Infinite Universe

Questions about Objectivism
21

I can see where you’re going, but I think you’ll need to explain it a bit further to me. I understand there’s nothing ‘outside’ the universe, but what sort of location are you moving into? I mean… even outer-space isn’t a perfect vacuum, there’s all sorts of stuff flying about. What’s this potentiality you speak of?

My definition of “space” is “the set of all possible places that can be occupied by any object.” This covers both the colloquial usage (the “space” in a room) and the mathematical and cosmic usages.

“Places” in turn are specified in terms of distances to other objects and angles between them.

“Distances” in turn are defined in terms of “length,” and “length” is a property of an object. The distance between two objects is the length of the (hypothetical) object that would fit between them.

“Angles” can be described in terms of proportional lengths, but it’s complicated. (Think of similar triangles.)

So “space” is actually a fairly complex concept. But it is not a thing in itself, it’s a set of possibilities.

Be careful not to reify it. (Many cosmological theories do just that, and it may be a fundamental error.)

A couple of notes on this:

– Just because space is an abstraction doesn’t mean it’s unreal. It’s real, but it’s a property of entities and where they can be positioned with respect to each other. It does not exist independently of the entities, just like, if I have 428 potatoes, the “428” doesn’t exist apart from the potatoes. The “428” is a property of the potatoes, namely, their number.

– It is also possible to consider such things as “curved space” such as non-Euclidean space. These do not reify space either; they specify how distances can change when entities move in certain ways (e.g., “parallel”).

Finally, these are my own thoughts (and the previous post, too), and I have not checked them against ITOE yet. :slight_smile:

22

I understand there’s nothing ‘outside’ the universe, but what sort of location are you moving into?

And anything that would be “outside” of the universe would in fact be the universe, so as you recognize, there is no “outside” of the universe.

I certainly understand that it is important to explore this issue, but (as I’m sure you understand) it can only be discussed in terms of theory. No one has been to the outer reaches of the universe. No one has even seen the outer reaches of space through the best most super-duperist of telescopes. I’m not even aware of any evidence that is known to man what the fringes of our universe holds (if there are even fringes).

23

– Just because space is an abstraction doesn’t mean it’s unreal. It’s real, but it’s a property of entities and where they can be positioned with respect to each other. It does not exist independently of the entities, just like, if I have 428 potatoes, the “428” doesn’t exist apart from the potatoes. The “428” is a property of the potatoes, namely, their number.

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.

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

Bob Kolker

24

if Objectivism holds the universe as the sum of all its parts, what does it mean when it says - “All entities in the universe may be finite, but the set of entities need not be”? Does this mean the universe is or is not infinite?

There are two ways that the universe may be finite or not, to my knowledge, and neither seem particularly problematic to me. The first way is for the universe to be “very big”, which seems to be permitted by the phrase, “but the set of entities [in the universe] need not be [finite.]” Here, as I recall discussing in another thread, one simply claims that for any finite list of spatiotemporal existents that you may conjure, there is always some such existent not on the list. This works in much the same way that the natural numbers work. Create any finite list and you will always miss at least one. While I know of no specific proof that this describes reality, scientists claim to have good evidence for the case. So I take this description as at least more likely than not.

Does this mean that the universe, being infinite, is without definition? I don’t see why it should. A comprehensive listing is not a definition. If it were, then we would have no definition of the natural numbers. However, if you ask me to tell you what are the natural numbers, and you gave me no effective limit on the amount of time I have to tell you which are the natural numbers, I could sit here forever and list off each and every one. Likewise, in reverse, you could think of any thing you want and ask me, “Is this a natural number?” and I would answer “Yes,” or “No,” correspondingly with perfect accuracy. Hence it seems we have an effective definition of an infinite set. That is because the members of the set are perfectly distinguished from every thing that is not in the set, and everything not in the set is perfectly distinguished from things in the set. We could just as well apply this to the universe, assuming it is “very large”. You could ask me to show you every single thing in the universe and, given infinite time and unlimited locomotive power, I could show you everything. Likewise, show me anything you like and I could tell you whether it is in the universe or not. The later is not much of a hurdle to clear when every answer is going to be “Yes,” unless you ask me about a thing that does not exist.

