Can an actual infinite exist?

This is one of the key premises of the Kalam cosmological argument, the claim that the universe could not have existed for an infnite amount of time and that it therefore must have had a beginning. I'm not really interested in discussing whether or not the universe began as much as I am in discussing this premise.

So why do some say that an actual infinite is impossible? Well one point which I've heard fairly often is that if the universe did exist forever then we would have never reached the present point in time. Lets let our friend VenomFangX explain, just watch up to 0:48 to get the relevant bit. Or if you want a more credible source you can hear it from danwallacefan (yup that's him), watch from 1:05-2:08.

Ok go and watch the videos, I'll wait here.

Are you done? Allrighty I want to bring up a rebuttal to this claim. To me it seems very obvious but I've never heard anyone else use it which suggests that I either haven't looked hard enough or that I haven't fully thought this through.

Lets use VenomFang's example, if someone says to you that they will give you a chocolate bar after an infinite amount of time then you will never recieve that chocolate bar because you could never say that an infinite amount of time had passed. I would agree with this, saying that there is an end to infinity is directly contradicting its definition which is of course "without end".

There is one thing which seems to have slipped under the radar however. In this example the point in time in which the actual infinite ends cannot exist however the point in time in which the actual infinite began does indeed exist. We think of finite frames of time in terms of their beginnings (B)and their ends (E). The time it takes you to read this for example can be modeled by a beginning in time and an end in time:

B(you start reading)-------------------E(you finish reading).

With infinity though it seems to be a little different. There is a beginning followed by a period of time that never ends or an end which was preceded by a period of time that never began. Lets take the chocolate bar example again and model it:

B(I'll give you a chocolate bar after an infinite amount of time)-----------------------------(ad infinitum)

There was the beginning and an infinite period of time with no end. What about the following form of infinity, one that includes an end but no beginning.

(regress to infinity)-------------------------------------E(You read this topic during the present point in time)

This form of infinity is just as valid as the chocolate bar example, it only makes a beginning impossible rather than an end.

So what's the problem with VenomFangX and danwallacefan's arguments? They assume a beginning to their proposed infinite time frame. If we say that an actual infinite is beginningless however then it becomes perfectly possible to say that it has an end. In this way their arguments do not show that actual infinites are impossible, only that an actual infinite that has begun cannot end.

Tell me if that makes sense or not?

...

So why do some say that an actual infinite is impossible? Well one point which I've heard fairly often is that if the universe did exist forever then we would have never reached the present point in time. Lets let our friend VenomFangX explain, just watch up to 0:48 to get the relevant bit. Or if you want a more credible source you can hear it from danwallacefan (yup that's him), watch from 1:05-2:08.

...domatron23

To me the specific argument in the paragraph I quoted seems quite simple to answer:

(ad infinitum)-------------------------------------- PRESENT TIME -------------------------------------(ad infinitum)

:?

I don't see where the problem is, but again as I said I am no expert, so...

:?

(oh and I didn't watch danwallacefan's video. Later, sorry :P)(oh and I don't know what to answer to the poll :? I am not sure I have decided that I am not sure...)

[QUOTE="domatron23"]

...

So why do some say that an actual infinite is impossible? Well one point which I've heard fairly often is that if the universe did exist forever then we would have never reached the present point in time. Lets let our friend VenomFangX explain, just watch up to 0:48 to get the relevant bit. Or if you want a more credible source you can hear it from danwallacefan (yup that's him), watch from 1:05-2:08.

...Teenaged

To me the specific argument in the paragraph I quoted seems quite simple to answer:

(ad infinitum)-------------------------------------- PRESENT TIME -------------------------------------(ad infinitum)

:?

I don't see where the problem is, but again as I said I am no expert, so...

:?

Oh no don't worry you're on the same track as me. You're right the argument is devilishly simple to answer (although this only makes me suspicious that I'm missing something obvious).

(oh and I didn't watch danwallacefan's video. Later, sorry :P)(oh and I don't know what to answer to the poll :? I am not sure I have decided that I am not sure...)

Teenaged

Yeah I'm in the same boat too, haven't made up my mind one way or another.

