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Arguments Against Infinite Quantity

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This is an argument that I came up with a couple of years ago. I've never seen it elsewhere, but I'm sure it's been made before. Over the years, I've whittled it down to something very concise and complete, so far as I'm concerned:

Time and existence are inseparable; things exist not only in space, but in time as well. A result of this is that the number of things which exist is a constant at any instant. To put it another way, at any instant, the set containing all things in existence is finite. Therefore, there can not be an infinite amount of things.

That's the argument. I think the idea is basic enough that it doesn't need any explanation, but just in case the argument is not as complete as I think, I will expand upon it anyway:

1. The future does not exist.

Thus,

2. if an infinite number of things exists, then it exists right now.

However,

3. if there is an infinite set, one of it's properties must be that if a person set out to count the elements in the set, that person would be counting for an infinite amount of time.

Therefore,

4. There can not be an infinite number of things in existence because a being with an adequate lifespan and the right instruments could count the number of things which exist at any point in time.

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Does not an 'adequate lifespan' encapsulate a 'future'?

In saying "adequate lifespan" I'm making the assumption that there will be enough time to complete the job, which is an assumption independent of whether or not the future exists. Edited by Alexandros
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Both adequate lifespan and the idea of enough time, both acknowledge a future, unless being refered to in past tense. Reality cannot be faked.

They acknowledge only that given any moment in time, there will likely be a moment that follows it. It does not acknowledge that the future exists. "Future" describes a point in time that comes after the present moment in time. Relative to the present, which is always only an instant in time, the future does not exist. To exist is to be in the present. To say otherwise is to say that whether or not a thing exists is independent of time.

Let's put that idea to the test. Actually, let's not. Not because I don't feel like it, but because it is actually impossible not to describe existence without implicitly referencing a time. Try it out: there was a time when the Earth didn't exist; now the Earth does exist. How would you reconcile this fact with a timeless existence?

Time is independent of consciousness.

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Time and existence are inseparable; things exist not only in space, but in time as well. A result of this is that the number of things which exist is a constant at any instant. To put it another way, at any instant, the set containing all things in existence is finite. Therefore, there can not be an infinite amount of things.

1. The future does not exist.

Thus,

2. if an infinite number of things exists, then it exists right now.

However,

3. if there is an infinite set, one of it's properties must be that if a person set out to count the elements in the set, that person would be counting for an infinite amount of time.

Therefore,

4. There can not be an infinite number of things in existence because a being with an adequate lifespan and the right instruments could count the number of things which exist at any point in time.

The argument can be described as circular or as "begging the question" because 4 assumes the universe is finite, which was the point to be proven.

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The argument can be described as circular or as "begging the question" because 4 assumes the universe is finite, which was the point to be proven.

I do not consider "existence" and the "universe" to be synonymous. It may or may not be that our universe is all there is to existence.

I've stated that time and existence are inseparable. I do not believe that time is a human creation or that there is a point where time ceases to exist or ceases to matter. Where there is a process, there are actions or events taking place after other actions or events. If there is no "after", there can be no processes. If there are no processes, then there can be no life as "Life is a process of self-sustaining and self-generated action" (Ayn Rand). But, clearly there is life.

It follows that the universe is finite. If something is infinite, there can be no point in time when it is finite. Put another way, something which is infinite is infinite in the instant. Therefore, something which is infinite must exist in the future because everything is finite in the present. But the existence of free will negates the existence of the future. Also, the definition of "to exist" negates the existence of the future: something which exists exists in the present; the definitions of "future" and "present" contradict each other.

There is more I can say, but I think this covers it.

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For someone who denies the 'future', you utilize it rather accurately from a present tense perspective, just prior to your re-denial of it.

As to a distinction between existence and the universe (note the singular usage of 'the universe', prior to a possessive plural? invocation) you have not elaborated.

Your command and grasp of the language is making your point difficult to comprehend.

Edited by dream_weaver
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For someone who denies the 'future', you utilize it rather accurately from a present tense perspective, just prior to your re-denial of it.

As to a distinction between existence and the universe (note the singular usage of 'the universe', prior to a possessive plural? invocation) you have not elaborated.

Your command and grasp of the language is making your point difficult to comprehend.

If you are finding it difficult to comprehend, I assure you it is not because of any failings in my use of the language. You seem to think that simply by mentioning a concept, I am inherently asserting that it is reflected in reality. This is your problem.

By saying that the future doesn't exist, I am simply making use of its definition. Since the concept "future" has no meaning if not related to the concept "time", it can only be shown not to exist if the present is considered. The future is "time that is to be or come hereafter" (this is just a statement of the word's definition).

To exist is to be.

