The Infinite and the Finite

Metaphysics and Epistemology
1

Objectivism claims that the universe is finite. But it also claims that the universe has existed forever and will exist forever (the universe being “everything that exists”). Isn’t the definition of the universe a definition of infinity? How can we claim that it is finite, but has existed forever, and is obviously endless in space and time?

I’m guessing that the explanation to this is that the universe is perceptible, and in this sense it is finite, though this “finity” goes on in infinite amounts of time and space. But I want to hear a proper, well-reasoned, clearly defined explanation from an intelligent objectivist.

Irrational numbers and Physical constants
Irrational numbers and Physical constants
Irrational numbers and Physical constants
2

The universe is “all that exists”, and time is not independent of that existence. Therefore, it is meaningless (and contradictory) to speak of “a time before existence”, idem “after”. For all time, past and future, the universe exists. This btw applies to “space” as well, so there is no “space” beyond the universe.

Suppose we consider the two most distantly-separated particles in the universe. The number of particles is finite, and distance between two entities can be measured and sorted according to a numeric scale – thus such a notion is perfectly sensible (it doesn’t imply that there is a unique most-distantly separated pair). The distance between the particles is finite, thus that is how “long” the universe is. There exists nothing more remote than those two particles, and you can repeat that procedure to determine the finite bounding box that is the imaginary cubic size of the universe, a finite amount. The same with time.

3

The universe is “all that exists”, and time is not independent of that existence. Therefore, it is meaningless (and contradictory) to speak of “a time before existence”, idem “after”. For all time, past and future, the universe exists. This btw applies to “space” as well, so there is no “space” beyond the universe.

Suppose we consider the two most distantly-separated particles in the universe. The number of particles is finite, and distance between two entities can be measured and sorted according to a numeric scale – thus such a notion is perfectly sensible (it doesn’t imply that there is a unique most-distantly separated pair). The distance between the particles is finite, thus that is how “long” the universe is. There exists nothing more remote than those two particles, and you can repeat that procedure to determine the finite bounding box that is the imaginary cubic size of the universe, a finite amount. The same with time.

Thank you, that helps to clear some things up.

So there needs to be a distinction between “infinity” in the metaphysical sense, which is contradictory, and “infinity” in the mathematical sense. Because if abstraction is “measurement omission,” then this subsumes an “infinite” number of that entity, though this may or may not exist. The distance between your particles is finite, but may exist in any amount. So for metaphysical things to actually exist, they must exist in finite form. But the process of conceptualization takes on a hypothetical “infinity”. Therefore, the proper concept of “infinity” applies only to epistemology, not to metaphysics, because nothing can truly exist in “infinite” amount.

If this isn’t a paraphrase of Rand’s viewpoint, correct me, but I think it is. Is it safe to say that the “primacy of consciousness” is what has taken mathematical, conceptual infinity and placed it where it doesn’t belong, in the metaphysical realm? Therefore, is religion the indirect source of all of our confusions in physics, with regard to “independent time and space”?

4

Thank you, that helps to clear some things up.

So there needs to be a distinction between “infinity” in the metaphysical sense, which is contradictory

I’m not sure that’s correct, because one aspect that must be considered in the universe is time.

The universe may have finite distances, but time, as far as we can tell, is not finite. The universe is all that exists, all that has ever existed, and all that will ever exist. How long will it last? Infinitely long. How long has it lasted? Many say, “Since the big bang” - but this is misleading.

Physics tells us that energy can not be created or destroyed, and matter is a form of solid energy. Since matter can neither be created nor destroyed, it must have always existed. There may be a finite quantity of energy/matter in the universe, but its overall existence is not finite.

The current state of matter organization started with the Big Bang, but before the Bang, all of the matter of the universe was compressed in a singularity (or a near singularity anyway). What existed prior to the big bang? Everything - scrunched up very small. The big bang didn’t appear out of nothingness - the matter and energy had to be there already in order for it to explode and create our current incarnation of the universe.

5

I’m not sure that’s correct, because one aspect that must be considered in the universe is time.

The universe may have finite distances, but time, as far as we can tell, is not finite. The universe is all that exists, all that has ever existed, and all that will ever exist. How long will it last? Infinitely long. How long has it lasted? Many say, “Since the big bang” - but this is misleading.

Physics tells us that energy can not be created or destroyed, and matter is a form of solid energy. Since matter can neither be created nor destroyed, it must have always existed. There may be a finite quantity of energy/matter in the universe, but its overall existence is not finite.

The current state of matter organization started with the Big Bang, but before the Bang, all of the matter of the universe was compressed in a singularity (or a near singularity anyway). What existed prior to the big bang? Everything - scrunched up very small. The big bang didn’t appear out of nothingness - the matter and energy had to be there already in order for it to explode and create our current incarnation of the universe.