The way I see it maybe the main objection one could pose for an infinite universe is that everything must have start, as a consequence of it having a cause and a creator (if one accepts that of course). Even so, the first posed necessity alone (a start) is not supported as something absolutely necessary and quite frankly who can say for sure without making assertions that the universe MUST have a beginning/start?

Oh sorry no, that would not actually negate the idea of an infinite universe (in general), but a universe that existed ad infinitum towards the past.

Once someone supports the idea that the universe MUST have a beginning/start, then automativally, for him/her, that premise works as an argument for the existence of god. But since this argument is not based on something certain but something that just seems logical or expectable from the things we see in nature (everything has a start - although someone might argue that the evolution process makes everything not have a start [not a dinstinct one]), the simply it cannot be used as an argument.

That's how in the notion of god is used as a "wild card", for people who want to fill gaps (existant or gaps created by lack of knowledge - I go with the latter), and as long as there are gaps, some people will want to use that "wild card".

EDIT: In my humble opinion. :|

Once someone supports the idea that the universe MUST have a beginning/start, then automatically, for him/her, that premise works as an argument for the existence of god. But since this argument is not based on something certain but something that just seems logical or expectable from the things we see in nature (everything has a start - although someone might argue that the evolution process makes everything not have a start [not a dinstinct one]), the simply it cannot be used as an argument.

That's how in the notion of god is used as a "wild card", for people who want to feel gaps (existant or gaps created by lack of knowledge - I go with the latter), and as long as there are gaps, some people will want to use that "wild card".

Teenaged

I think time is a difficult subject to talk about.

There are two different types of time that people refer to when they talk about "Time" in general.

1. Physical time. This is the fourth dimension we exist in. It is a physical thing which is part of our universe. It has laws and facts that govern it and it exists

2. Abstract time. Abstract time is the concept of time, or the ability to put events in specific order. It is an idea we use to measure the universe around us. It does not really exist.

This is one of the key premises of the Kalam cosmological argument, the claim that the universe could not have existed for an infnite amount of time and that it therefore must have had a beginning. I'm not really interested in discussing whether or not the universe began as much as I am in discussing this premise.

So why do some say that an actual infinite is impossible? Well one point which I've heard fairly often is that if the universe did exist forever then we would have never reached the present point in time. Lets let our friend VenomFangX explain, just watch up to 0:48 to get the relevant bit. Or if you want a more credible source you can hear it from danwallacefan (yup that's him), watch from 1:05-2:08.

Ok go and watch the videos, I'll wait here.

Are you done? Allrighty I want to bring up a rebuttal to this claim. To me it seems very obvious but I've never heard anyone else use it which suggests that I either haven't looked hard enough or that I haven't fully thought this through.

Lets use VenomFang's example, if someone says to you that they will give you a chocolate bar after an infinite amount of time then you will never recieve that chocolate bar because you could never say that an infinite amount of time had passed. I would agree with this, saying that there is an end to infinity is directly contradicting its definition which is of course "without end".

There is one thing which seems to have slipped under the radar however. In this example the point in time in which the actual infinite ends cannot exist however the point in time in which the actual infinite began does indeed exist. We think of finite frames of time in terms of their beginnings (B)and their ends (E). The time it takes you to read this for example can be modeled by a beginning in time and an end in time:

B(you start reading)-------------------E(you finish reading).

With infinity though it seems to be a little different. There is a beginning followed by a period of time that never ends or an end which was preceded by a period of time that never began. Lets take the chocolate bar example again and model it:

B(I'll give you a chocolate bar after an infinite amount of time)-----------------------------(ad infinitum)

There was the beginning and an infinite period of time with no end. What about the following form of infinity, one that includes an end but no beginning.

(regress to infinity)-------------------------------------E(You read this topic during the present point in time)

This form of infinity is just as valid as the chocolate bar example, it only makes a beginning impossible rather than an end.

So what's the problem with VenomFangX and danwallacefan's arguments? They assume a beginning to their proposed infinite time frame. If we say that an actual infinite is beginningless however then it becomes perfectly possible to say that it has an end. In this way their arguments do not show that actual infinites are impossible, only that an actual infinite that has begun cannot end.

