## Request for Help re the Notion of Potential Infinity

Use this philosophy forum to discuss and debate general philosophy topics that don't fit into one of the other categories.

This forum is NOT for factual, informational or scientific questions about philosophy (e.g. "What year was Socrates born?"); such homework-help-style questions can be asked and answered on PhiloPedia: The Philosophy Wiki. If your question is not already answered on the appropriate PhiloPedia page, then see How to Request Content on PhiloPedia to see how to ask your informational question using the wiki.
LuckyR
Moderator
Posts: 2979
Joined: January 18th, 2015, 1:16 am

### Re: Request for Help re the Notion of Potential Infinity

Perhaps I didn't describe what I was driving at very clearly. My point using a snail is to highlight the lack of perceptive and computational power of the snail intellect such that it may not be able to appreciate the third dimension just as we can't appreciate the fifth, so probably could be fooled into thinking it was traveling straight when in fact it was traveling in a loop.
"As usual... it depends."

chewybrian
Posts: 188
Joined: May 9th, 2018, 7:17 pm
Favorite Philosopher: Epictetus
Location: Florida man

### Re: Request for Help re the Notion of Potential Infinity

ThomasHobbes wrote:
May 31st, 2018, 6:06 pm
Infinity has two meanings one makes sense the other absurd.

1) Size indeterminate. Meaning unknown size or quality. This makes sense.

2) Unending. This is meaningless. Take an infinitely long piece of string. No other string can be as big. Now cut the string! What have you got? Two absurdly long pieces of string. Cut them both again and you simply multiply the absurdity. With each action to double the size of the string. This contravenes the conservation of mass, and simply makes no common sense. QED there is no such quantity as an infinite (unending) quantity.
I am missing this, as it seems you've switched the sensible and absurd labels. The set of all integers is by definition infinite. This set naturally attaches to time or distance, with whatever counting interval of time or distance you wish, and the implication is that either goes on forever, isn't it? My mind isn't trying to tell me there is an edge of the universe, or if there is, that there is nothing on the other side, or no other side. Neither is it trying to warn me that time ends next Thursday at 8 a.m., thus showing the Bengals could never win the Super Bowl.

You can't "take an infinitely long piece of string", so of course whatever follows means nothing. But there could be finite objects in an infinite universe without contradiction. I can't see how the fact that an object of infinite size does not exist negates infinity, either. As soon as we have more than one thing, no thing can be infinitely large, but so what?

I can't reach infinity or touch it or whatever. But the concept makes sense, and considering time or space as finite begs the question of what is on the other side. Making their size 'indeterminate' implies they have a finite but unknown size. Perhaps all time and space can fit in my pocket, or some adequately larger pocket? That doesn't seem right at all.
ThomasHobbes wrote:
May 31st, 2018, 7:25 pm
Only if you presuppose the absurdity of infinite time.
All empirical indications show that time had a beginning, and is therefore not infinite. And since the future does not yet exist, time has a continual ending.
Do you mean the big bang? Isn't this more of a B.C./A.D. situation? Do we know for sure there is not an infinite series of big bangs, or other big bangs, other universes...? Our ability to see back into time may necessarily end with the big bang. That might just imply that we can never know what happened prior, but does not seem to prove nothing happened prior. Maybe we could see it if we were able to step outside our own universe. Maybe there will be another big bang later, and the future beings will then be unable to know of four barrel carburetors or toaster strudels.
LuckyR wrote:
June 2nd, 2018, 2:23 am
...the snail intellect such that it may not be able to appreciate the third dimension just as we can't appreciate the fifth...

I like them fine. Let the sun shine in, man...

ThomasHobbes
Posts: 942
Joined: May 5th, 2018, 5:53 pm

### Re: Request for Help re the Notion of Potential Infinity

chewybrian wrote:
June 2nd, 2018, 8:07 am
ThomasHobbes wrote:
May 31st, 2018, 6:06 pm
Infinity has two meanings one makes sense the other absurd.

1) Size indeterminate. Meaning unknown size or quality. This makes sense.

2) Unending. This is meaningless. Take an infinitely long piece of string. No other string can be as big. Now cut the string! What have you got? Two absurdly long pieces of string. Cut them both again and you simply multiply the absurdity. With each action to double the size of the string. This contravenes the conservation of mass, and simply makes no common sense. QED there is no such quantity as an infinite (unending) quantity.
I am missing this, as it seems you've switched the sensible and absurd labels. The set of all integers is by definition infinite.
The set of integers does not exist. It is just an idea.
This set naturally attaches to time or distance, with whatever counting interval of time or distance you wish, and the implication is that either goes on forever, isn't it?
A piece of string of infinite length cannot be expressed by an integer. What have integers got to do with my exampkle.
My mind isn't trying to tell me there is an edge of the universe, or if there is, that there is nothing on the other side, or no other side. Neither is it trying to warn me that time ends next Thursday at 8 a.m., thus showing the Bengals could never win the Super Bowl.