It’s mathematically infinite, not metaphysically. There can be no such thing as metaphyiscal infinity. It’s an impossible term, just like omnipotence and omniscience.

“There may be a finite quantity of energy/matter in the universe, but its overall existence is not finite”

–You should be able to see the problem with this statement. If it exists in finite form, then its existence is finite. It does not and cannot exist in infinite form. Infinity is only a hypothetical concept, pertaining to consciousness and its ability to abstract and omit measurement. Since quantity is numerical and a form of measurement, it is right to say that “x” stands for an infinity number of whatever it stands for, algebraically speaking, but this doesn’t mean that “x” can actually exist in an infinite number, because that is impossible. Infinity is impossible existentially, which is why it’s consciousness’s method of “omitting measurement.” Thought it’s clear that things actually do exist in specific measurements. The consciousness, for the sake of saving time, can choose to actually ignore, in a sense, the specific measurements and focus only on the essential characteristics of the entity, but the entity in reality does and has to exist in a definite quality.

Reversing this and assigning infinity, the indefinite, is like claiming that the universe omits measurement, which is obviously not the case. Everything that exists, exists in a definite quality and quantity, or we wouldn’t be able to perceive it. I’m talking about matter, but it applies to space in time, since they are relative concepts, not independent, as my bud up above said, because they can’t logically exist independent of reality or the universe.

Now in light of this, what do we think about some physicists’ claims that “the universe is constantly expanding”? I think this is a package deal, where the universe means simultaneously “all we know about the existence of matter” and “everything that exists”, which are obviously two very different definitions. By the second definition, “everything that exists” cannot possibly be expanding. Expanding into what? Where? Into more that exists? Into more space? No, because space cannot exist outside of existence.

6

There can be no such thing as metaphyiscal infinity. It’s an impossible term, just like omnipotence and omniscience.

Serious question: Why?

It’s been a *long* time since I took metaphysics, and I haven’t read up on Objectivist Metaphysics yet (working on epistemology), so I’m confused as to why this is thought to be the case.

7

So there needs to be a distinction between “infinity” in the metaphysical sense, which is contradictory, and “infinity” in the mathematical sense.

Yes, and thus I prefer to speak of unbounded methods, for example counting is an unbounded method and doesn’t involve an actual infinity of things.

Is it safe to say that the “primacy of consciousness” is what has taken mathematical, conceptual infinity and placed it where it doesn’t belong, in the metaphysical realm? Therefore, is religion the indirect source of all of our confusions in physics, with regard to “independent time and space”?

That may be so. If we were living in a Vedic-derived philosophical world I would not hesitate to agree; I just don’t understand the relationship between philosophy and religion in Ancient Greece well enough to have an opinion, but it certainly seems likely.

8

Yes, and thus I prefer to speak of unbounded methods, for example counting is an unbounded method and doesn’t involve an actual infinity of things.That may be so. If we were living in a Vedic-derived philosophical world I would not hesitate to agree; I just don’t understand the relationship between philosophy and religion in Ancient Greece well enough to have an opinion, but it certainly seems likely.

All early civilizations had religion. Greece was the first to separate “mythos” and “numos”, or myth from nature. Some exceptions aside, the majority of Greek religion recognized the gods as finite creatures who just happened to have supernatural qualities. They weren’t actually omnipotent or omniscient, not even Zeus. They couldn’t rebel against reality, and they could not create ex nihilo. They had human shapes and qualities, unlike the judeo-christian God who can basically do whatever the hell he wants.

9

Serious question: Why?

It’s been a *long* time since I took metaphysics, and I haven’t read up on Objectivist Metaphysics yet (working on epistemology), so I’m confused as to why this is thought to be the case.

Because it contradicts basic axioms. Everything that exists, exists, and exists as something, in some quality and some quantity. Infinity throws that out the window, forgetting the Law of Identity. It says that everything and anything that exists exists in any quality and quantity (which also includes no quality and quantity) and this is a contradiction. The infinite can only be a hypothetical concept, pertaining to measurement omission. But things in the universe have to have definite qualities and quantities in order to exist.

Imagine what infinity would look like. Take the case of a hotel with an infinite number of rooms. A customer asks if there are any rooms available and the manager says “yes”. But can they ever really be filled? It isn’t existentially possible to fill all of those rooms, even if there were an infinite number of costumers, because infinity HAS no definite quantity. It’s a contradictory notion, when applied to that which exists.