Tell me if that makes sense or not?

domatron23

GabuEx, that would only be a problem if God has an infinite temporal past. precious few theists actually claim that. Most agree that God, being the origin of time, exist (s/ed) timelesslydanwallacefan

Two questions:

1. In what sense would that not still make God's existence infinite?

2. What, exactly, does that even mean? Time is the path from one static three dimensional image to the next, which is why it's often regarded as the fourth dimension. Nothing "happens" in the common sense of the word except through the course of time. If something exists without time, it seems to me that it would necessarily be unable to do anything.

I would prefer it if this was answered without the get-out-of-jail-free card of "God can do anything", too. I'm looking for a real logical explanation of how God did something without time existing when he did it.

No no no, the problem of a vicious infinite regress does not depend on assuming that there was a beginning that occured an infinite amount of time ago, in fact the argument is strengthened if we assume that there was no beginning. danwallacefan

Are you saying that a beginningless period of time is still not an actual infinite or that it's impossible? Elaboration please.

[QUOTE="danwallacefan"] No no no, the problem of a vicious infinite regress does not depend on assuming that there was a beginning that occured an infinite amount of time ago, in fact the argument is strengthened if we assume that there was no beginning. domatron23

Are you saying that a beginningless period of time is still not an actual infinite or that it's impossible? Elaboration please.

GabuEx

1: Its not infinite because there isn't any infinite being traversed, like a beginningless temporal past

2: How would you respond to the point that actual tense is a basic belief, or at least coheres best with our basic beliefs?

[QUOTE="domatron23"]

[QUOTE="danwallacefan"] No no no, the problem of a vicious infinite regress does not depend on assuming that there was a beginning that occured an infinite amount of time ago, in fact the argument is strengthened if we assume that there was no beginning. danwallacefan

Are you saying that a beginningless period of time is still not an actual infinite or that it's impossible? Elaboration please.

Well yeah that's kind of the whole point of the argument.

The claim was that an actual infinite could not exist because otherwise we would have never reached the present point in time. My rebuttal is, as you have just affirmed, that an actual infinite is implied if we deny a beginning.

So doesn't that kind of invalidate your and VenomFang's argument against an actual infinite, or have I missed something?

If I remember right, the arguments goes something like... Our universe: CREATION----------------------------------------MEASUREABLE TIME----------------------------------------END OF DAYS Time outside our universe: INFINITY-------------------------------RIGHT NOW-------------------------INFINITY Being infinite, time outside our universe cannot be measured and it could conceivably be argued that it doesn't exist, at least not the way we understand and think of it. In a place outside our universe, an infinite being like God could exist. And of course, if one does, the matter of that being's age is more or less moot--if time where that being lives does not exist in a measurable way, can such a being even be said to have an age? ChiliDragon

Red: From my prespective, no, because to my knowledge god is ageless (isn't that what the Bible says also?) On that ground I have thought that it is possible to connect that ageless god with time itself, in a sense that maybe from one prespective god may be time itself. Now I don't know how that works or if that description goes on to describe a completely different god. I don't know tbh. :?

But again those thoughts I have probably derive from my "favourite" imagery of god in which god is actually all the natural forces that keep the World together, and presumably that would make god the embodiment of time itself, as well as the embodiment of other wordly "powers", in a sense that he/she/it is neither controlled by those powers, neither is he/she/it beyond them; he/she/it isthose forces. But again that's my totally personal opinion (I haven't "locked" on to it yet) and the rant is over as of now. :P

[QUOTE="danwallacefan"][QUOTE="domatron23"]

[QUOTE="danwallacefan"] No no no, the problem of a vicious infinite regress does not depend on assuming that there was a beginning that occured an infinite amount of time ago, in fact the argument is strengthened if we assume that there was no beginning. domatron23

Are you saying that a beginningless period of time is still not an actual infinite or that it's impossible? Elaboration please.

Well yeah that's kind of the whole point of the argument.

The claim was that an actual infinite could not exist because otherwise we would have never reached the present point in time. My rebuttal is, as you have just affirmed, that an actual infinite is implied if we deny a beginning.

So doesn't that kind of invalidate your and VenomFang's argument against an actual infinite, or have I missed something?

