Nate Smith

An Ageless Universe

84 posts in this topic

I'll ask the question another way:  Is it okay to ask, ... "What is the mass of the matter in the universe?"

What do you mean by "mass?" The definition is key. Suppose the definition is: mass is the resistance of an entity to an applied force, as in mass = force / acceleration. For the same applied force, then, a small-mass object has a larger acceleration than a large-mass object, other things being equal.

Does the universe, then, have a net mass? For that question to be meaningful, one would have to apply a force to the universe as a whole, which would mean from outside the universe. But that's impossible, so one can't apply the concept of mass to the context of the universe as a whole. The question is as meaningless as asking: "What is the color of seven?"

Questions like these are seductive because we observe larger and larger scales of objects and their correspondingly larger masses: paper clips to kitty cats to people to houses to skyscrapers to moons and planets to stars to galaxies. But in each case, we can observe and measure relationships between these particular entities and others, and from that infer a mass. For instance, you can stand on a bathroom scale and measure your weight, which is proportional to your mass. The weight is the force of attraction between you and the planet Earth. From more complex observations, we can "weigh" planets, and from Newton's law of gravity (or General Relativity) compute the mass of the planet. Yet, we are observing the interactions of entities: the planet and the sun, or a moon and its planet.

But there's no entity outside of the universe to interact with the universe, with the sum of all existents. The interaction itself -- the force -- doesn't exist. That means the related attribute -- mass -- doesn't exist, either.

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Alex, after reading your answers to my last questions, I realized there are more fundamental issues to be dealt with before those answers will be meaningful to me.  So I am going to ignore them for now and try and get to the beginning with some better questions.

What exactly do you mean when you say that the universe is not finite in size, but it is finite.  In what respect is it finite?

Why I regard the universe as finite is a good question, but before I answer allow me to say that I do not think that this issue is "more fundamental." One can understand that the universe (as I depict it) is not infinite before one understands that it is finite. I say this, because there are people who agree with my essay (or at least agree that my physical picture of the universe is neither infinite nor inconsistent with philosophical axioms), and yet are not willing to say that the universe is finite.

That being said, my essential answer to your question is that there is no "respect" in which the universe is finite, at least in the sense of there being some finite attribute that the universe possesses. Rather, when one says that the universe is finite, I don't think that this need mean more than the simple fact that the universe possesses identity. And what is its identity? That it is the sum total of that which exists. (If you would like further explanation, Phil Oliver and I had an interesting debate concerning this issue, which you can read starting with this post .)

I'll ask the question another way:  Is it okay to ask, "How many atoms exist?" or, "What is the mass of the matter in the universe?" 

Again, I think you are asking a different question here, one which does not depend on your deciding whether the universe as such is finite or not. But, anyway, no, it is not okay to ask "How many atoms exist?" or "What is the mass of the matter in the universe?" Since the universe does not have spatial boundaries, one cannot coherently ask any question which requires one to quantify the contents of the universe as whole. A quantity is a bounded set of entities, and "bounded" is exactly what the universe is not.

...I'm trying to understand if you are claiming that matter can continue indefinitely in no particular amount.  This is what sounds like an existing infinity to me.

I am claiming that, but again, I deny that it constitutes an infinity.

Allow me to frame the issue this way: assuming you think that metaphysical infinities contradict the law of identity, try and see if you can draw out what it is about my physical picture of the universe which contradicts the law of identity. Where is the contradiction in saying: "The universe is neither a finite quantity nor an infinite quantity, but simply outside the context of 'quantity' altogether"?

I'll wait for the answer to this before I continue with more questions.

Thanks again.

No problem! I definitely appreciate that this is a difficult issue.

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-------------

No problem!  I definitely appreciate that this is a difficult issue.

I am curious why the issue of the universe's physical extension appears to be more difficult to grasp than the issue of the universe's temporal extension. At least for me, it is fairly easy to grasp that the concept of "the beginning of the universe" is contradictory. Yet, although I agree that the universe is not infinite, the arguments are not as readily evident or clear. Since time is a relationship among spatial entities (time is the measured or measurable period during which an action, process, or condition exists or continues), why can't the same argument about temporal existence be used for spatial existence?

