinite amount of events, happening within it. Doesn't that violate A is A?

I guess there isn't really anything wrong with the finite part, it would seem a bit odd though when thinking about it in both a non-plenum or plenum universe. The non-plenum being the fact that if you "left" the universe, there being no edge, just leaving the vicinity of all those other existents, and kept looking back at it the scale of the universe would look pretty small a ways out there. And I think I explained earlier the weirdness of the plenum finiteness, there being an edge, what is outside, and so forth.

If anyone can share their thoughts on the subject that would be great.

The concept of a "plenum" depends on a concept of space.  Since children do not begin their lives knowing about points defined by coordinate systems, we should not take the concept of space as an unquestioned primary.  The standard of objectivity demands that we take some time to understand how a concept as abstract as space derives in a logical fashion from perceptual observation.  Towards that end, I pose four questions to you:

1. What facts in reality give rise to the concept of space?

2. What concepts did you need to form before you could form a concept of space? And before those concepts?

3. What did you need to know in order to form a concept of space?

4. How did you form the concept of space? What similarities and differences were you concerned with?

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I should elaborate on the hierarchy involved.

The concept of point refers to a specific location.  We identify specific locations by reference to nearby entities.

In geometry, points are defined by use of a coordinate system.  The x-y-z coordinate system was defined after someone noticed some tiles in the corner of a room.  The polar coordinate system was developed after the ancients considered circles and chords.

Before you can even think of defining a coordinate system, you need to consider spatial relationships among real objects.

Your computer monitor is the above the floor.

One could not deny that the monitor really is above the floor.  The concept of "above" applies to an existent relationship involving two other existents.  The monitor is an entity.  The floor can be viewed as part of another entity.  The concept of existent permits you to subsume under and focus on the relationship.  It permits you to subsume under and focus on that which depends on entities but can be studied separately.

So entities are not the only existents.  Relationships are existents too.

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The concept of a "plenum" depends on a concept of space.  Since children do not begin their lives knowing about points defined by coordinate systems, we should not take the concept of space as an unquestioned primary.  The standard of objectivity demands that we take some time to understand how a concept as abstract as space derives in a logical fashion from perceptual observation.  Towards that end, I pose four questions to you:

1. What facts in reality give rise to the concept of space?

2. What concepts did you need to form before you could form a concept of space? And before those concepts?

3. What did you need to know in order to form a concept of space?

4. How did you form the concept of space? What similarities and differences were you concerned with?

1. The basic facts are existents in reality (a floor, a computer monitor), and they can be positioned in any manner in relation to another.

2. You needed the concepts of actual existents, and relational concepts such as apart (they are 3 feet apart).

3. I think that is the same as 1 and 2.

4. That would take a longer time to explain.

Edited by abott1776
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The concept of a "plenum" depends on a concept of space.  Since children do not begin their lives knowing about points defined by coordinate systems, we should not take the concept of space as an unquestioned primary.  The standard of objectivity demands that we take some time to understand how a concept as abstract as space derives in a logical fashion from perceptual observation.  Towards that end, I pose four questions to you:

1. What facts in reality give rise to the concept of space?

2. What concepts did you need to form before you could form a concept of space? And before those concepts?

3. What did you need to know in order to form a concept of space?

4. How did you form the concept of space? What similarities and differences were you concerned with?

After thinking about this I don't see where you are going with this. Was my usage of the concept space wrong? Explain any errors in my original post about plenum, space, etc.

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I think of it by imagining myself floating in outer space and holding my hands about a foot apart from each other.   Looking at the "space" in-between my hands, I try to imagine what it would mean for that space not to exist (or not to be possible, if you prefer).

As you mentioned, the "empty space" does not exist as an entity.  Its identity is a relational measurement.   So, for as many events that are known, you have a definite (not infinite) size of the universe.

So, perhaps the answer to you would be that the "infinite amount of events" you mentioned is simply a contradiction in terms because an "amount" is, by definition, finite.

You could also flip it and go the other way (kinda like your example of scaling the universe down).  Take a grain of sand and you can measure distances smaller and smaller across that grain for as long as you have decimal points.  In that case you're measuring an actual entity the whole time... and you can still measure forever.