[QUOTE="ChiliDragon"]

If I remember right, the arguments goes something like... Our universe: CREATION----------------------------------------MEASUREABLE TIME----------------------------------------END OF DAYS Time outside our universe: INFINITY-------------------------------RIGHT NOW-------------------------INFINITY Being infinite, time outside our universe cannot be measured and it could conceivably be argued that it doesn't exist, at least not the way we understand and think of it. In a place outside our universe, an infinite being like God could exist. And of course, if one does, the matter of that being's age is more or less moot--if time where that being lives does not exist in a measurable way, can such a being even be said to have an age? Teenaged

Red: From my prespective, no, because to my knowledge god is ageless (isn't that what the Bible says also?) On that ground I have thought that it is possible to connect that ageless god with time itself, in a sense that maybe from one prespective god may be time itself. Now I don't know how that works or if that description goes on to describe a completely different god. I don't know tbh. :?

But again those thoughts I have probably derive from my "favourite" imagery of god in which god is actually all the natural forces that keep the World together, and presumably that would make god the embodiment of time itself, as well as the embodiment of other wordly "powers", in a sense that he/she/it is neither controlled by those powers, neither is he/she/it beyond them; he/she/it isthose forces. But again that's my totally personal opinion (I haven't "locked" on to it yet) and the rant is over as of now. :P

It's a good one! :P

If you ever design an RPG game where god fits your description in this passage. let me know I'll pick it up...

When it comes to "time" I still find it hard to imagine a reality without time. How can something happen without consuming time?

Also, what precisely is "temporal past" Dom and Dan keeps talking about? :? 

well the point that you missed is that Hilbert's Hotel, my argument against traversing the infinite, only apply to the existence of actual infinites and the possibility of traversing them. If we are right here right now and before this moment is an infinite temporal past with no beginning, then there was an actual infinite. My argument never assumes that there was a beginning. danwallacefan

Okay, that's fine but Hilberts hotel makes a different claim then the one you and VenomFangX explained in the videos I provided.

The argument I was discussing was this one, taken from your essay about the arguments for the existence of God:

Assuming the existence of tense, temporal existence has traversed every moment before the present moment to arrive at the present moment. But if we suppose that the temporal past is truly infinite, then we should not be here right now because in order for ANY moment to arrive, there will always be one more moment to traverse. But we are right here right now debating the existence of God.danwallacefan

Do you agree that an argument against the existence of actual infinite in this form does indeed assume a beginning?

Anyways I'll address your other argument because it's very much relevant to the question. I'll reproduce what you've said about Hilbert's hotel from the same essay:

If the universe never began to exist, then there was an actually infinite amount of time before the present moment. Now if actual infinites cannot exist, then it logically follows that the temporal past is not infinite, and, hence, began to exist. To defend this premise I will use the analogy of Hilbert's Hotel, which was created by David Hilbert, the greatest mathematician of the last century. Imagine that you have a hotel with an infinite amount of rooms. Now suppose that a guest arrives. How does the hotel clerk give this guest a room? Simple, he shifts the person in room #1 to room #2, the guest in room #2 to room #3, and so on ad infinitum. You now have an infinite amount of rooms even though before each room was full. The absurdities don't quite end there however. Now imagine that an infinite amount of guests arrive, how does the clerk give all of them a room? Simple, he shifts the person in room #2 to room #4, the guest in room #3 to room #6, the guest in room #4 to room #8, and so on ad infinitum. You now have an infinite amount of rooms available even though all rooms were full. Now imagine that all the guests in the odd numbered rooms leave the hotel. How does the clerk fill all the rooms? simple, all he has to do is shift the occupants in reverse order as he did before, and now all the hotel rooms are full. David Hilbert used this to prove that infinites simply do not exist in the real world, they are only a concept which exists in the mind.danwallacefan

As far as I can tell the only thing that Hilbert's Hotel succeeds in doing is proving that a infinite set does not behave in the same way as a finite set, which to be honest isn't a big accomplishment given that infinity has different properties than natural numbers. Anways lets see what Hilbert is saying:

The number of rooms (R) =infinity

The number of guests (G) =infinity

I suppose that we are to first assume that R=G which is fair enough. In saying that though it becomes easy to fall into the trap of thinking "If G were greater or lesser than R then they would no longer be equal" or "If one more guest were to arrive then there wouldn't be any room left".