You can't "take an infinitely long piece of string", so of course whatever follows means nothing.
of course- because there is no such thing as infinity. You can't take an infinitely big any thing, including the universe. An infinite universe cannot be measured for the reason I told you.
But there could be finite objects in an infinite universe without contradiction.
Duh.
How?
ThomasHobbes wrote:
May 31st, 2018, 7:25 pm
Only if you presuppose the absurdity of infinite time.
All empirical indications show that time had a beginning, and is therefore not infinite. And since the future does not yet exist, time has a continual ending.
Do you mean the big bang? Isn't this more of a B.C./A.D. situation?
[/quote]
No.

Present awareness
Posts: 1261
Joined: February 3rd, 2014, 7:02 pm

### Re: Request for Help re the Notion of Potential Infinity

Not only are there an infinite amount of numbers in mathematics and an infinite amount of time and space in the universe, but one may also go infinitely larger or infinitely smaller in size, compared to any given object. How can this statement be proven? Give me a number and I’ll add one more to it. Give me a time and I’ll add one more minute. Give me a distance and I’ll add one more mile. All opposites produce each other, there can be no light, without dark, no large without small. As proven in QM, the very act of observation changes the result.
Even though you can see me, I might not be here.

chewybrian
Posts: 188
Joined: May 9th, 2018, 7:17 pm
Favorite Philosopher: Epictetus
Location: Florida man

### Re: Request for Help re the Notion of Potential Infinity

ThomasHobbes wrote:
June 2nd, 2018, 8:39 pm
The set of integers does not exist. It is just an idea...A piece of string of infinite length cannot be expressed by an integer. What have integers got to do with my exampkle.
Well, I began with the perspective that there is not solid agreement on these issues. A couple minutes with google verified this.

Ideas are real. Integers are a natural way to understand infinity. We all already have this set worked into our brains. Picture an x, y, and z axis and tag the intervals as inches or miles, and you have an easy picture of infinite space. And there is nothing in our experience to tell us this is not reality. The same goes with a timeline.

I'm not a 'Rain man' or a physicist, so I only have my common understanding, and that's what I see.

ThomasHobbes
Posts: 942
Joined: May 5th, 2018, 5:53 pm

### Re: Request for Help re the Notion of Potential Infinity

chewybrian wrote:
June 3rd, 2018, 6:53 am
Ideas are real.
ROTFLMFHO
Yes, and wet is dry, nature is nurture, empty is full, and black is white. And with that you run along and get run over on the next zebra crossing.

I'm out!

Halc
Posts: 201
Joined: March 17th, 2018, 9:47 pm

### Re: Request for Help re the Notion of Potential Infinity

chewybrian wrote:
June 3rd, 2018, 6:53 am
Well, I began with the perspective that there is not solid agreement on these issues. A couple minutes with google verified this.

Ideas are real.
I agreed with the entire post except for those same three words. As you said above, there is not solid agreement on these issues, and the reality of ideas is one of those points of disagreements. Now ThomasHobbes ridicules your opinion on this point, without any backing. So don't worry overmuch about it. The points made in your post are valid regardless of the reality of ideas or of integers.

T.H. seems to have a view that time is bounded on both ends by the BB and the present, but that fact doesn't prevent a spaceship from making further progress due to reaching the end of time. Seems contradictory to me, but its not my view.
The future doesn't exist, but apparently the past does. This is quite an unconventional view. A presentist would say the past does not exist either, and thus no dimension (size) to time at all. I would say both exist, and the duration ahead of us is bounded only by the end of time. That seems to be infinity only in the mathematical sense. If no crunch or rip, heat death is the effective end of time, even if maximum entropy is something only approached, never actually achieved. Physically, (not mathematically), there will eventually be no distinction, and time will end.

chewybrian
Posts: 188
Joined: May 9th, 2018, 7:17 pm
Favorite Philosopher: Epictetus
Location: Florida man

### Re: Request for Help re the Notion of Potential Infinity

ThomasHobbes wrote:
June 3rd, 2018, 8:06 am
chewybrian wrote:
June 3rd, 2018, 6:53 am
Ideas are real.
ROTFLMFHO
Yes, and wet is dry, nature is nurture, empty is full, and black is white. And with that you run along and get run over on the next zebra crossing.