*Disclaimer on above:  I think.  :-)

Not sure if this is what you're looking for, but there was a lot of discussion around this subject in this thread:  The Potential Infinity Contradiction

Edited by freestyle
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After thinking about this I don't see where you are going with this. Was my usage of the concept space wrong? Explain any errors in my original post about plenum, space, etc.

Your concept of "apart" would not have been possible without isolating and distinguishing spatial relationships from every other kind of existent you know.  Relationships don't exist apart from entities.

First you learn about entities.  Then you learn about spatial relationships among entities, such as "above".  Then you take some entities as references for defining a coordinate system.  Then you can talk about "2-space" or "3-space".

"Space" has no existence apart from relationships.

The referent of "space" is not some framework within which entities move.  It is simply the extent defined by entities, moving or not.

That extent is not some non-existence.

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I think of it by imagining myself floating in outer space and holding my hands about a foot apart from each other.   Looking at the "space" in-between my hands, I try to imagine what it would mean for that space not to exist (or not to be possible, if you prefer).

As you mentioned, the "empty space" does not exist as an entity.  Its identity is a relational measurement.   So, for as many events that are known, you have a definite (not infinite) size of the universe.

So, perhaps the answer to you would be that the "infinite amount of events" you mentioned is simply a contradiction in terms because an "amount" is, by definition, finite.

You could also flip it and go the other way (kinda like your example of scaling the universe down).  Take a grain of sand and you can measure distances smaller and smaller across that grain for as long as you have decimal points.  In that case you're measuring an actual entity the whole time... and you can still measure forever.

*Disclaimer on above:  I think.  :-)

Not sure if this is what you're looking for, but there was a lot of discussion around this subject in this thread:  The Potential Infinity Contradiction

You are treating space as an existent, in that second sentence. All that space is is a relationship concept between existents. The space between your two hands is a distance. The plenum argument says that there must be other existents in that space (distance). I am saying that is not necessary. When I say space is a relational concept, how is that affirming that non-existence exists?

This is how I would think about the subject of eternity

Eternity is a kin to saying the universe is infinite in size.It seems to me that there is a problem with both the universe having a beginning or it being eternal. To say something is eternal is to say it has gone through an infinite amount of states. Would that not be an actual infinity?

This is how I have usually challenged that thinking:

Another way to think about the eternity of every existent in the universe, is that there is no time apart from change, in relation to some other change. When we say 4 billion years ago the earth was created, we don't mean some metaphysical universal time, we are saying 4 billion rotations of the earth around the sun (a change) the earth evolved from this collection of debris to what it is today (another change). When I've been really eager to be pensive and abstract I have often tried to think of the universe as being without time but with change. To talk about the time of the universe would be to talk about the change of the universe compared to some other change. But like LP said what other change? All you have are all the changes within the universe.

The next question, I can think of is how can there be an infinite changes, as the eternity suggests, no beginning change, no ending change. It is that classic, infinite regress, used against proponents of a god.

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I think of it by imagining myself floating in outer space and holding my hands about a foot apart from each other.   Looking at the "space" in-between my hands, I try to imagine what it would mean for that space not to exist (or not to be possible, if you prefer).

As you mentioned, the "empty space" does not exist as an entity.  Its identity is a relational measurement.   So, for as many events that are known, you have a definite (not infinite) size of the universe.

So, perhaps the answer to you would be that the "infinite amount of events" you mentioned is simply a contradiction in terms because an "amount" is, by definition, finite.

You could also flip it and go the other way (kinda like your example of scaling the universe down).  Take a grain of sand and you can measure distances smaller and smaller across that grain for as long as you have decimal points.  In that case you're measuring an actual entity the whole time... and you can still measure forever.

*Disclaimer on above:  I think.  :-)

Not sure if this is what you're looking for, but there was a lot of discussion around this subject in this thread:  The Potential Infinity Contradiction

You are treating space as an existent, in that second sentence. All that space is is a relationship concept between existents. The space between your two hands is a distance. The plenum argument says that there must be other existents in that space (distance). I am saying that is not necessary. When I say space is a relational concept, how is that affirming that non-existence exists?

This is how I would think about the subject of eternity

Eternity is a kin to saying the universe is infinite in size.It seems to me that there is a problem with both the universe having a beginning or it being eternal. To say something is eternal is to say it has gone through an infinite amount of states. Would that not be an actual infinity?