Omnipotence has the same principle. The traditional question, “Can God create a rock so big that he can’t move it?” reveals the problem. It’s incomprehensible, it’s impossible. This is why, in epistemology, infinity (measurement omission) is a method of blocking out information, of assuming temporary “ignorance” for the purpose of abstraction. In this process, the “infinite” is forgotten, and the focus is on the abstracted entity, not the measurement, since the measurements are blocked out and omitted. This is why Rand says that, in the relation between concepts and their designated entities in reality, the entities must exist in some quantity, but may exist in any quantity. This is hypothetical and applies only to consciousness, because, existentially, nothing could exist in ANY quanity, or it wouldn’t exist.

10

A very clear explanation

Thank you, I get it now, I think.

11

First off the “infinite” is a concept of method and cannot exist metaphysically. It is not true that time is “infinite”. Time within the universe is eternal-- there is a difference. Time is only a relationship between existents within the universe, and does not apply to the universe as a whole.

Space also is not and can not be “infinite”. Space is finite and unbounded.

The following link explains in detail what I am talking about. It was written by a former member of this forum and he personally gave me permission to link to it.

http://www.geocities.com/rationalphysics/U…nded_Finite.htm

Hope this explain it for you. If not this is something I do understand in detail.

12

Can you to explain to me, in explicit detail, what you mean when you say “infinity,” and how exactly it conflicts with the Law of Identity, because what I mean when I say “infinity” sounds suspiciously like what your friend means when he says “unbounded.”

Be warned, I’ve yet to take Calculus, so I lack a background on “mathematical infinity,” but from what I’ve logically deduced, it seems an icky mess. You may need to start there.

13

Can you to explain to me, in explicit detail, what you mean when you say “infinity,” and how exactly it conflicts with the Law of Identity, because what I mean when I say “infinity” sounds suspiciously like what your friend means when he says “unbounded.”

When you use a word like “you”, conventionally it’s helpful to be clear what the referent is. In fact, etymologically it means “unboundedness” or “not-ending-ness”. Typical contemporary views of “infinity” derive from a strange mathematical mis-speaking, where people talk of an “infinite number of…”. I have had more than one mathematician tell me that I really ought to say something like “the cardinality of the set… is infinite”. We know that there can be a billion grains of sand, or a quadrillion electrons. So whever you use the “Number+Noun” structure, that implies at least the possibility of such a thing existing. The problem is that “infinity” is not a number, yet people confuse it with a number.

14

First off the “infinite” is a concept of method and cannot exist metaphysically. It is not true that time is “infinite”. Time within the universe is eternal-- there is a difference. Time is only a relationship between existents within the universe, and does not apply to the universe as a whole.

Space also is not and can not be “infinite”. Space is finite and unbounded.

The following link explains in detail what I am talking about. It was written by a former member of this forum and he personally gave me permission to link to it.

http://www.geocities.com/rationalphysics/U…nded_Finite.htm

Hope this explain it for you. If not this is something I do understand in detail.

I’m a little confused on this point. In David Odden’s example, he uses “the most distant particles” to illustrated the finiteness of the universe. Here you say that time and space are unbounded and finite. This seems a direct contradiction, unless you can provide a definition of “infinite” different from David’s (unbounded).

In the example of the furthest particles, I imagine two distant photons traveling in opposite directions. If time is unbounded, then they could have separated at any point in the past, and can thus be any distance apart, and will continue to fly apart forever.

These two photons, flying apart for eternity, would seem to be a definitizing example of infinity, if their initial separation were an event furthest in past time from the present. At a point in time furthest in the future from the present, the photons will still be flying apart from each other, but an instant later, the then-furthest point in future, they will be even farther apart. This continues indefinitely as time and space expand infinitely.

So the question remains, is the infinite necessarily “what” “is” “now,” or does the concept of “infinity” properly apply to the indefinite future of existence?

15

In David Odden’s example, he uses “the most distant particles” to illustrated the finiteness of the universe. Here you say that time and space are unbounded and finite. This seems a direct contradiction, unless you can provide a definition of “infinite” different from David’s (unbounded).

I’m confused over the confusion. I haven’t advanced a position as to whether there are upper limits on time and space relations, i.e. is it the case that the two furthest particles can be no further apart than X (or no closer together than Y)? I have no reason to believe that there are such size limits on the universe (at the lower end I mean as “fundamental limit”, not derived from other facts) but if there were, it would not be horrifying to me.

So the question remains, is the infinite necessarily “what” “is” “now,” or does the concept of “infinity” properly apply to the indefinite future of existence?

The only sane way to talk about the infinite is as an unbounded measurement, one with no principled limit, but one which always has a definite (finite) value when dealing with an actual instance.

