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Infinity and Existence

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Akin
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Hello,

Recently I have been discussing the topic of the Objectivist Metaphysics, and have found something that I need clarification with. I hope somebody can assist me.

on page 31 of OPAR, Mr. Peikoff states, " Is God infinite "infinite" does note mean large' it means larger than any specific quantity, i.e., of no specific quantity. An infinite quantity would be a quantity without identity. But A is A. Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well"

However, both Peikoff and Rand acknowledge that existence must have always existed. They have stated that the axiom of existence exists, encompasses the concept: Existence always has been, is, and will be.

I don't remember where this information is cited, but I am aware that the Objectivist definition of time is a measurement between two things. This solves the problem of time being infinite as there can be no infinity. Time is always a finite and specific quantity, regardless of how large the measurement of time is.

My problem then, is my ability to make sense of how the existence always has been and always will be, yet can not be infinite. I have a some ideas, but I am curious as to whether I am missing something.

Thank you for your help!

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However, both Peikoff and Rand acknowledge that existence must have always existed. They have stated that the axiom of existence exists, encompasses the concept: Existence always has been, is, and will be.

I don't remember where this information is cited, but I am aware that the Objectivist definition of time is a measurement between two things. This solves the problem of time being infinite as there can be no infinity. Time is always a finite and specific quantity, regardless of how large the measurement of time is.

My problem then, is my ability to make sense of how the existence always has been and always will be, yet can not be infinite. I have a some ideas, but I am curious as to whether I am missing something.

Thank you for your help!

Time is a measurement of motion; as such, it is a type of relationship. Time applies only within the universe, when you define a standard—such as the motion of the earth around the sun. If you take that as a unit, you can say: “This person has a certain relationship to that motion; he has existed for three revolutions; he is three years old.” But when you get to the universe as a whole, obviously no standard is applicable. You cannot get outside the universe. The universe is eternal in the literal sense: non-temporal, out of time.

That might help. It might not...

The philosophy of Time is tricky no matter what branch you follow.

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You say you are having trouble making sense of eternity - in what way do you mean this?

I found it very difficult at first to conceive of an eternally unbounded universe, one in which you would never reach the edge, but without implying infinity. As Peikoff touches on in his latest podcast though, this is of course very difficult, because any visualisation you try to create in your head is necessarily going to be of some kind of finite, bounded model. It is impossible to visual the eternally existing, eternally 'large' universe, owing to the very fact that it is not like what we normally visualise.

In that same podcast, someone made the astute point that you can only really understand it conceptually. He used the example of the horizon: one can never really go beyond the horizon, owing to the nature of the Earth being spherical. You'll just keep going round and round. The same thing applies to the universe - you can think, in pure conceptual terms, "Oh, it must be unbounded", but you can't think of it in perceptual terms, as an unbounded thing, because we just don't perceive unbounded things, and never have. I might add that, in fact, owing to the nature of us as being developed to live and understand the world in our normal, three-dimensional, bounded, format, we may never be able to visualise the universe as whole.

A more succinct way of putting this is, to quote the Bond title: Tomorrow never dies. As soon as you're just about to reach it, there's always one day more.

Incidentally, this may have been what lead Ayn Rand to her little known, and unpublished, hypothesis of a 'spherical time'. Personally, I enjoy seeing each new hypothesis about how time and space might be 'shaped', but I think it is an ultimately fruitless endeavor. It might help us one day, and maybe one day we can model the unbounded universe in some manner, but until the time when we need to start going there, I really don't think you need to be that worried.

Edited by Tenure
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Actually mathematicians describe the surface of a sphere as being finite but unbounded--there isn't an edge to it you'd bump into or fall off of as you were traveling in it. They then move to the universe by analogy--a 3-dimensional surface-analog of a 4-dimensional sphere-analog. Now we certainly cannot *visualize* it but the math does work.

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Actually mathematicians describe the surface of a sphere as being finite but unbounded--there isn't an edge to it you'd bump into or fall off of as you were traveling in it. They then move to the universe by analogy--a 3-dimensional surface-analog of a 4-dimensional sphere-analog. Now we certainly cannot *visualize* it but the math does work.

I think that sort of resonates with Einstein:

It follows from what has been said, that closed spaces without limits are conceivable...As a result of this discussion, a most interesting question arises for astronomers and physicists, and that is whether the universe in which we live is infinite, or whether it is finite in the manner of the spherical universe. Our experience is far from sufficient to enable us to answer this question. But the general theory of relativity permits of our answering it with a moderate degree of certainty, and in this connect the difficulty mentioned in Chpt 30 finds its solution.