This is how I have usually challenged that thinking:

Another way to think about the eternity of every existent in the universe, is that there is no time apart from change, in relation to some other change. When we say 4 billion years ago the earth was created, we don't mean some metaphysical universal time, we are saying 4 billion rotations of the earth around the sun (a change) the earth evolved from this collection of debris to what it is today (another change). When I've been really eager to be pensive and abstract I have often tried to think of the universe as being without time but with change. To talk about the time of the universe would be to talk about the change of the universe compared to some other change. But like LP said what other change? All you have are all the changes within the universe.

The next question, I can think of is how can there be an infinite changes, as the eternity suggests, no beginning change, no ending change. It is that classic, infinite regress, used against proponents of a god.

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Your concept of "apart" would not have been possible without isolating and distinguishing spatial relationships from every other kind of existent you know.  Relationships don't exist apart from entities.

First you learn about entities.  Then you learn about spatial relationships among entities, such as "above".  Then you take some entities as references for defining a coordinate system.  Then you can talk about "2-space" or "3-space".

"Space" has no existence apart from relationships.

The referent of "space" is not some framework within which entities move.  It is simply the extent defined by entities, moving or not.

That extent is not some non-existence.

I answered those numbered questions of yours in the beginning. I know you can't have the concept of space without the precondition of concepts of entities. I know it is a relational concept.

I think it is important to make the distinction between space and a void. Space is a relational concept between existents. A void is the concept that given (in a simplified example) two entities, that do not touch, there are no other entities in between those two entities. I am not referencing space as being a non-existent. Space in that sentence merely relates the two entities, not the nature of what is between the two entites. That nature is the concept, void.

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I answered those numbered questions of yours in the beginning. I know you can't have the concept of space without the precondition of concepts of entities. I know it is a relational concept.

I think it is important to make the distinction between space and a void. Space is a relational concept between existents. A void is the concept that given (in a simplified example) two entities, that do not touch, there are no other entities in between those two entities. I am not referencing space as being a non-existent. Space in that sentence merely relates the two entities, not the nature of what is between the two entites. That nature is the concept, void.

How would you know whether there was a void between two particular entities?  What if future scientists discovered smaller entities than we currently know?

The manner in which this "void" is defined seems to demand omniscience.

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How would you know whether there was a void between two particular entities?  What if future scientists discovered smaller entities than we currently know?

The manner in which this "void" is defined seems to demand omniscience.

By those first two questions, you seem to be putting the question of a plenum, in the realm of science. According to LP, it is in the realm of metaphysics, which is it?

Omniscience, so does a plenum.

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By those first two questions, you seem to be putting the question of a plenum, in the realm of science. According to LP, it is in the realm of metaphysics, which is it?

Omniscience, so does a plenum.

When I see "void" used by philosophers, I usually think of the one that's supposed to contain nothing. But you know that there is no nothing.   You're talking about the absence of entities.  That doesn't match any definition of "void" I've seen.

OTOH, I don't know any word that names the absence of entities.  I have to use the phrase "absent of entities".  But there is no nature to a logical absence beyond the relationship of absence.

So what are you talking about?

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You are treating space as an existent, in that second sentence. All that space is is a relationship concept between existents. The space between your two hands is a distance. The plenum argument says that there must be other existents in that space (distance). I am saying that is not necessary. When I say space is a relational concept, how is that affirming that non-existence exists?

I was, yes, for the purpose of illustrating something.   When I say to imagine nothingness not being, it should be read as an obvious contradiction.  While it doesn't make sense, it does (for me) make it very clear that I cannot have an "edge of," or the "outside of," the universe.  That is also a contradiction.

The plenum argument, as I think you're representing it, would take into account your hands (ie. the entities that allow you to identify the measurement of "the" space) and therefore would account for the existents you mention.

But I was most definitely not affirming that non-existence exists.  The opposite is true.  Existence existes.

But just to be clear: When you say, "I don't understand, however, why the universe has to be a plenum", can you point to exactly where you got that from (if I missed it above).  I'd like to read it in full context.

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When I see "void" used by philosophers, I usually think of the one that's supposed to contain nothing. But you know that there is no nothing.   You're talking about the absence of entities.  That doesn't match any definition of "void" I've seen.

OTOH, I don't know any word that names the absence of entities.  I have to use the phrase "absent of entities".  But there is no nature to a logical absence beyond the relationship of absence.

So what are you talking about?