16

When you use a word like “you”, conventionally it’s helpful to be clear what the referent is. In fact, etymologically it means “unboundedness” or “not-ending-ness”. Typical contemporary views of “infinity” derive from a strange mathematical mis-speaking, where people talk of an “infinite number of…”. I have had more than one mathematician tell me that I really ought to say something like “the cardinality of the set… is infinite”. We know that there can be a billion grains of sand, or a quadrillion electrons. So whever you use the “Number+Noun” structure, that implies at least the possibility of such a thing existing. The problem is that “infinity” is not a number, yet people confuse it with a number.

I clicked on this thread via the main forum and did not realize that there was more posts than EC’s. My apologies.

So, basically your saying that because one property of existence is number, which by nature must be bound and finite. You can’t have a infinite number because number is by definition finite, but you can have a finite number of movement and objects within in an unbound area of space and time, then? It seems that the problem seems to me that two people are using two different words to mean the same thing. One is just using his word conceptually wrong.

17

I’m a little confused on this point. In David Odden’s example, he uses “the most distant particles” to illustrated the finiteness of the universe. Here you say that time and space are unbounded and finite. This seems a direct contradiction, unless you can provide a definition of “infinite” different from David’s (unbounded).

In the example of the furthest particles, I imagine two distant photons traveling in opposite directions. If time is unbounded, then they could have separated at any point in the past, and can thus be any distance apart, and will continue to fly apart forever.

These two photons, flying apart for eternity, would seem to be a definitizing example of infinity, if their initial separation were an event furthest in past time from the present. At a point in time furthest in the future from the present, the photons will still be flying apart from each other, but an instant later, the then-furthest point in future, they will be even farther apart. This continues indefinitely as time and space expand infinitely.

So the question remains, is the infinite necessarily “what” “is” “now,” or does the concept of “infinity” properly apply to the indefinite future of existence?

Time and space don’t apply to existence or the universe as such. They are just relations between existents within the universe. As Alex explained in the essay I linked to even the concept of infinity (besides being a metaphysical impossibility) can not be applied to time, space, or the “amount” of existents in the universe because the concept of “numbers” can not be applied because it steals the concept from “quantity”. There can be no quantity without bounds defining one point from another. Space is unbounded therefore there is no quantity and no number, especially “infinite” that can be applied to it as a whole. The universe as such possesses no size, it is “asizal”. This is similar with regards to time. There is no bounds or limits on time in either direction. And to speak of a “duration” of time passing one must have a starting point and an ending point. Time can not apply to the universe as such because the universe temporally has no bounds. It is eternal.

Infinity is simply a concept of method. This means it can only be used epistemologically in regards to mathematical computations to represent a limit. Infinity is not a number it is a funtional representative of very large or very small numbers. It is a mathematical tool that only exists as an abstract concept. An actua, metaphysical “infinity” would be a direct violation of the Law of Identity, because an “infinity” as such would possess no definite identity.

18

It’s mathematically infinite, not metaphysically. There can be no such thing as metaphyiscal infinity. It’s an impossible term, just like omnipotence and omniscience.

Sorry, I know this is not the point of this topic, but I was wondering why omniscience is an impossible term. Not that I disagree with you, I just don’t know how to prove it.

(Edit: Spelling)

19

Again, try not to confuse the existential with the conceptual. We can conceive of only finite things, and only finite things can exist. Infinity is a hypothetical concept that does not exist existentially, but can only be posited in conceptual terms. Infinity literally means non-existence. Just as contradictions can’t exist in reality, but we can think about them and even believe in them. Conceptualization is a process of blocking out, omitting particular measurements. It abstracts from existence. But in actual existence, everything exists in actual, finite, concrete measurements. It’s the same with regard to infinity. Infinity does not exist, it is not a number, not a measurement, not possible, not conceiveable. As long as things are in existence, including space and time, they exist, exist as something, and exist finitely.

Thus, the universe, being everything that exists, cannot have anything infinite within it. And it is wrong to say that the universe itself is infinite, because it is by definition only the composition of all things finite.

20

I want to add a point that I think is needed. Infinity, being a conceptual tool, doesn’t really mean “boundless,” “eternal,” or “unending”. It actually just means “not finite”. The point is that it’s a maleable, hypothetical concept. Saying, “suppose you have an infinite number of dollar, what would you spend it on?” is actually just like saying, “suppose you had enough dollars to spend it on whatever you would buy, what would you spend it on?” Infinity is like a hypothetical “enough,” allowing you to forget particulars of the moment for a process of abstraction.

This is quite different from the idea of a boundless spatial and temporal universe, because space and time are within the universe, not outside of it, and they are only concepts relative to other objects, concepts of measurement. Therefore, niether can logically be “infinite”, since infinity is measurement omission, and since the amount of actual matter and entities are obviously finite. Saying that the universe has existed forever and will exist forever is not a statement of infinity, it is unbounded finity, as the above link says.