He goes on to conceive of the universe as unbounded yet finite, as you mentioned.

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While I'm very familiar with the visual explanation Steve put forward, I've never heard of this "roller-coaster model thing" you mentioned, and that site you link to doesn't seem to be one to take seriously. Is it like a mobius strip?

Yes, that's one example. I can't seem to find any good images at the moment, but yeah, that's one of the models I've seen. It's not an important point. I just think they're funny.

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I haven't studied theoretical physics very much, but what about describing the universe as a fractal, like the Mandlebrot set? At any stage or distance you will see the same pattern, and no matter how far you zoom in or out you see the same thing. What if the universe is unbound by the dimension of size? Inside each atom, another piece of the universe, and our verse, encased by an atom?

Again, just my imagination going wild.

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  • 3 weeks later...
Hello,

Recently I have been discussing the topic of the Objectivist Metaphysics, and have found something that I need clarification with. I hope somebody can assist me.

on page 31 of OPAR, Mr. Peikoff states, " Is God infinite "infinite" does note mean large' it means larger than any specific quantity, i.e., of no specific quantity. An infinite quantity would be a quantity without identity. But A is A. Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well"

However, both Peikoff and Rand acknowledge that existence must have always existed. They have stated that the axiom of existence exists, encompasses the concept: Existence always has been, is, and will be.

I don't remember where this information is cited, but I am aware that the Objectivist definition of time is a measurement between two things. This solves the problem of time being infinite as there can be no infinity. Time is always a finite and specific quantity, regardless of how large the measurement of time is.

My problem then, is my ability to make sense of how the existence always has been and always will be, yet can not be infinite. I have a some ideas, but I am curious as to whether I am missing something.

Thank you for your help!

The Universe has a finite beginning in the past under any constant time-unit, as has been proven by physics (see Linde, Linde, and Mezhlumian, "From the Big Bang Theory to the Theory of a Stationary Universe"). Additionally, prominent singularity theorems assert that there existed a singularity point approaching infinite density and approaching zero size which gave birth to the universe as it is.

I always say that the more I see of the world, the more I like Ayn Rand. Rand, not familiar with this very technical theorem (as she wasn't properly a physicist), asserted through philosophical consideration - and quite correctly so - that the Universe, while eternal, is finite in internal quality. Although she and Peikoff are quite correct in stating that existence qua existence has no relational quantity with time, and is thus eternal in the technical philosophical sense (i.e. literally outside of time), this doesn't mean that internal actions cannot be considered via means of an analysis of the impossibility of an infinite set of causal history.

More modern and less fundamental thinking Christian theists from the Aristotelean school of thought - like my friend Dr. Bill Craig, whom I hold in the same "half respect" regard (although in a less important modern sense) as Ayn Rand held Aquinas - holds, as Rand does, that the set of causation is finite, and thus leads to God:

1) Everything that begins to exist has a cause;

2) The Universe began to exist;

3) Therefore, the Universe has a cause.

Now, as Dr. Peikoff has pointed out in a recent radio broadcast, there's a problem with Premise 2. The Universe is the set of everything that exists. It is permanent. But Dr. Craig has faced this criticism before, but Craig clarifies, in a sense, that what he means here is that the Universe sprang from a First Cause, as the Big Bang Theory asserts.

Peikoff is absolutely right. And so is Craig. But, while Craig is additionally correct that this First Cause is internally and externally timeless (similar to Rand's sense of "eternal"), he is wrong in asserting that the First Cause is a conscious Divine being willing the matter, energy, and motion of our Universe out of literally nothing through a (timelessly existing!?) "completely free" decision.

Craig is asserting that the Big Bang theory in physics mirrors the metaphysical necessity for a finite causal history and proves that, as Rand already anticipated in Galt's speech (paraphrased): God created everything that exists from nothing by means of arbitrary whim. This doesn't seem like an attractive option.

Unfortunately for Craig and completely in line with Rand - a strict author and philosopher not knowing of the deep physics itself - the Big Bang theory implies that the Singularity caused the Universe, since it actually existed and since it must, by philosophy AND by physics, contain all constituents of matter and energy (fermions and bosons, etc.) superimposed in a state with infinitesimal size (which is fine, because these fundamental building blocks themselves have infinitesimal size).

Applying any time unit to this process (i.e. any unit of relational motion ) yields that this cosmic singularity existed only at t=0, i.e. it did not exist necessarily for any duration of time. Therefore, it is argued by some people ascribing to the floating concept of some "absolute notion of time" that this singularity therefore couldn't have technically existed. But not only does physics point to a relational need for time, philosophy does as well, since time is necessarily an epistemological assessment of a constant metaphysical relation (i.e. "second" epistemologically is related to the metaphysical motion of light over a set small displacement). In metaphysics, we do not have some "god clock" to relay the race; we only have causation and motion of the fundamental existents of reality. Period.