I'm out!
I am not claiming Bigfoot is real; I am saying the 4th amendment is real. If you want to use a technical definition of 'real', you should state it.

I am not a professional philosopher. So, I may have used unclear language, misunderstood something, or I may be ignorant or just not that bright. Who cares, unless someone is kind enough to show me my error so I can move forward?

If I face up honestly and try to learn and grow, I can still be a philosopher, just as I can shoot 100 and still be a golfer. I don't claim to be the next Arnold Palmer. But, if I cheat, throw clubs, mock my opponents or quit the round, I disrespect the game, no matter my skill level.

chewybrian
Posts: 188
Joined: May 9th, 2018, 7:17 pm
Favorite Philosopher: Epictetus
Location: Florida man

### Re: Request for Help re the Notion of Potential Infinity

Halc wrote:
June 3rd, 2018, 9:05 am
chewybrian wrote:
June 3rd, 2018, 6:53 am
Well, I began with the perspective that there is not solid agreement on these issues. A couple minutes with google verified this.

Ideas are real.
I agreed with the entire post except for those same three words. As you said above, there is not solid agreement on these issues, and the reality of ideas is one of those points of disagreements. Now ThomasHobbes ridicules your opinion on this point, without any backing. So don't worry overmuch about it. The points made in your post are valid regardless of the reality of ideas or of integers.

T.H. seems to have a view that time is bounded on both ends by the BB and the present, but that fact doesn't prevent a spaceship from making further progress due to reaching the end of time. Seems contradictory to me, but its not my view.
The future doesn't exist, but apparently the past does. This is quite an unconventional view. A presentist would say the past does not exist either, and thus no dimension (size) to time at all. I would say both exist, and the duration ahead of us is bounded only by the end of time. That seems to be infinity only in the mathematical sense. If no crunch or rip, heat death is the effective end of time, even if maximum entropy is something only approached, never actually achieved. Physically, (not mathematically), there will eventually be no distinction, and time will end.
Well, I'm not much concerned about disagreement with someone who does not want to make any effort to support their position, so no worry there.

Perhaps 'real' was a poor choice of wording, or maybe it has some special meaning to a physicist? I suspect we might agree ideas are not material, but they exist in some sense, at least impacting material things through us.

If you have an idea that time or space or finite, maybe you could point to a good source for the uninitiated to check out this idea. I can't even say I follow you yet to the 'time will end' conclusion, so I can't agree or disagree. It still makes sense to me that they will not end, but better information might sway me.

For me, philosophy is mostly about ethics, and less about science. I don't deny free will, so it seems critical to protect mine and respect others', and to grow up emotionally so that doing so comes easier. We all have a long way to go in this regard. It's about self-improvement, learning to be happier, and to have a better impact on society. It's quite powerful in this usage. I don't say it is not valid to see it differently, but not fair for either us to assume the other should see everything from their view. I'm sure they both have their place and worth.

Eduk
Posts: 1791
Joined: December 8th, 2016, 7:08 am
Favorite Philosopher: Socrates

### Re: Request for Help re the Notion of Potential Infinity

By definition something real cannot be infinite. for example I can't physically have an infinitely long pencil. After all there would be no way to measure both ends.
Therefore if it is impossible to have an infinite object it is also impossible to have something real which is potentially infinite. This means space, whatever space is, isn't potentially infinite.
Of course most people confuse really really big with infinite. In this sense space is certainly infinite. But only in that sense.
Conceptually however it is trivial to have an infinite object. And it is undoubtedly an important and useful mathematical concept. Surely concepts have existence of a sort but it is not the same kind of existence as a physical object. Which is exactly the point that the tree falling in the forest making a sound or not is addressing.

Halc
Posts: 201
Joined: March 17th, 2018, 9:47 pm

### Re: Request for Help re the Notion of Potential Infinity

chewybrian wrote:
June 3rd, 2018, 10:16 am
Perhaps 'real' was a poor choice of wording, or maybe it has some special meaning to a physicist? I suspect we might agree ideas are not material, but they exist in some sense, at least impacting material things through us.
'Real' has special meaning in metaphysics. OK, this topic was not posted in the metaphysics section, but the opinions being asserted by ThomasHobbes are metaphysical opinions.
If you have an idea that time or space or finite, maybe you could point to a good source for the uninitiated to check out this idea.
'Big crunch' happens when expansion stops, turns around, and the whole universe collapses into a sigularity again, ending time. This seems unlikely given that the expansion is accelerating, not slowing.
"Big rip" is runaway expansion where space expands faster than even the nuclear strong force can hold the simplest things together. There is no action after that, no more entropy to create, so an abrupt end to time. You can google any of these terms.
Barrinig those two fates, "heat death" just means the universe dissolves into a haze of non-interacting radiation, and is the end of time like the other two, just not so abruptly.