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I am curious why the issue of the universe's physical extension appears to be more difficult to grasp than the issue of the universe's temporal extension.  At least for me, it is fairly easy to grasp that the concept of "the beginning of the universe" is contradictory.  Yet, although I agree that the universe is not infinite, the arguments are not as readily evident or clear.  Since time is a relationship among spatial entities (time is the measured or measurable period during which an action, process, or condition exists or continues), why can't the same argument about temporal existence be used for spatial existence?

It's hard to answer that when I don't have a good grasp of these issues yet. I will say though that most people have an intuitive notion that things which exist must exist in some particular quantity. Alex's claim that that this is not necessary is counter-intuitive. It's much easier for me (and probably most people) to accept the fact that existents don't spontaneously come to be, and therefore there is no beginning to time, than to believe that existents can be in no particular amount (at least physical existents).

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What I need to do is retrace the steps of the Objectivist metaphysics in ITOE. There I might find a mistake in my own thinking. At this moment I don't have my copy with me, so I won't say much, but I can raise one question.

In the beginning of our conceptual development, we see that things exist, and that they also exist in some particular way. We form the implicit concepts of existence and identity. I am comfortable with this.

Another observation we have (probably much later on) is that everything that exists (within any chosen group of things) does so in some particular quantity. As I mentioned in the last post, there certainly seems to be an intuitive notion that we can carry this principle to larger and larger quantities. Isn't this how we draw the conclusion that infinity isn't possible? Eventually we apply that principle to the sum of all existents, i.e., the universe. I still see this as a very good argument, even though Alex referred to it as the fallacy of composition. My problem is not that there is no 'border' to the universe, but that there can be a limitless quantity of anything.

Alex challenged me to find how his picture of the universe might violate the Law of Identity. I will try and do this, but at least I think I'm starting to get to some more fundament principles behind this issue.

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It's hard to answer that when I don't have a good grasp of these issues yet.  I will say though that most people have an intuitive notion that things which exist must exist in some particular quantity.  Alex's claim that that this is not necessary is counter-intuitive.  It's much easier for me (and probably most people) to accept the fact that existents don't spontaneously come to be, and therefore there is no beginning to time, than to believe that existents can be in no particular amount (at least physical existents).

One problem you're making, which I think Alex pointed out, is your assumption that the universe is a "thing" or "existent." The universe is not a thing any more than existence is a thing. The universe is just an equivalent term, but within the context of physics rather than philosophy. If you grasp that existence has no quantity, then the same principle applies to the universe.

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I'll ask the question another way:  Is it okay to ask, ... "What is the mass of the matter in the universe?"

What do you mean by "mass?" The definition is key. Suppose the definition is: mass is the resistance of an entity to an applied force, as in mass = force / acceleration. For the same applied force, then, a small-mass object has a larger acceleration than a large-mass object, other things being equal.

Does the universe, then, have a net mass? For that question to be meaningful, one would have to apply a force to the universe as a whole, which would mean from outside the universe. But that's impossible, so one can't apply the concept of mass to the context of the universe as a whole. The question is as meaningless as asking: "What is the color of seven?"

...

But there's no entity outside of the universe to interact with the universe, with the sum of all existents. The interaction itself -- the force -- doesn't exist. That means the related attribute -- mass -- doesn't exist, either.

Ed,

I agree with what you say about it being meaningless to ask "what is the mass of the universe". However, that question ("What is the mass of the universe?"), I take to be different than the one that Nate asked ("What is the mass of the matter in the universe?") The first attempts to wrongly treat the universe as an entity that has mass. The second is an attempt to sum up the masses of all of the matter that is in the universe. As such, it would just result in a sum; it wouldn't be a physical property of anything. It definitely would not be the mass of the universe.

The second question seems legitimate to me, if the universe is finite.

....

Some of the arguments in this and other "cosmology" threads seem to turn on the question of what it means to be "finite". Does it mean just "having identity" and "not being infinite"? Or does it mean that there is just so much of something and not any more?