A void is a volume of space (space meaning say a distance between two protons, or two hands or two galaxies, space as a relational concept) that contains no thing, no entities. An "absence of entities" is a void.

Maybe from what you were reading in wacky philosophers they tried to make a void, a thing. All I am saying a void conceptually is is an absence of entities in a volume as compared to a volume filled with entities. If there was a volume of oxygen filled to the brim, then all the oxygen molecules were extracted out, you would have a void, an absence of all those molecules.

Is that clear enough?

If LP would say that is impossible, because the universe is a plenum, would he be correct?

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I was, yes, for the purpose of illustrating something.   When I say to imagine nothingness not being, it should be read as an obvious contradiction.  While it doesn't make sense, it does (for me) make it very clear that I cannot have an "edge of," or the "outside of," the universe.  That is also a contradiction.

The plenum argument, as I think you're representing it, would take into account your hands (ie. the entities that allow you to identify the measurement of "the" space) and therefore would account for the existents you mention.

But I was most definitely not affirming that non-existence exists.  The opposite is true.  Existence existes.

But just to be clear: When you say, "I don't understand, however, why the universe has to be a plenum", can you point to exactly where you got that from (if I missed it above).  I'd like to read it in full context.

He says that in his history of philosophy course when talking about Heraclitus and his idea, in which LP agrees, that the universe has to be a plenum because "there can't be nothing", nothing cannot exist.

LP goes over some questions on the Universe in these links:

http://www.peikoff.com/page/6/?s=universe#list

http://www.peikoff.com/page/5/?s=universe#list

In the first link, in an answer, he makes the claim that there is existence, a plenum by his accounts, filled to the brim with existents, whether that be protons, neutrons, electrons, and presumably some unknown other stuff we haven't discovered yet, and then there is a boundary to it and non-existence. He claims that if you were to try to travel to that boundary, and "through" it, you physically couldn't.

To me, as soon as you put forth this claim to a "boundary", the next thing I think of is a boundary between what and what. That other what beings something that exists, not some "non-existence", it seems ludicrous to me.

When you say my hands are the existents in the plenum argument, no, not according to LP, there would have to be some other existents in between them. He would not accept any absence of entities in between them.

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Others probably have a better understanding of this. I welcome their additions or corrections.

Lawrence Krauss recently wrote a book called, A Universe From Nothing. I haven't read it, but I have listened to him speak on the subject. He argues that the void of space has properties, including (but, as far as I know, not limited to) being a sort of unstable state of energy. He describes it as a sort of zero-value state on a scale with both positive and negative values. At any given moment that void could spew out two oppositely charged particles, like a positron and an electron. This is as accurate as my cave-man  brain can describe it. The point is that the void of space has properties, which supports the plenum argument. Inexplicably, Krauss gets upset with philosophers who tell him that this means the universe didn't come from nothing.

Also, he says that the universe can propagate no faster than the speed of light. Because we know the approximate age of the universe, he says we know approximately how wide it is.

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As an addendum I'd like to say that I'm uncomfortable with the way scientists use the word, "universe." To me, that always meant everything that exists, or everything that has, does and will exist. And then they start talking about multiverses, which forces a redefinition of universe to describe a mere fraction of what that word used to mean. It also requires a new word, which I'm not sure has been coined yet. Omniverse, maybe?

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There are a number of misconceptions above. Consider the following:

Take a bucket of water tied to a rope outside on a clear night, spin the bucket and watch what happens to the water. The water wells up on the sides of the bucket and is depressed in the middle but only when the bucket spins relative to the stars. If there were no stars, what would the water be spinning relative to? There could be no sense in which the water could be said to be spinning without the stars. The welling up of the water is not possible without the stars. In this way, the mass of the distant galaxies has a sensible effect on you. Since this is the case, in what sense is the space between you and those galaxies empty? Information from all the galaxies within a finite distance from you is acting upon you.

Similarly, if you were to be hoisted 100 miles above the surface of the earth, you would fall to earth due to something trasmitted through the space between you and the earth. That "empty" space is not exactly empty.

The idea of going outside of the matter within the universe to an empty region is an abstraction having no perceivable examples and so is rejected for the same reason God and ghosts are rejected. What is more, there are geometric models for which the universe is finite but without boundary. In these models, if you go far enough in one direction, then you end up where you started. This too is an abstraction with no basis in perception, but it shows that the presumption of an ability to go far enough to leave the finite region occupied by matter is a non sequitur.