Time going forever is more of a mathematical sense, but seems to have no equivalent in physics. At some point, there will not be another hour in front of you regardless of your fate of choice.

There is a cyclic theory that the universe bangs over and over, and thus infinite time. This violates thermodynamic law, but that law might not apply over multiple bangs. So in that sense, time would be infinite in both directions. I think this model was proposed only as a solution to a naive view of time (that the universe is an object that exists in time, not that time is defined by the non-object that is the universe).

As for a limit to space, I have no reference for that. Perhaps it wraps like a balloon, and if you go far enough, you get back to the start. No edge that way, but a finite size nonetheless. If we're shaped like that, the wrap is more distant than the expansion rate lets us see. It is impossible to actually return to Earth by going in a straight line like Dachshund describes. I know of no viable model that says there is an edge, and if you were there, you would see matter all on one side and none in the other direction.

Halc
Posts: 201
Joined: March 17th, 2018, 9:47 pm

### Re: Request for Help re the Notion of Potential Infinity

Eduk wrote:
June 3rd, 2018, 11:16 am
By definition something real cannot be infinite. for example I can't physically have an infinitely long pencil. After all there would be no way to measure both ends.
What definition of 'real' precludes something infinite? If there was such a thing, it would not have an end to measure, but I see no requirement to being 'real' that it must have all ends measurable.

The universe is infinite in may definitions (no limit to space at least, and very much no spatial 'end' to measure), and the universe is traditionally considered to be real. Some might define the universe to be bounded by Earth's event horizon, in which case there is an end to measure, but the event horizon is a place where you are not, not a place you can be, so there's no boundary where you see stuff in only one direction.

Eduk
Posts: 1791
Joined: December 8th, 2016, 7:08 am
Favorite Philosopher: Socrates

### Re: Request for Help re the Notion of Potential Infinity

What is space? And how do you know there is no limit?
If I am measuring something a meter long I start at one end and then measure a meter. If I am measuring infinity how would I conceptually repeat the above process?

ThomasHobbes
Posts: 942
Joined: May 5th, 2018, 5:53 pm

### Re: Request for Help re the Notion of Potential Infinity

chewybrian wrote:
June 3rd, 2018, 9:44 am
ThomasHobbes wrote:
June 3rd, 2018, 8:06 am

ROTFLMFHO
Yes, and wet is dry, nature is nurture, empty is full, and black is white. And with that you run along and get run over on the next zebra crossing.

I'm out!
I am not claiming Bigfoot is real; I am saying the 4th amendment is real. If you want to use a technical definition of 'real', you should state it.

I am not a professional philosopher. So, I may have used unclear language, misunderstood something, or I may be ignorant or just not that bright. Who cares, unless someone is kind enough to show me my error so I can move forward?

If I face up honestly and try to learn and grow, I can still be a philosopher, just as I can shoot 100 and still be a golfer. I don't claim to be the next Arnold Palmer. But, if I cheat, throw clubs, mock my opponents or quit the round, I disrespect the game, no matter my skill level.
If it exists the Bog Foot would be real. But the 4th Amendment is wholly an ideal.
Given the actual discussion about the thread, we are asking about whether of not infinity is MORE than just an idea. Numbers do not exist in reality, but as ideas.
Big Foot may not exist at all, but if it did then it would not have the sort of "reality" ( see 'real'), of the sort of a rock or the earth.
We can all think about infinity as if it were an idea like 'happiness', or the 4th Amendment, but it seems to me that we were asking it it were real in the real sense of the universe having actual infinity of size.

ThomasHobbes
Posts: 942
Joined: May 5th, 2018, 5:53 pm

### Re: Request for Help re the Notion of Potential Infinity

Eduk wrote:
June 3rd, 2018, 2:36 pm
What is space? And how do you know there is no limit?
If I am measuring something a meter long I start at one end and then measure a meter. If I am measuring infinity how would I conceptually repeat the above process?
It's big.
All the indications are that it is vey big and getting bigger. But it is measurably big.
It's getting bigger faster than you can travel. There is no edge but it is expanding in all directions.
The science says, its not what you think it is, nor what we can easily conceive with a metre ruler