I need to collect my thoughts and think about them before I write any more on this subject.

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I am curious why the issue of the universe's physical extension appears to be more difficult to grasp than the issue of the universe's temporal extension.  At least for me, it is fairly easy to grasp that the concept of "the beginning of the universe" is contradictory.  Yet, although I agree that the universe is not infinite, the arguments are not as readily evident or clear.  Since time is a relationship among spatial entities (time is the measured or measurable period during which an action, process, or condition exists or continues), why can't the same argument about temporal existence be used for spatial existence?

Well, I think it can be used (in the sense in which I did use it in my essay), but you're right that it does appear to me more difficult to grasp that the universe is not spatially infinite than it is to grasp that it is not temporally infinite. I've never thought about this before, so I'm not sure why this would be the case. I'll keep thinking about it, though, so thanks for raising the issue.

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Ed,

I agree with what you say about it being meaningless to ask "what is the mass of the universe".  However, that question ("What is the mass of the universe?"), I take to be different than the one that Nate asked ("What is the mass of the matter in the universe?")  The first attempts to wrongly treat the universe as an entity that has mass.  The second is an attempt to sum up the masses of all of the matter that is in the universe.  As such, it would just result in a sum; it wouldn't be a physical property of anything.  It definitely would not be the mass of the universe.

But in fact, those are the same thing. My argument doesn't depend on treating the universe as an entity, but rather on the definition of mass and the nature of the universe as all-encompassing.

What do you mean by "sum[ming] up the masses of all the matter" in the universe? I'm guessing your thoughts are along the lines of: if there were 50 objects in the universe, each with mass X, then the mass of the "universe" would be 50 times X. (If you're thinking something else, let me know.)

But that doesn't work for the real universe. Again it goes back to the definition of mass as depending on an external force, as explained in my prior post. What would be the net external force that could be applied to every object in the universe? When I say the force applies to every object in the universe, I take that to be the same as saying it applies to the universe as a whole. I don't see a distinction between those two, as the universe is the collection of all that exists.

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Some of the arguments in this and other "cosmology" threads seem to turn on the question of what it means to be "finite".

Maybe some arguments do, although as I alluded to above, I still don't see why this needs to be answered before we can know that the universe is not temporally (or spatially) infinite (which is essentially the question that Nate Smith originally asked). I know that the universe is not infinite in any sense, and yet I am still to some extent considering whether it should be described as finite.

Does it mean just "having identity" and "not being infinite"?  Or does it mean that there is just so much of something and not any more?

It usually at least implies the latter -- but so does the phrase "having identity," and the universe certainly must possess identity. I think the universe is a special case of finitude, just like it is a somewhat special case of what it means to possess identity. But, again, I consider this a technical and non-fundamental question. (That being said, besides the thread I referenced above in which Phil Oliver and I had a lengthy discussion on this topic, also see this post of mine for further elaboration of my view.)

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Ed:

A more precise way to ask the question which avoids the notion of forces involved in mass is to ask: are there a finite (countable) number of distinct entities (say quarks) or an infinity in the universe?

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ELS, have you read my essay?  I don't ask that to be flip; I just ask, since you only quoted things I wrote in this thread, and I explain things much more fully in my essay.

Yes, Alex, I did. There were some things I disagreed with (or let's say questioned), but I'd have go back and review, since it's been a while ( I remember being impressed with the well-reasoned arguments, even given the disagreement). But, I'll respond to what is written in this forum, since that's where we're debating.

...the sheer fact that [AR] uses the word "sum" doesn't mean that she saw the universe as a quantity; I use the word "sum" to describe the universe and I don't mean it in that way.  After all, I (and those who agree with me) must use some word ("sum," "all," etc.) to describe the universe.

Perhaps I should stop and ask you what you mean by "quantity"? I assume the concept of "sum" has a quatitative reference. What else do you have in mind?

Do you think that the universe has a spatial boundary (an "edge")? 

Of course not. "Space", "spatial boundary" and "edge" are all concepts pertaining to the attributes of existents -- not to any collection of existents, except analogously (which is a far different concept).