This line of thinking works on the assumption that arithmetic functions (addition, multiplication etc) alter the value of infinity. It's an intuitive assumption because it works so well in our day to day experience but it's not true of an actual infinite. Saying that the addition of one person to an infinite number of guests would make the sum of guests greater is to misunderstand what is meant when it is said that something is infinite in number. To be infinite is to be never endingly great and as such the concept of "greater than" is meaningless (unless of course you can provide a number which is greater than infinity).

The behaviour of an actual infinity is counter-intuitive but that alone does not demonstrate its impossibility nor is it really surprising given that we only ever get to deal with finite sets in our day to day experience.

Also, what precisely is "temporal past" Dom and Dan keeps talking about? :?  7guns

Temporality just refers to the linear procession of time, so the temporal past is the way that past events have proceeded through time.

If time is infinite does it mean it cannot be measured? 7guns

Yeah I'd say so. Measurable things must be countable and infinity is certainly not countable. Minutes and seconds on the other hand are finite, countable and thus measurable.

If time has a beginning then there has to an end to it because if there isn't then time will be infinite...Right?7guns

Well no an end isn't necessitated by any means. If time has a beginning then it is a potential infinite, that is to say that it could continue without end but it currently hasn't. The set of numbers [1,2,3,4....] for example is a potential as opposed to an actual infinite.

What is the difference between "Time is infinite on both ends" and "Time has a beginning but no end"? 7guns

Not much really. Both forms have the same value just with different frames of reference.

Would it be possible to measure time in both the cases?7guns

Sure, you could measure a minute in the same way that you could count from one to sixty in the set [1,2,3,4......infinity], what you couldn't do though is count all the way from one through to infinity.

..............What is "time" really? If time is comprehensible only as an interval then shouldn't time be measurable even if it's infinite? 7guns

Regardless of how time is defined if it is infinite then it can't be measured. If an interval of time ranges from 0-infinity then it is still subject to all the absurdities that come with trying to quantify an infinite set. For example if you measured the total duration of an infinite universe would there be more seconds or more hours?

What kind of infinity is an "actual infinite" anyway?7guns

Its the complete kind. If I start counting from one upwards then I have started a potential infinite e.g. I could count forever without reaching an end. If I finish counting to infinity then I have completed an actual infinity (although a situation like that would mean that I never started counting).

_____________________________________________________________ Time, just like measurements such as length breadth and height, is a dimension! How can it not exist?7guns

I'm pretty sure that time exists. The question at hand is whether or not it can exist infinitely.

Thanks for such detailed explanations. Wasn't expecting that... :)

One thing you have made clear is that time cannot be measured in-case of an actual infinite...But still I would like to ask how would you define the time-line we are in now? A possible infinite?

_______________________________________________________

[QUOTE="7guns"] Time, just like measurements such as length breadth and height, is a dimension! How can it not exist?domatron23

I'm pretty sure that time exists. The question at hand is whether or not it can exist infinitely.

If time didn't exist infinitely that would mean things happened in the past that didn't consume time... Right? Hurts my head a little to be honest.:| 

Thanks for such detailed explanations. Wasn't expecting that... :)

One thing you have made clear is that time cannot be measured in-case of an actual infinite...But still I would like to ask how would you define the time-line we are in now? A possible infinite?7guns

Well I don't claim to know whether or not the universe has always existed but presuming it hasn't it would be a potential infinite I guess.

[QUOTE="domatron23"][QUOTE="7guns"] Time, just like measurements such as length breadth and height, is a dimension! How can it not exist?7guns

I'm pretty sure that time exists. The question at hand is whether or not it can exist infinitely.

If time didn't exist infinitely that would mean things happened in the past that didn't consume time... Right? Hurts my head a little to be honest.:| 

Um no, I don't know where you got that from.

Everything that happens consumes time its just that an infinite number of events can't be quantified that's all.

[QUOTE="ChiliDragon"]

And of course, if one does, the matter of that being's age is more or less moot--if time where that being lives does not exist in a measurable way, can such a being even be said to have an age? Teenaged

Red: From my prespective, no, because to my knowledge god is ageless (isn't that what the Bible says also?) On that ground I have thought that it is possible to connect that ageless god with time itself, in a sense that maybe from one prespective god may be time itself. Now I don't know how that works or if that description goes on to describe a completely different god. I don't know tbh. :?