In general relativity, masses change the shape of space around them. In this case, space is a something that has measurable properties. The properties of the space around you is affected by the distant galaxies, and you affect that space too.

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The most modern cosmologies have the universe expanding initially much faster than light. The constraints of the speed of light apply to objects within the universe and not to spacetime itself. Even so, there is a limit to how far you can observe determined by the thermal properties of the early universe. There is a finite amount you may observe, even if the universe is infinite. In other words, your universe is always finite.

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The universe cannot conceivably have an "edge".

It's been suggested that it may be spherical in higher dimensions [like Pac-Man; flying off of one side causes you to emerge on the other] or that it may be intuitively infinite; both are plausible to me.  However. . .

The concept of "length" is formed by comparing multiple entities, observing and identifying the differences in their sizes/shapes.

The concept of "distance" is formed by comparing multiple relationships between entities, observing and identifying the differences of their arrangements.

And while there is usually air inbetween any given pair of entities, that's derivative knowledge; a two-year-old forms the concept of "distance" specifically by considering them as separated by empty space.

So while the universe may be a metaphysical plenum (idk) that doesn't invalidate the concept of "space", which is relational between entities.  And I don't see how asserting that a hypothetical volume could truly be "empty" is an assertion of nonexistence; it's only asserting that there are 'no existents here' (which is just as valid as 'no jedi here').

What would be asserting the existence of a nothing is the concept of the universe's "edge" if it would be in any way discernable from the rest of the universe- because an edge divides one thing from another.

So if I were to declare that at some spot in space there is an "edge" of space, that would be a reification of the zero.  Specifically because it turns "space" from a relationship into its own entity.

Edited by Harrison Danneskjold
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A void is a volume of space (space meaning say a distance between two protons, or two hands or two galaxies, space as a relational concept) that contains no thing, no entities. An "absence of entities" is a void.

Maybe from what you were reading in wacky philosophers they tried to make a void, a thing. All I am saying a void conceptually is is an absence of entities in a volume as compared to a volume filled with entities. If there was a volume of oxygen filled to the brim, then all the oxygen molecules were extracted out, you would have a void, an absence of all those molecules.

Is that clear enough?

If LP would say that is impossible, because the universe is a plenum, would he be correct?

Ok so you are using "void" in a manner that was not specified in the dictionaries I've checked.

That's fine since we acknowledge that we are talking about a concept distinct from those defined in the dictionary.

I would say that if you remove all entities between two other entities, you end up with only the relationships between those two entities.

The totality of all that exists has no regions of non-existence.  One could say there is a "plenum" of existence, if one acknowledge the departure from the use of "plenum" in physics and chemistry.

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When you say my hands are the existents in the plenum argument, no, not according to LP, there would have to be some other existents in between them. He would not accept any absence of entities in between them.

Did you know that attributes are existents?  Did you know that relationships are existents?

Not all existents are entities.

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Did you know that attributes are existents?  Did you know that relationships are existents?

Not all existents are entities.

"To exist is to be something, as distinguished from the nothing of nonexistence, it is to be an entity of a specific nature made of specific attributes." Ayn Rand Lexicon

So the existents between my hands, could be something other than entities (electrons, protons, neutrons, etc.), like floating attributes?

I think you have made a fault.

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Ok so you are using "void" in a manner that was not specified in the dictionaries I've checked.

That's fine since we acknowledge that we are talking about a concept distinct from those defined in the dictionary.

I would say that if you remove all entities between two other entities, you end up with only the relationships between those two entities.

The totality of all that exists has no regions of non-existence.  One could say there is a "plenum" of existence, if one acknowledge the departure from the use of "plenum" in physics and chemistry.

When googling "void" I get on the top of the page: "a completely empty space"

I don't see how that is essentially different from the way I was using it, "space stripped of entities, existents".

I don't know what you mean by the third sentence.

I don't really care for the moment how chemistry or physics uses the term plenum if it is different from LP's. Existents = Entities = protons, neutrons, electrons, etc. all the known things to exist

Plenum, by LP, and this is all I care about for the moment, defines as to be existence filled to the brim with entities, there is no space between entities that does not also contain entities.

That is what I don't get to be necessary, philosophically.

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