If not, how can it be a delimited quantity?

The only "delimitation" is that the sum which exists is all there is.

If it is a "sum" it is whatever quantity exists.

The problem, I think you are having (you can inform me of any error), is in recognizing that the sum of that which exists (the universe) is continously changing: some existents are coming into existence, others are going out of existence, at different locations and at different times. (This has some very interesting physical and philosophical problems related to it.) So the "sum" is a constantly changing quantity.

Physically -- but not metaphysically.

What exists is the universe; regardless of "space"(location, position, distance) or "time" (measured change). All of the existents, irrespective of "time" or "space" exist-- and that fact is both physical and metaphysical. Whatever exists -- when and where it exists -- that is the universe.

It is a "sum" in the sense that it is all there is to whatever number of existents exist.

...But I am asking: why does it have to be a quantity? Where is the infinity in saying, "'All that exists' is not a (finite) quantity, just as 'all the events in the history of the universe' is not a (finite) quantity"?

Forget the invalid concept of "infinity".

The law of identity says "A is A"; it doesn't say "A is a quantity."

Don't confuse physical issues with metaphysical ones. The Law of Identity -- what exists, exists -- has a totally different (though obviously related) context with the quantitative context of human cognition.

...I'm interested in is seeing whether my ideas are consistent with reality, not with what Miss Rand said.  (I hope you don't take that statement the wrong way; I just want to explicate what I was (and wasn't) trying to prove with my essay, and with my words here.)

You've got a good mind, Alex. I, too, take what Ayn Rand observed, and then proceed to question. She, as you probably already know, would not have it any other way. She was absolute about the independence of one's mind.

The beautiful part is that by such independence, truth eventually comes out in the logic of the arguments.

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Alex's claim that that this is not necessary is counter-intuitive.

In Alex's essay he does not make claims; he makes very well-reasoned arguments. The one thing that is absent from this entire thread is anyone directly addressing the exact arguments made in the essay. I see the disagreements that have been voiced as analogous to someone swimming in deep water, never asking how they got there in the first place.

Nate, your original question involved an oblique attack on the old question of the age of the universe. You sought to re-formulate the issue in terms of the number of events, and now you are concerned about a "limitless quantity." But this is not itself the main issue; rather the question is whether we can assign a number to the quantity of entities in the universe. To worry about "limitless quantities" is like the analogy I gave of swimming in deep water; you can tread water fiercely but do you belong in that water in the first place?

The issue of quantities is a derivative one, and the place to start arguing, either for or against, is with the more fundamental arguments in Alex's essay regarding what may be properly attributed to the universe. In that vein, I would strongly suggest you read (or re-read) the first part of the essay and come to a conclusion in your own mind about whether or not it is meaningful to attribute a size to the universe. Alex argues that doing so is improper, and some further conclusions he draws are dependent on that. Arguing against, or struggling to understand these further conclusions is dependent on grasping the earlier ones. So the place to begin is with a firm understanding of whether "size" can be attributed to the universe at all. What you conclude about that will frame your further conclusions.

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Ed:

A more precise way to ask the question which avoids the notion of forces involved in mass is to ask:  are there a finite (countable) number of distinct entities (say quarks) or an infinity in the universe?

You might enjoy reading Alex S........'s essay on "The Unbounded, Finite Universe". Alex argues that yours is not a well-defined question.

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What do you mean by "sum[ming] up the masses of all the matter" in the universe?  I'm guessing your thoughts are along the lines of: if there were 50 objects in the universe, each with mass X, then the mass of the "universe" would be 50 times X.  (If you're thinking something else, let me know.) 

Adding up the masses of all the matter, if that could be done, would yield just that: a sum, and the total mass of things in the universe would be 50 times X, to use your example. But that is not the same as saying that the mass of the universe would be 50 times X, or even that there is such a thing as the mass of the universe. (I agree that there isn't.)