[QUOTE="Teenaged"]

[QUOTE="ChiliDragon"]

And of course, if one does, the matter of that being's age is more or less moot--if time where that being lives does not exist in a measurable way, can such a being even be said to have an age? ChiliDragon

Red: From my prespective, no, because to my knowledge god is ageless (isn't that what the Bible says also?) On that ground I have thought that it is possible to connect that ageless god with time itself, in a sense that maybe from one prespective god may be time itself. Now I don't know how that works or if that description goes on to describe a completely different god. I don't know tbh. :?

This stuff makes my brain cry. ;__;Funky_Llama

[QUOTE="Funky_Llama"]This stuff makes my brain cry. ;__;Elraptor

[QUOTE="7guns"][QUOTE="domatron23"][QUOTE="7guns"] Time, just like measurements such as length breadth and height, is a dimension! How can it not exist?domatron23

Domatron, regarding your counter-argument against my arguments against an actual infinite, I have these 2 points in response

1: With regard to the traversing the infinite, It does not assume that there was ever a beginning. the arguments begin with the present and work backwards. Even if we assume it to be beginningless, there is still always more moments to traverse before that said moment can be traversed. This is a vicious regress, and if true, we should not be here right now

2: With regard to Hilbert's Hotel, I think that by admitting that an infinite set behaves differently than a normal set, you admit that its nothing more than a concept. Sets in reality behave like finite arithmetic sets. But further, your explanation of an infinite as "never endingly great" seems explain it in terms of potential infinites rather than actual infinites, as if there are always more as you traverse the set.

and one user said that their brains cry, I have to second Domatron's response, this stuff is fun (for me, philosophy of religion is like crack:D)

I get it that you are trying to say time didnt exist infinitely. But its hard to picture a reality without time. How would the other dimensions fit into a reality without time?7guns

[QUOTE="7guns"]I get it that you are trying to say time didnt exist infinitely. But its hard to picture a reality without time. How would the other dimensions fit into a reality without time?ChiliDragon

This leades to Big Bang...

Domatron, regarding your counter-argument against my arguments against an actual infinite, I have these 2 points in response

1: With regard to the traversing the infinite, It does not assume that there was ever a beginning. the arguments begin with the present and work backwards. Even if we assume it to be beginningless, there is still always more moments to traverse before that said moment can be traversed. This is a vicious regress, and if true, we should not be here right nowdanwallacefan

It doesn't assume a beginning? Well if that's the case then it is an invalid argument because the conclusion that every point in time cannot be traversed does not follow. The bolded simply isn't true in a universe with no beginning because it can be said that an infinite number of moments have already occured.

2: With regard to Hilbert's Hotel, I think that by admitting that an infinite set behaves differently than a normal set, you admit that its nothing more than a concept. Sets in reality behave like finite arithmetic sets.danwallacefan

Well of course every set that we observe in reality behaves like a finite arithmetic set, that's because they are finite sets. No big surprise there.

You seem to be saying this though: every set that we observe in reality is finite and behaves acccording to arithmetic functions, therefore every set in reality is finite and behaves according to arithmetic functions. That is not a valid argument at all and does not imply that actual infinites must be conceptual.

But further, your explanation of an infinite as "never endingly great" seems explain it in terms of potential infinites rather than actual infinites, as if there are always more as you traverse the set. danwallacefan

Well there are always more points to traverse as you move across an infinite set, that's what it means to be never-ending (or never-beginning if we think of it backwards). I'm not sure why you say "as if" like it's surprising or something.

Okay this is a bit of a brain scratcher but I think it might be relevant in regards to the claim that traversing the infinite is impossible.

Okay so we all know Zeno's paradoxes and the problem of movement. If you don't know about them have a read.

Say that someone moves from point 1 to point 2. Have they not, by completing this movement, moved through an infinite set of points? We could model the movement like this [1, 1.5, 1.75, 1.875, 1.9375.........2] with the distance from point 1 to point 2 halving every step.

