Infinite Universe

[y_feldblum]

For a space (a mathematical abstraction, whose referents include the set of all potential spatiotemporal "places" in this universe), one of these conditions holds.

1. It is finite and it has a boundary all around, an edge. One can move within the universe up to the edge, but then one can go no further. An example is: a ball.

2. It is finite and it has no boundary. By the laws of mathematics, a finite space that has no boundary is itself a boundary of some other finite space. One can move as far as one like in any direction without coming up against any kind of edge, but after some time, one will simply wrap back around to where one has been. An example is: a sphere (the outside edge of a ball).

3. It is infinite and it has no boundary. One can move as far as one like in any direction. An example is: the Euclidean space of Newtonian physics.

[MisterSwig]

Empty space is not a thing, and so cannot be counted as part of the universe. Space is a potential, just like the set of real numbers is a potential.

Are you saying that outer space does not exist? If it exists, then it is a part of the universe. If it does not exist, then how did you identify it as a "potential"?

By the way, real numbers exist as concepts in our head. I wonder if you are implying that outer space is merely a concept in our head.

Outer space must be composed of something. If there was nothing out there, how could planets move through it? If there was nothing between the planets and the stars, everything would be collected together into one giant mass, wouldn't it?

It took us awhile to discover that there were actually gaseous elements floating around in Earth's space. Perhaps we should not assume that outer space is filled with nothing.

[Robert J. Kolker]

It took us awhile to discover that there were actually gaseous elements floating around in Earth's space. Perhaps we should not assume that outer space is filled with nothing.

Most of the baryonic matter (stuff made of atoms) is hydrogen, followed by helium. Space is filled with very diffuse hydrogen gas. The elements above hydrogen and helium on the periodic table constitute less then one percent of the remaining baryonic matter in the cosmos.

If Dark Matter exists we know there is at least 10 times as much as baryonic matter. Space is filled with it, if it exists at all.

Bob Kolker

[necrovore]

Two replies in one here:

If you add one more potato to a -pile consisting of 428 other potatoes- how have you altered any properties possessed by any of the the other 428? 428 is a property of the -pile-, not any potato in the the pile.

I did say that it was a property of "the potatoes," not of each potato.

Would I be incorrect to assume you deny the existence of the empty set?

Zero and the empty set and the concept of "nothing" are abstract conveniences. A count cannot exist independently of the things being counted; you cannot have three without having three of something, be they potatoes or politicians or whatever. Zero is a special case because you not only cannot have zero, you cannot have zero of anything, because by the very definition of zero, zero of something is really nothing. And "nothing" itself doesn't exist, it has no referent.

Zero, nothing, and the empty set are not invalid concepts, but they would be if you tried to reify them. The whole point of having an empty set or a concept of "nothing" is so that you can denote the absence of a thing (or a set with an absence of elements), not so that you can refer to a thing actually outside of your head, in actual existence.

Since concepts are formed by measurement-omission, I would argue that the concept of "nothing" is what's left when you omit all measurements.

The concepts of zero and the empty set exist, because I am using those concepts in this post. But whether a concept exists and whether its referent exist are separate questions!

Are you saying that outer space does not exist? If it exists, then it is a part of the universe. If it does not exist, then how did you identify it as a "potential"?

By the way, real numbers exist as concepts in our head. I wonder if you are implying that outer space is merely a concept in our head.

Outer space is a derivative concept. It does not denote an existent but a potential that belongs to other existents. The existents themselves have been abstracted out (the existents are among the omitted measurements, in other words). Space is a property of the objects in it! (Thus, an empty universe would have no space.)

Real numbers are a derivative concept also. They do not denote existents but an abstraction about counts and measurements, which in turn are properties of existents.

Outer space must be composed of something. If there was nothing out there, how could planets move through it?

That, I think, is reifying space.

If there was nothing between the planets and the stars, everything would be collected together into one giant mass, wouldn't it?

There is potential between the planets and the stars for other objects, or even for the objects themselves if they move closer together, and this potential we call "space."

It took us awhile to discover that there were actually gaseous elements floating around in Earth's space. Perhaps we should not assume that outer space is filled with nothing.

There is no such assumption embedded in the concept. A given region of space can be occupied or empty. If it is occupied, its occupant can be moved or displaced. I can fill an aquarium with water and then wonder if there is enough space for all the fish. The "space" refers to the potential locations for the fish, locations which are presently occupied by water. A fish would occupy such a location by displacing water from that location.

However, I see no reason to assume that all space is occupied. The planets do not displace anything when they move. If they did, the friction would cause them to fall out of orbit. They hit occasional particles, such as hydrogen atoms, and this does slow them down a little -- but there is still space between the particles.

[y_feldblum]

Since concepts are formed by measurement-omission, I would argue that the concept of "nothing" is what's left when you omit all measurements.

I would argue that the concept "existent" - whose referents are everything - omits all measurements. "Nothing" is a concept of method.