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Stephen:

Indeed, it was interesting on a first run through, I'll read it again tomorrow morning, the one thing I saw that seems to differentiate my question from his, I'm asking from a physics sense to measure:

Thus, the two questions, "Have a finite number of events transpired throughout the entire history of the universe?" and "Are there a finite number of entities in the universe?" are essentially the same: they both steal the concept of number from the concept of quantity.

from the end of his essay, it makes no more sense to talk about a finite number of entities on the planet earth, there is my computer, it is an entity, each computer key is an entity, each RAM chip is an entity, each molecule is an entity, each has a distinct identity, and I would say that their are infinitely many ways to classify any system into entities. In short the universe is no different then any (closed or open) system.

My question involved entities delimited by a specific quality (that they possess the quality of being a quark) and just like asking how many tons of Iron there are on earth is large, I think both are still finite.

To sum up, my question by defining a specific quality makes it irreducible to his.

On another note, is there an Objectivist definition of infinity?

-- NAS

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Adding up the masses of all the matter, if that could be done, would yield just that: a sum, and the total mass of things in the universe would be 50 times X, to use your example.  But that is not the same as saying that the mass of the universe would be 50 times X, or even that there is such a thing as the mass of the universe.  (I agree that there isn't.)

Why aren't they the same thing? You've asserted it, but not proved it.

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it makes no more sense to talk about a finite number of entities on the planet earth, there is my computer, it is an entity, each computer key is an entity, each RAM chip is an entity, each molecule is an entity, each has a distinct identity, and I would say that their are infinitely many ways to classify any system into entities.  In short the universe is no different then any (closed or open) system.

My question involved entities delimited by a specific quality (that they possess the quality of being a quark) and just like asking how many tons of Iron there are on earth is large, I think both are still finite.

First, there is not literally "infinitely many ways to classify any system into entities." There are only a finite number of ways to classify a finite number of systems into a finite number of entities. Second, the essential difference, in this respect, between the Earth and the universe is that the Earth is bounded and the universe is not. When you speak of a quantity, of quarks or otherwise, you need to specify the spatial bounds. This can be accomplished with the Earth, but not with the universe.

On another note, is there an Objectivist definition of infinity?

I do not know of any formal definition that was ever made, but in ITOE "infinity" as a valid concept is characterized as a concept of method, not a metaphysical existent. A potential, not an actual.

"An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence." (ITOE, p. 17.)

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Indeed, it ["The Unbounded, Finite Universe"] was interesting on a first run through, I'll read it again tomorrow morning ...

Incidentally, I think re-reading it is a good idea. I read the essay several times before I really "got it." The words are deceptively simple, but the ideas that they form are quite profound.

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First, there is not literally "infinitely many ways to classify any system into entities." There are only a finite number of ways to classify a finite number of systems into a finite number of entities.

Just to be clear, I meant this to apply to the example given on a strict metaphysical level (computer -> computer key -> ram chip -> molecule), not in terms of a mathematical component like "those molecules to the right of this one by each of the angles 1.x {x -> 0, inf}.

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If I may make this layman's observation: the statement "If I (or you) add up the mass of all the things in the universe..." has a problem. It assumes that I (or you0 have the ability to perform this feat of weighing and adding in our lifetime, which in itself assumes a knowledge of the universe which you (or I) do not have. So, just to say(or think) that much---"If I add up all..."---is to not be in contact with reality.

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Yes, Alex, I did. There were some things I disagreed with (or let's say questioned), but I'd have go back and review, since it's been a while ( I remember being impressed with the well-reasoned arguments, even given the disagreement). But, I'll respond to what is written in this forum, since that's where we're debating.

Thanks for your kind words, here and elsewhere. However, I do hope you go back and read my essay, and what's more I strongly encourage you to directly address more than what I have written here. For, I agree with Stephen that my arguments have not yet really been addressed in this thread, and in order to do so it is imperative that my essay itself be addressed. That is, after all, where I have laid out my arguments for all to see, for which this (or any other) thread is not a substitute.

Perhaps I should stop and ask you what you mean by "quantity"?

A quantity is bounded group of things; it is an amount of something that you can specify by saying, "I'm talking about the entities between here and here."

I assume the concept of "sum" has a quatitative reference. What else do you have in mind?