Now I'm not saying that the person in question has traversed an infinite distance, just that they have traversed an infinite set of points within a finite distance. This scenario is prey to all of the same mathematical absurdities that are found in Hilbert's hotel yet it is something that happens in reality all the time.

What does everyone think? Good argument, bad argument or confusing argument?

Okay this is a bit of a brain scratcher but I think it might be relevant in regards to the claim that traversing the infinite is impossible.

Okay so we all know Zeno's paradoxes and the problem of movement. If you don't know about them have a read.

Say that someone moves from point 1 to point 2. Have they not, by completing this movement, moved through an infinite set of points? We could model the movement like this [1, 1.5, 1.75, 1.875, 1.9375.........2] with the distance from point 1 to point 2 halving every step.

Now I'm not saying that the person in question has traversed an infinite distance, just that they have traversed an infinite set of points within a finite distance. This scenario is prey to all of the same mathematical absurdities that are found in Hilbert's hotel yet it is something that happens in reality all the time.

What does everyone think? Good argument, bad argument or confusing argument?

domatron23

[QUOTE="domatron23"]

Okay this is a bit of a brain scratcher but I think it might be relevant in regards to the claim that traversing the infinite is impossible.

Okay so we all know Zeno's paradoxes and the problem of movement. If you don't know about them have a read.

Say that someone moves from point 1 to point 2. Have they not, by completing this movement, moved through an infinite set of points? We could model the movement like this [1, 1.5, 1.75, 1.875, 1.9375.........2] with the distance from point 1 to point 2 halving every step.

Now I'm not saying that the person in question has traversed an infinite distance, just that they have traversed an infinite set of points within a finite distance. This scenario is prey to all of the same mathematical absurdities that are found in Hilbert's hotel yet it is something that happens in reality all the time.

What does everyone think? Good argument, bad argument or confusing argument?

danwallacefan

Well I didn't say that the distance from 1 to 2 was an actual infinite, I'm well aware that the sum of its parts is a finite number.

As for potential infinites well you are right to say that the set [1, 1.5, 1.75, 1.875, 1.9375.........] is a potential infinite. We can keep on dividing as long as we like without ever reaching 2 which is the end point of the set. The fact that this set never actually reaches its end point only serves to illustrate what I was saying however, which is that there are an infinite number of points between 1 and 2 and that these points can be traversed.

Domatron, are you a fan of Quentin Smith?

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

Domatron, are you a fan of Quentin Smith?

 

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

danwallacefan

Never heard of the dude before.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

domatron23

An actual infinite can not conform to any of those rules due to the nature of itself, mathematically speaking. Subtraction, addition, multiplication and division are all more or less meaningless in relation to an infinite number.

[QUOTE="danwallacefan"]

Domatron, are you a fan of Quentin Smith?

 

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

domatron23

Never heard of the dude before.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

[QUOTE="domatron23"]

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

inoperativeRS

An actual infinite can not conform to any of those rules due to the nature of itself, mathematically speaking. Subtraction, addition, multiplication and division are all more or less meaningless in relation to an infinite number.

[QUOTE="domatron23"][QUOTE="danwallacefan"]

Domatron, are you a fan of Quentin Smith?

 

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

danwallacefan

Never heard of the dude before.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

Yeah you're going to have to explain that one to me.

[QUOTE="danwallacefan"][QUOTE="domatron23"][QUOTE="danwallacefan"]

Domatron, are you a fan of Quentin Smith?

 

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

domatron23

Never heard of the dude before.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

Yeah you're going to have to explain that one to me.

[QUOTE="domatron23"][QUOTE="danwallacefan"][QUOTE="domatron23"][QUOTE="danwallacefan"]

Domatron, are you a fan of Quentin Smith?

 

Anyway, I was reading through my copy of Time and Eternity, and I came upon an argument from Smith which was vaguely similar to your response to Hilbert's Hotel, namely that it just shows that infinite sets behave differently than finite sets, and therefore there's no contradiction.

However, as Craig noted in response to Smith, The problem is that your counter-argument only establishes strict logical possibility. These absurdities disprove broad logical possibility because they violate basic rules of logic (laws of logic are laws of metaphysics)

Funky_Llama

Never heard of the dude before.

What rule of logic states that an actual infinite must conform with rules of addition and subtraction etc.