Now we can see from the definition of "future" and what it means to exist that the future does not exist. Put another way: a time which could be described by the word "future" has not yet occurred, and therefore it does not exist.

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Aside from reality being all that there is to deal with, it must be sad not to have a future. Unless you are going to refute Zeno's paradox by arguing that time is not infinitely divisible (presumably in the future, since by the time you view this it will be in the past) or some other aspect to which infinity is yanked from its mathematical moorings, it is just good to know that you acknowledge that you are are not inherently asserting something that is reflected in reality.

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Aside from reality being all that there is to deal with, it must be sad not to have a future. Unless you are going to refute Zeno's paradox by arguing that time is not infinitely divisible (presumably in the future, since by the time you view this it will be in the past) or some other aspect to which infinity is yanked from its mathematical moorings, it is just good to know that you acknowledge that you are are not inherently asserting something that is reflected in reality.

Bringing up Zeno's paradox will not change the fact that you can not possibly reconcile the definitions of "existence" and "future" in a way that allows the future to exist. Inherent in "to exist" is a time. You must deal with this.

That being said, I have quite a lot to deal with as well. When I started thinking about Zeno's paradox, my mind wandered away from this conversation and a few things occurred to me that require much pondering. I'll start a thread once I reach a satisfactory conclusion.

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...

Time and existence are inseparable; things exist not only in space, but in time as well. A result of this is that the number of things which exist is a constant at any instant. To put it another way, at any instant, the set containing all things in existence is finite. Therefore, there can not be an infinite amount of things.

...

Oh...Alex..Alex. This seems to be pretty problematic.

Firstly things do not "exist in time". What is time? Well I am going to quote Mr Peikoff here, as I just happen to agree with this quote:

"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." - Leonard Peikoff, “The Philosophy of Objectivism”.

So I am not entirely sure why you would assert that things exist "in time" as well as "in space" ( to paraphrase you a little). Despite what physics might assert, time is not a dimension or a property of space, or anything besides what it is described as above. So unless I miss something, your claim of existence "in time" does not make a lot of sense.

You proceed as though you actually do consider time to be something else (what exactly I am not sure). What evidence do you have for this? Do not try to bother claiming Relativity or such proves such things, it does not. I dont know if you planned to do that, but just in case you were : Dont waste your effort ;)

"Future" is a concept which pertains to events which are yet to happen or to facts which will we wish to identify will hold at a time or date after the present moment. It is also nothing more than this. How does it make sense to claim that it does not exist? Are we to believe that the concept has no referents? This is not the case, the referents would be whichever events we wish to consider which have not occured or the facts we wish to consider.

So how does it make any sense to deny that the future exists? Does it have a tangible existence? No, it is a concept. Do things exist "in the future" ? Well in a sense it could be said they do. What this statement identifies is that at a later time and / or date, that a certain existent / existents will continue to exist. What is the issue here? I see none.

So in short, I find this chain of thought to be a little confusing, messy and seemingly quite possibly quite false / misleading.

Edited by Prometheus98876
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I'm don't think that one can meaningfully talk about the extent of the universe unless it is qualified, e.g., the extent of the observable universe. Surely it's true that the distance between any two entities in the universe is finite and surely it's true that the extent of any entity is finite. I think, in this sense, it is correct to say that the universe is not infinite, i.e., that there are no infinite distances, infinite extents, etc.

Agreed.

Nonetheless, there is no logical reason that distances and extents cannot be arbitrarily large, i.e., have no upper bound.

"No logical reason"? as in does not imply a contradiction?

That sounds like the analytic-synthetic dichotomy.

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  • 4 weeks later...

Oh...Alex..Alex. This seems to be pretty problematic.

Firstly things do not "exist in time". What is time? Well I am going to quote Mr Peikoff here, as I just happen to agree with this quote:

"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." - Leonard Peikoff, “The Philosophy of Objectivism”.

This quote is confusing to me. Peikoff is attempting to prove the universe is non-temporal by appealing to something "outside the universe" which we can't get to. Isn't such an appeal meaningless? Like trying to have a conversation with someone who insists you answer questions like "Where is the universe, then?" The question is meaningless, and therefore no kind of proof can be derived from it. Can you explain how Peikoff has avoided this, or where I am misinterpreting/misunderstanding?

"Time is a measurement of motion." Thus, where there is motion, time can be measured. If time is not a property of the universe, then there can be no motion of the universe. But, doesn't this also mean that there can not be motion within the universe? Imagine a box with a ball in it. We can say that the ball exists in the interior of the box. If there is no motion associated with the box, does the ball still exist in the interior of the box? I say no, because the box doesn't exist. I say the box doesn't exist because if there is no motion associated with the box, then it can’t consist of any combination of molecules, atoms, quarks, or bosons, and since this is all there is to consist of, the box must not exist.