And what is happening at this supposedly "impossible" t=0? The Universe, by the necessary proof of mathematics in accordance to data that has been properly observed and interpreted in physics, existed "at this time" in a motionless, distanceless state. There was no "time" that the universe existed in this state, nor was there a "time before t=0" where this state didn't exist, as lesser theists screaming that atheists believe that the Universe arose from nothing constantly blather. This is where Rand and Peikoff truly come in - not only is there no external referent, as they correctly state, but there is not an internal referent, either. At "t=0," the cosmic singularity isn't "there for a vanishing instant." Since there is no motion, it simply is. It doesn't "spring from the nothing before"; there is no "before" and there is no "nothing," since existence exists and the fundamental constituents of reality are necessarily eternal philosophically and physically, as discussed above.

At the "t=0" Cosmic Singularity State, in short, the Universe simply was. Just as it simply is today. Only, no motion marked any internal time.

How could such a state cause the Universe to exist in its (internally and externally) timeless state? In that state, all fundamental components of matter existed in a hyper-superimposed state, with the spins of the fermions granting absolute "instability," similar to an unstable atom today. So, although the Singularity existed in a timeless state, the instability of its components in internal relation necessarily entailed separation, meaning: motion, and therefore time and space, as a necessary result.

Do not confuse the Singularity with some sort of pellet existing in some infinite space hanging out for some past-infinite time before the Big Bang. There is no "space outside the Universe," even in this superimposed state, since all components of existence existed within this state, providing no referent for "space" (imagining the Singularity from the outside with your mind does not count; the metaphysical existents making up your mind precedes such imaginary placement "outside" because all components of existence are "inside"). Likewise, it did not "hang around for a past-infinite amount of time," since there is no motion internally and externally and therefore no time at all. The singularity birthed space and time from this state due to the identities of the constituents contained within. It is not only a sufficient cause of the Universe, but due to the equations of Special Relativity and especially the Second Law of Thermodynamics, coupled with the Law of Conservation of Matter, it is the necessary cause, one that - again by the Law of Conservation - could not itself have been farted out of nothing by some hypothetical, contradictory Triune God, or any being for that matter.

Edited by Flagg
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If it's unpublished, how do you know about it?

From the following quote in this essay which is a good read on the topic:

Dr. Harry Binswanger mentions in the first question period of his lecture Selected Topics in the Philosophy of Science that Miss Rand had a theory that she called "circular time," which Dr. Binswanger said he unfortunately did not learn very much about.
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How could such a state cause the Universe to exist in its (internally and externally) timeless state? In that state, all fundamental components of matter existed in a hyper-superimposed state, with the spins of the fermions granting absolute "instability," similar to an unstable atom today. So, although the Singularity existed in a timeless state, the instability of its components in internal relation necessarily entailed separation, meaning: motion, and therefore time and space, as a necessary result.

Wait, how can there be any instability in a timeless state?

Or do you mean it in the same sense that it would be a ''lengltless'' or a ''Widthless'' state because they all require multiple ''somethings''?

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  • 4 weeks later...
Wait, how can there be any instability in a timeless state?

Or do you mean it in the same sense that it would be a ''lengltless'' or a ''Widthless'' state because they all require multiple ''somethings''?

I've done further study; the First Cause need not even be lengthless or widthless. Hawking's equations denote a First State, if brought into nowadays, that would be some kind of pellet of size to the order of 10^-33 m. So we don't even have to worry about the implied topology.

Hawking asks us to imagine some sort of disorderly causation state here where there can be no "before" or "after." It meshes up with physics - that the first Universal state is of maximal disorder - but how can it mesh up with Objectivism and the actual notion of causation? Here's where I seize on Hawking with philosophy - such a small clown-car state of the Universe - containing all that exists - won't even have "space" enough to separate causes. What this means is, for any constituent in this soup ak, and for all other constituents a1, a2, ..., ak-1, ak+1, ..., an, ak's identity affects all other identities in the universal set at the same time. This creates some kind of incomprehensibly large spiderweb of causation (but not infinite in size, of course) that all happens simultaneously.

This causes a wavefunction-collapse. Some argue the collapse had a 95% chance of happening; some have argued (and of course I hold) for 100%.

How can this sort of causation make sense?