Yeah you're going to have to explain that one to me.

seriously, Hilbert's Hotel contradicts itself. 

Broad logical possibilities are so because they're not contradictory. 

ergo, actual infinites don't exist. 

seriously, Hilbert's Hotel contradicts itself.danwallacefan

The only real thing it shows is that something in its formulation seems to be impossible, one obvious other possibility being the assertion that every room in a hotel with infinite rooms can possibly be filled.

Of course, we, being finite beings, are woefully inequipped to truly understand the concept of infinity, so it could also perhaps be the case that Hilbert's hotel is perfectly fine (after all, mathematically it is perfectly consistent and unproblematic) and that it's just that we are attempting to think of it in finite terms - which could very well be the point at which the wrongness begins to creep into play. It's the same sort of thinking that leads people to fervently deny that 0.999... is equal to 1 - they think to themselves "well, there must be a rightmost 3!" when there is no such thing, and this is precisely the same problem: thinking of an infinite in finite terms.

And it seems to me that the rejection of an actual infinite carries with it just as many things that are unintuitive as the acceptance of such a thing. For example, if there does not exist any actual spatial infinite, then there must be a barrier that demarcates the end of space - but then one could ask the obvious question: what the heck is beyond that barrier? Even if the answer is "nothing", empty space is still space, which means that there could not even be empty space in that direction.

It's really little different for time, too - if there is an "absolute zero" in terms of time, then, well, what happened before that point?

Really, before you start poking holes in others' assertions, you'd do well to first consider whether your own assertions have their own holes that one can find.

And it seems to me that the rejection of an actual infinite carries with it just as many things that are unintuitive as the acceptance of such a thing. For example, if there does not exist any actual spatial infinite, then there must be a barrier that demarcates the end of space - but then one could ask the obvious question: what the heck is beyond that barrier?GabuEx

It's the same sort of thinking that leads people to fervently deny that 0.333... is equal to 1 - they think to themselves "well, there must be a rightmost 3!" when there is no such thing, and this is precisely the same problem: thinking of an infinite in finite terms.

GabuEx

The Dungeon Dimensions. Be very frightened.ChiliDragon

Is that a reference to something that I'm not getting? :P

It's the same sort of thinking that leads people to fervently deny that 0.333... is equal to 1 - they think to themselves "well, there must be a rightmost 3!" when there is no such thing, and this is precisely the same problem: thinking of an infinite in finite terms.GabuEx

I fervently deny your assertion.

Most of the time I steer away from threads like this one, for the simple reason that my brain too, is sensitive and may "begin to cry" (I always love Llama's responses). However, I'll make an exception today. Ok, let's go.

First things first, I think that an actual infinite can exist. I also think, like Teenaged, that: (infinite)------Present Time----(infinite). It is also logical (in my mind at least :P) to assume that numbers are infinte, since I can count from 1,2,3 and onwards, never reaching the "last number" and the end of the numerical set, thus making it an "infinite set". In the same sense, I can count backwars (3,2,1,0,-1) and still not manage to reach the "first number". We also say that circles are made of infinite, immaterial points. I can, however, draw a circle in a set of axis and single out point A, whose coordinates are (0,5). This point and point B(6,19) are the edges of an arch, which has a length of x cm and the circle's overall length is Z cm. So you see, these numbers can be traversed. I've already wasted 3 minutes of my precious time and this debate can go on for an eternity. :P

As far as Hilbert's Hotel is concerned, I think there are many problems with it. Simply saying that it is self-cotradictory doesn't make it justice. First of all, I don't think it is possible to "fill" a hotel with infinite rooms, even if you have infinite guests. And how exactly can you say that two infinites are equal? From my (admittedly limited) knowledge in Maths, I seem to remember that infinite/infinite#1 (imagine that "infinite"="lying down 8" and "#" = "doesn't equal").

I think that the main problem with "infinite sets", is that you can't know they're infinite, until an infinite amount of time, numbers, rooms etc. has passed, been counted, been filled etc. And, as fate would have it, this is impossible for us to do. :P "We are finite beings, cursed to seek the infinite." (Author unknown, by me at least :?) Ok, that's the end, I can already feel my brain cells burning... :P