Well, I have the universe in mind. It is true that words like "sum" and "all" normally refer to quantities, but the universe is to some extent sui generis because it lacks spatial boundaries and thus falls outside the context from which we formed idea of "quantity" to begin with.

The problem, I think you are having (you can inform me of any error), is in recognizing that the sum of that which exists (the universe) is continously changing ...

No, this is unrelated to my position. My point is that the universe is outside the context of concepts like "quantity" and "size," and the burden of proof is on you to demonstrate that they do apply. I have, however, seen more assertion than demonstration on this point.

Don't confuse physical issues with metaphysical ones. The Law of Identity -- what exists, exists -- has a totally different (though obviously related) context with the quantitative context of human cognition.

I don't follow you. I was merely pointing out that one cannot claim that the universe is a quantity simply by invoking the law of identity. If you have an argument that makes use of more than the law of identity in this regard, by all means share and I will be happy to address it.

I'm not sure what else to say about your post, ELS, because quite honestly, I couldn't see how a lot of it related to criticizing my ideas. Again, there really isn't a substitute for actually pointing out in my essay where you think a particular argument of mine goes astray, and I hope you will choose to do this as our discussion continues.

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First, there is not literally "infinitely many ways to classify any system into entities." There are only a finite number of ways to classify a finite number of systems into a finite number of entities. Second, the essential difference, in this respect, between the Earth and the universe is that the Earth is bounded and the universe is not. When you speak of a quantity, of quarks or otherwise, you need to specify the spatial bounds. This can be accomplished with the Earth, but not with the universe.

I do not know of any formal definition that was ever made, but in ITOE "infinity" as a valid concept is characterized as a concept of method, not a metaphysical existent. A potential, not an actual.

"An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence." (ITOE, p. 17.)

I am confused about why there is so much confusion about the concept infinity. Is anyone confused about the metaphysical principle that "there is no nothing" yet mathematically, one expresses it with the concept of zero? The concept zero does not imply that nothing exists. Yet when we use the concept infinity, somehow this implies that infinity exists, whether in spatial or temporal extension. To my understanding, the concept zero simply means that no quantity has yet been specified for whatever unit is under consideration. Infinity simply means that no matter what quantity is being considered, on can always add one more unit to that quantity. In neither case does this imply that zero or infinity actually exists.

The importance of units is vitally important. Consider this example. Mathematically one can take the number 6 and keep adding 10 until "infinity." Now, let's say I am 6 feet tall. Suppose I add 10 pounds to my 6 feet. I am still 6 feet. I can keep adding 10 pounds till infinity but I will still be 6 feet (pretty fat though :) ). So the only way to "get to infinity" is if the units are the same. So the next question is, how can I "get to infinity" if I can only add finite quantities together. This should solve the problem (I hope). One can never get to infinity in any physical system in which the specific units are specified. Infinity is strictly a mathematical concept and should be restricted to that realm.

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I am confused about why there is so much confusion about the concept infinity.  Is anyone confused about the metaphysical principle that "there is no nothing" yet mathematically, one expresses it with the concept of zero?

Actually, I think there is just as much confusion over a metaphysical zero as there is over a metaphysical infinity. It's just that latter may be talked about more than the former. I have had or read many discussions about the existence of literally nothing between two objects. A universe with a metaphysical hole is just as nonsensical as a universe with a metaphysical infinity, and each represents a similar sort of epistemological confusion. Which, I think, answers your question about why the confusion; poor epistemology.

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Actually, I think there is just as much confusion over a metaphysical zero as there is over a metaphysical infinity. It's just that latter may be talked about more than the former. I have had or read many discussions about the existence of literally nothing between two objects. A universe with a metaphysical hole is just as nonsensical as a universe with a metaphysical infinity, and each represents a similar sort of epistemological confusion. Which, I think, answers your question about why the confusion; poor epistemology.

I agree with you, but I was mainly aiming at those people in this thread who are interested in Objectivist principles. Zero and infinity have puzzled people for millenia but grasping the axiom "existence exists" would seem to clarify some of those confusions.

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