The other way for the universe, or any defined set of stuff, can be infinite is by being “very small”. That is, by being infinitely divisible. Though this concept is not expressly contradicted by the quote, “All entities in the universe may be finite, but the set of entities need not be,” the quote does seem to imply that nothing can be infinitely divisible. Yet I don’t see why this should be. Suppose that you have a rock, which we call X, and you divide it into two and get pieces X_1 and Y_1. You then divide X_1 to get X_2 and Y_2, and so you carry on this pattern. For what reason must you reach some point at which your division must cease? At every stage you must have a piece that, following the pattern of naming used above, is named X_n for some finite n. But why must there be a particular greatest number that n could be? Put another way, it seems perfectly possible that for any given X_n, there will be an X_n+1 and Y_n+1. Each particular part X_n for any finite n will be well-defined. I will be able to show you each X_n, granted unlimited time and divisive power, and for every thing you show me I can tell you whether it’s an X_n or not. How can I ensure the later? Well, give me unlimited time and I will produce every X_n for each finite n. If the thing you show me is an X_n, I will produce it at some finite stage. If it is not, I will never tell you that it is an X_n. The only hitch is that if you show me something that is not an X_n and ask me whether it is and X_n for some finite n, I will not have a test to show that it is not one. That is, I could never tell you, “This is not an X_n.” Is that important for a definition? I don’t think so. It would never lead me into error. That is, I would never say “This is an X_n,” when it’s not. And I would never say, “This is not an X_n,” when it is. And moreover, everything will either be an X_n or not an X_n–it’s just that in some cases, I must always remain agnostic.

Still, what definitely does seem like evasion is this whole, ‘don’t try to imagine the beginning of the universe, because it’s too abstract’. I don’t get that. The first bit of energy, in the very first split-second of time, required no reason to come about? It just seems, that with the Law of Causality, that an eternally recycling universe - in terms of physical matter, not metaphysics - makes more sense overall.

I don’t see why this should be. Let’s say that the universe recycles. Where did this whole process of recycling come from? Why is there something rather than nothing? Why is there any existence at all? Whether you have a universe that recycles or one that has a beginning and an end, it is nonsense to ask, “Why is it here?” You must first start with the fact that it is here. That is automatic and given. To try to go underneath that fact is to try to go underneath an axiom. If you want to question an axiom, well, you’re on your own.

I see no problem with the idea that the universe had a “first moment”. And if you ask me, “What made it exist?” I would say that the question is unintelligible. It was, by definition, the first moment. Nothing preceded it, so nothing could make it exist. It just was. In the same way that the universe “just is” and needs no explanation for being, the first moment “just was”.

25

I understand there’s nothing ‘outside’ the universe, but what sort of location are you moving into?

Tenure, let me give you a quote from Dr. Peikoff, which you won’t find on your O’ist CD-ROM. It’s from his “The Philosophy of Objectivism” lecture series from 1976, in Lecture 2, it’s also in the Lexicon. This quote has helped me tremendously understand things about the universe, that I never could have grasp myself, even through all the material that I had read, all the years of headache were totally relieved when I had read this:

The universe is the total of that which exists - not merely the earth or the stars or the galaxies, but everything. Obviously then there can b no such thing as the "cause of the universe…

Is the universe then unlimited in size? No. Everything which exists is finite, including the universe. What then, you ask, is “outside the universe”, if it is finite? This question is invalid. The phrase “outside the universe” has no referent. The universe is everything. “Outside the universe” stands for “that which is where everything isn’t.” There is no such place. There isn’t even nothing “out there”: there is not “out there.”

26

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.

27

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.

28

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

29

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.

30

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.