So, it can be said that the universe must be in motion because we can observe that things do exist within the universe. But, this suggests that there is an outside to the universe, because something in motion must be moving inside of something. If this is the case, does it matter that we "cannot get outside the universe?" If we can logically prove that the universe is contained in something, then time can apply to the universe because there is something to relate it to. (I’m aware this creates an infinite regress, I’m just hoping you’ll point out where I’ve gone wrong.)

So I am not entirely sure why you would assert that things exist "in time" as well as "in space" ( to paraphrase you a little). Despite what physics might assert, time is not a dimension or a property of space, or anything besides what it is described as above. So unless I miss something, your claim of existence "in time" does not make a lot of sense.

You proceed as though you actually do consider time to be something else (what exactly I am not sure). What evidence do you have for this? Do not try to bother claiming Relativity or such proves such things, it does not. I dont know if you planned to do that, but just in case you were : Dont waste your effort

If time is just a measurement, then isn’t space also just a measurement, and therefore it does not exist either? It seems to fit the same criteria as time. You are there, I am here; we know here is not there because of some measurement of the space between us, as we know now is not then because of some measurement of time between them. If the universe is all there is, then “no standard is applicable” as “you can not get outside the universe”. So, the universe must be non-spatial as well as non-temporal.

As you can tell, I don’t think Peikoff’s explanation is sufficient.

"Future" is a concept which pertains to events which are yet to happen or to facts which will we wish to identify will hold at a time or date after the present moment. It is also nothing more than this. How does it make sense to claim that it does not exist? Are we to believe that the concept has no referents? This is not the case, the referents would be whichever events we wish to consider which have not occured or the facts we wish to consider.

So how does it make any sense to deny that the future exists? Does it have a tangible existence? No, it is a concept. Do things exist "in the future" ? Well in a sense it could be said they do. What this statement identifies is that at a later time and / or date, that a certain existent / existents will continue to exist. What is the issue here? I see none.

I wasn’t denying the existence of the concept. I was denying that there exists some time which has not occurred where there are tangible things. There would be a place associated with that time where these tangible things existed. If such a time and place did exist, I can’t think of anything else to call it but “the future”. Sorry for the confusion.

[And sorry for the long hiatus. I’ve been face first in my textbooks for a solid month :P]

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  • 1 month later...

3) Identity.

Some have said that the notion of an actual infinity violates the law of identity, which states that everything which is, is; or put another way, everything has a specific identity. However, I don't see how this law is violated by an actual infinity. On another recent topic about the claim that "existence exists", it was noted that this statement carries no more philosophical weight than to point out that "nothing is not a thing", that one cannot contradict oneself. In the same way, since the law of identity seems to say basically this, I don't see how the law of identity has anything to bear on this topic. It has been said that infinity is not a "specific" quantity, as if it is a quantity, but just not a specific one. But using the notion of infinity stated in the beginning, this is clearly not true. We know exactly what a map is, and exactly what an injective map is, and what the set of natural numbers are, so we should know exactly what an injective map from the natural numbers to some other set is, regardless of which set we are talking about. Thus there is nothing "unspecific" about this conception of infinity.

Thus in order to pursue this line of argument, one needs to state how exactly the law of identity precludes the possibility of such an injective map, or how the notion of an injective map as I've described above is somehow not specific.

I have not had sufficient time to read all the posts in order to know if what I have to say is going to be redundant (covered by someone else already). If my points have already been covered, I apologize.

I'm working off of your third objection.

It seems there are 3 "possibilities" regarding the existence of an infinite set:

Past, Present, and Future.

Regarding the past, it is usually referred to as an "infinite regress". A regress is a series going back into the past. An infinite regress is supposed to refer to a series going back into the past forever. A series, though, must have a beginning. An "infinite series" would have no beginning. If a series does not begin, then it does not exist. Therefore an "infinite regress" is a "series which does not exist". To say that an infinite regress exists is to say that a non-existent series exists. It is a contradiction.

Regarding the present, it is usually referred to as an "infinite set". But any set which exists in its entirety at a definite moment in time (i.e. the present), must be definite (not infinite). An non-finite set would need to stretch on outside of any definite point in time. Therefore a "present infinite set" is a "definite and non-definite set". It is a contradiction.

Regarding the future, I think that this is what is referred to by philosophers as a "potential infinity". That is to say that the set has the potential to continue on forever into the future. This is possible. But there could be no definite moment in time at which the set could be said to be "infinite" for the reasons stated above concerning the "present infinite set".

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