Well, loosely, since causation denotes time, we still have a state internally and externally outside of time. Now, don't imagine - in either case - that we have some sort of soup of all the constituents of reality just hanging out for some past eternity pushing against one another and then suddenly going "geez, let's make a universe today!" No. The state here is outside of time, not eternally present (an invalid statement in the case of this Universal State, since it by definition has no precedent causal referent). It simply is, as the universe as a whole is now, but also internally, as well.

The effect is the universe. Bang.

We thus have a finite chain of causes, with an eternal universe, making sense both in physics and Objectivism. I like it.

Comments?

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Flagg,

Interesting, thought-provoking stuff.

There are currently many cosmological theories of the universe's history, of which the big bang singularity is but one. See:

http://www.metaresearch.org/cosmology/DidT...eABeginning.asp

http://www.metaresearch.org/cosmology/BB-top-30.asp

And the myriad associated references.

I point these out because you seem to regard singularities and big bangs as "proven". They are not, but we can simply accept, for the sake of discussion now, that this theory has some empirical evidence and instead talk about its logical validity. By the way, could you link me to where it has been shown, philosophically, that there must be a "First Cause"?

First off, you state that all the universe's constituents are compressed into an infinitesimal (not zero) region, by which you mean there is 0 distance between all constituents. Each constituent is pressed right up against each other one.

Fine, additionally you emphasize that "time" is relational, it's more or less "in our heads". Objectively there are only objects, the motions of objects, and causation. Also agreed. The concept "absolute time" is a misnomer/floating concept analogous to "absolute velocity". These concepts, time and velocity, are always relational. We only quantify them by comparing at least two objects and their motions. On the other hand, "object" is not relational, it exists independent of identification or comparison. Time, velocity, music, etc. exist only by virtue of an identified comparison and relationship. There is no "God clock".

You say that the singularity "did not exist for any duration of time". Nothing exists for a duration of time! They simply exist. Exist is static, it is independent of motion. This ball exists whether it ever moves.

You assign the singularity "t=0". I don't know if you mean this literally or not. I can assign any instant t=0 if I want, and let relative motion progress from there. What I mean is that any "instant" or "cross section" of time is of course motionless, by definition. There is, by definition no "time" that the universe or any system is in a single specific state at some instant. In this regard the instant you have described as "singularity" is no different than any other instant. The only distinctive characteristic is that it is "distanceless". So it's as dense as it can get, but of course the constituents had to move toward each other to become that dense. So there's nothing special about this singularity, it's just another instant. If we look at the next instant nothing is moving either, each object is simply at a new location. And so and and so forth for each instant we care to visualize/imagine.Your insistence that this instant is somehow special and absolutely must be the "first" is weird. I haven't seen a justification of this beyond stating that it is "mathematically proven".

"At the "t=0" Cosmic Singularity State, in short, the Universe simply was. Just as it simply is today. Only, no motion marked any internal time." -Flagg

The universe is just as time-less today as it has ever been. You're trying to say that there was no motion, then there was motion. But that doesn't make any sense. What is "motionless" but "one instant of time"? At the next instant we see new locations. There is never any "internal time" at any instant, not today or yesterday, until consciousness comes about with the ability to record and remember previous locations. Of course objects move in the absence of conscious entities' observations. Time is essentially motion+observer. So the only distinction I'm seeing is that this singularity is as dense as possible and contains no conscious observers.

You go on to discuss instability and how the necessary effect/result of this state was that the entities would move outward/apart from each other. But why do you demand that this be the "first state"? Surely the entities had to be brought together in order to achieve this state. You talk about it "birthing space and time" by which you mean it "created motion". This seems to mean that we got motion from motionless, a contradiction.

It makes much more sense to simply say that the universe is eternal and has always been in motion. There is no "First Cause" by definition because every cause has a cause and every effect has an effect. If observation indicates that the universe was previously more dense the logical conclusion is that it expanded from that and, before that, it contracted, etc.

In your second post you bring up some interesting ideas, namely that there is no separation between entities so they all affect each other in accordance with their identities simultaneously. That's fine, but why insist that this is the "first state"? Such a "first state" would have no cause and seem to violate causality. It's more likely that the constituents actually collapsed inward then exploded outward.

Your justification is that this singularity "exists outside of time". By which, from everything you've said, you're saying there was no motion. So we have motion from no motion, how do you reconcile this apparent contradiction? There's no motion, then suddenly there is. One justification you give is that all the constituents are "not spatially separated" and thus *interact* simultaneously in accordance with their identities. But "interact" is a verb, it invokes motion! But you're saying this state is motionless/timeless. How can we have an interaction in a timeless/motionless state? You have missed this key aspect, that interaction/influence itself is dynamic and, as such, cannot occur "outside of time".

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